Map: transport whose composed rank exceeds one

[NGL321]

Split out of #517 on 2026-09-05 at the user's instruction (their ruling Q3(a)), on the evidence that composed rank collapse is not a cold-start or supply problem and cannot be reached from #517's surface. #517 keeps the apex ladder and the arm's command and hands back to #127 at its own T4; this map carries the transport architecture, and #127 blocks on it.

Destination

An architecture for transport, and the rule that trains it, under which rim-core influence holds on the world loop and rim-to-core detectability is restored as the bar rather than the diagnostic — both re-indexed off the apex.

Done when a stated change to how transport is parameterised and trained has been decided — not built — such that a perturbation is argued to remain distinguishable from what stands on the edge across the sensorimotor loop, with the ADR amendments that change requires named and their cost stated.

Replaced on 2026-09-08 by B27. The previous destination — composed rim-to-apex effective rank exceeds one — is indicted in every word: composed never touches the stalks (B17), rim-to-apex presumes a privileged top the map has retired (B23), and rank is dominated by gain (B21: 20–50× per hop, reach 2–3 hops, so seven hops costs 10–12 orders). The map did not lack a state-level sensorimotor bar; it replaced one. CONTEXT.md already holds both objects — ADR-0021's detectability (distinguishable from what stands on the edge, not clear a wall) and ADR-0026's rim-core influence on the world loop, which is the command-to-consequence loop and therefore already carries the active-predictive-coding requirement. "Reach" is on the glossary's Avoid list and stays out of the vocabulary.

Named ADR cost: ADR-0021 (promoted back to the bar, re-indexed off the apex), ADR-0026 (re-indexed), ADR-0003 plus the Internal rim and Drive boundary cell glossary entries, ADR-0011 (variable-radius locality). ADR-0032 is unchanged and load-bearing — its band blocks the shrink-to-flat road to path-independence, leaving only the width-1 road, which a representation floor closes.

Composed effective rank is retired as a bar. It may be reported as a diagnostic; it may not be a pass condition.

Why this is its own map

Three readings, taken independently, say the collapse is endogenous and structural:

• T2's zero-supply control. Composed rank falls 1.298 → 1.0845 ± 0.0023 with no exogenous supply at all; every induced condition lands within 0.007 of it, one within 0.0001.

• The full dome never had the rank to begin with (T3, ledger row 6 on

  #520). Composed rim-to-apex effective rank over the

  256 patch chains reads 1.025 at construction — before a tick is run (actuator 1.074, proprioceptive

  1.080, touch 1.022). The shallow dome started at 1.298 and fell; the full dome starts at ~1.03 and

  converges to one. No surface read anywhere on Map: the constant-evidence collapse and the variation famine at the cold start #517 has approached 1.5. This is the strongest single

  statement of the problem: the collapse is not only endogenous, it is largely prior to learning, and

  any account that explains only the decay from 1.025 to 1.000 has explained the smaller half.

• T3's full dome at 100k. Composed rim-to-apex ER reads 1.000 ± 0.000 in both arms — the frozen baseline and the winning apex intervention alike. Max over chains 1.171 baseline, 1.641 winner.

• R-A's mechanism. The only constraint-clean sufficiency result for a long product's rank is the degenerate band, which ADR-0032 already imposes and holds to σ_min/σ_max = 0.9999995 on 1339 of 1364 maps. But that argument needs square orthogonal factors; ADR-0032 yields rectangular partial isometries, so seven hops compose as projections onto seven differing subspaces and converge to their intersection — one direction or none, for seven generic 3–4 dimensional subspaces in a 12-wide chart. Squareness is unavailable because ADR-0004 commits to k < n. This ADR-0004 × ADR-0032 interaction was previously unstated.

  Struck by #533, which tried to break it as instructed and did. hop_operator is F_out · F_inᵀ with both maps m × n and incident on the same relay cell, so each interior hop is 4×4 — already square — the ambient is the stalk n = 32, the subspaces are lane-width m, and k is not a term in the composed object at all. What is unavailable is orthogonality, not squareness. Under ADR-0032's floor, hop = σ²·U_out(V_outᵀV_in)U_inᵀ, so the composed spectrum is a product of seven principal-angle cosine matrices between each relay cell's two incident carried subspaces — which predicts the 1.025 construction reading and the 1.641 chain max, both of which the intersection argument strains on. The three collapse readings above stand; only their mechanism changes.

So composed rank 1.000 was determined by the architecture before a tick ran. No supply, drive, or reward ever moved it, which is exactly what every run showed.

The candidate that costs nothing, and the one that may

Re-ranked by #533. The three below were ranked against an intersection argument that no longer holds. Candidate 1 must now state its mechanism against principal angles, not against an intersection — a sum of Kronecker products makes each factor richer but leaves each hop a map between the same two carried subspaces. Candidate 2 genuinely breaks the product-of-cosines form and is the second-line move. Ahead of all three sit two cheaper levers #533 surfaced — relaxing ADR-0010's c, and loosening the privacy invariant — carried on #540.

From R-A's ranking:

1. Channel-heterogeneous transport — a sum of Kronecker products (Roth & Liebig). Violates none of ADR-0004, ADR-0008, the no-reward bar, or the no-batch constraint. Still linear; adds no term to any update. Its price is architectural.

2. Additive identity / residual h ← (I+T)h (GCNII, skip connections). The user ruled on 2026-09-05 (Q2(a)) that ADR-0008 does not reach this — ADR-0008's bar is scoped to the prediction rule in its own words ("the transport rule carries an additive term and the prediction rule carries none"), and (I+T) is a change to the shape of the transport map, not a term on ΔK. It is therefore ADR-0004/0032 territory, not ADR-0008's.

3. Raising the band ceiling above 1/λ (Oono–Suzuki) — costs ADR-0015 + ADR-0022/0032.

ADR-0015 already names a fallback of this species. Its words: the standing fight between gradient and projection "is the observable that triggers the fallback from a dense K to a structured one, since the right template for a stability constraint is a direct parameterisation rather than a penalty." Whether that trigger has fired is being read on #517 as a task; note the fallback names K while candidate 1 restructures transport — same principle, adjacent object, and the difference is this map's to resolve.

Notes

Inherited from #517 and #127 by reference, not restated. Per edge, never per level (#181). A rig's data ages with main; name the surface (#455 rule). Invented constants deferred until necessary, not banned. An edit hands off to its own ticket. Only the falsifying end of a pre-registered ratio is a verdict.

Plan, don't do. This map decides an architecture; it does not build one. A prototype ticket may make something cheap to react to, but the destination is a decision with its ADR cost named.

The destination itself is under review on B27. B17 found that composed_reads multiplies learned restriction maps and never touches the stalks, so this map's bar is a property of the transport operator and says nothing about whether signal travels the directions it retains — and the user ruled that the apex is not privileged and the dome is an architectural wager, not the architecture. "Rim-to-apex" may therefore encode the hierarchical picture this architecture exists to reject. Do not add readings against the current bar without reading B17 first.

R-A's reconciliation was the load-bearing claim. #533 checked it and broke it — on the instrument, not on judgement. Its five ceded scoping calls fell with it. The collapse readings survive; the mechanism is principal-angle collapse and the indicted ADR was the wrong one. Read a claim against composed_reads before building on it.

The destination was under review on B27 and has been replaced. That ticket also widened this map's scope from how transport is parameterised to transport and the rule that trains it — not split, because B25 establishes the parameterisation's optimum is set by the objective, so a map that may change one and not the other cannot reach a decision. Plan, don't do still stands: the objective is decided here, not built.

The dome is no longer architecture. B23's falsifier fired and B27 called the wager lost: no bar, reading or ADR on this map may appeal to level. The dome remains the scaffold readings are taken on; it justifies nothing.

Three things the vision no longer claims, struck on B27 and not to be reintroduced without new evidence: the cell as a set of hats; path-independence at distance (unavailable, not deferred); and strength by condensation — CONTEXT.md's Collectively is binding (counted, not summed; #232 measured the summed sense empty and the entry says the retired sense may not walk back in).

Carving raises this map's own divisor, and a carving candidate must price it. B39: removing an edge can only lengthen a shortest path, so a dense graph differentiating to sparsity raises world_loop(c) monotonically and makes ADR-0026's necessary condition strictly harder. Standing constraint: any carving candidate reports its effect on world_loop lengths — at minimum and not exclusively, on the user's amendment that this is necessary but not sufficient. Not a veto and not a lever; a cost that runs the wrong way and was invisible until B39.

The honesty check moves with the thing it checks. B43 (#607): ADR-0021's bottleneck is a max over paths of a min over that path's edges, so shortening a path raises it by orders at B21's per-hop gain — the same shortening that lowers ADR-0026's divisor. A topological candidate therefore passes the amplitude clause by construction, and an unaimed random rewiring passed it by seven orders. Standing constraint, the dual of B39's: any candidate that shortens paths states its amplitude against its own hop count, not against the unrelayed baseline. What that null should be is B45 (#611)'s.

ADR-0026 is split, and only its quantifiers are struck. B39: τ̂_c / world_loop(c) appeals to no level — #383 built the divisor that way and loop_length.world_loops is BFS from SENSORIMOTOR cells, so it computes unchanged on the carved graph. The predicate over it did appeal to level — rim-to-apex paths, the per-stratum inbound count, the L1 outbound universal — and has been in breach of this map's own no-level rule since B27. Do not quote a max-min-over-paths conduction verdict, B38's §4 absolutes included; the per-cell ratio is untouched.

Reversibility is a standing constraint, and it is graded. B41, on the user's ruling: a carve is a reallocation and never a deletion — any candidate states how a pruned edge's warrant stays readable, and pruning that cannot be undone is not admissible. Universal reversibility is not required and the degree may vary; the bar is functional, that a cell whose dynamics change can still come to communicate meaningfully, which means its stalk can change commensurately. It reaches the node stalk mask as well as Edge.m — graph.py:693's "the mask closes and never re-opens" is now under it, and B42 ruled that half: the mask is fixed at construction by inheritance from the superseded capacity bound, not by decision, so it becomes a learned, gated object carrying reversibility through the gate. p is an initialisation, not a constant. It is the constraint that would have caught B34's floor two tickets earlier: the floor was a reversibility mechanism nobody had priced. A second reading rule rides with it: m_e = 0 is the representation of a pruned edge, so every topological instrument reads the carried graph (m_e > 0), not dome.edges — benchmarks/loop_length.py:181 is width-blind, and read through it a carve reports zero effect on world_loop and B39's constraint measures nothing.

Closure is satisfiable by collapse, and locality does not rescue it. B42: a hop at a cell is S_out S_inᵀ — a rectangular identity where two incident edges take the same rows, exactly zero where they take disjoint ones — so exact path-independence exists only at audience differentiation 0.0000, a cell saying one thing to all its neighbours. The shortest local cycles run through a single cell, so local closure is the demand that a cell say the same thing on every lane: scoping to B27's coherent-region form does not mitigate the collapse, it selects for it. Standing constraint: any objective carrying a local holonomy term states what stops its optimum being collapsed lanes, and reports audience differentiation at a cell alongside the holonomy it achieves. Scoped by B54, and the collapse is narrower than this entry said: there is no setting that gives both is true of identification, the full-stalk statistic, and false of channel_return — B42's own 605-stagger-seed42.json carries channel_return 1.0000 at unit gain at audience differentiation 0.3000 and 0.3333, in a fourth column its published table omitted. The collapse argument stands unchanged for full-stalk exactness; it does not transfer to holonomy read on the sub-bundle the loop actually carries. The standing constraint itself stands, and B54 discharges it against a different term than B33's, which stays suspended.

Two instruments, two objects — do not quote one as the other. B49: B21's 20–50x per hop is a dynamical impulse on node stalks through sheaf.tick() (already ~100x by hop one), and #533/#537's cosines are the transport operator, which B17 established never touches the stalks. They differ by roughly two orders per hop. Attenuation is misalignment is struck as an identity — it is the weld, and docs/analogies/think-tank.md §2 states it as fact pending B51. Standing constraint: a reading states which of the two objects it is on, and no argument may carry a number from one to the other. Two corrections ride with it: ER 1.000 is domination, not annihilation (full rank 3 on the median chain, σ₂/σ₁ 0.005 at 20k), and n reaches — #533 §4's ratio premise is false on main and #540's point 2 inherits it.

τ̂ is blind to the return, and retention is priced in non-normality. B44 (#610) put channel_return at 1.0000 and ADR-0021's bottleneck five orders up (9.76e-14 → 1.37e-08) on one trained surface, and per-cell τ̂ did not move outside a single trial's own noise (paired shift −1/0/0/0 against a within-arm null of |Δ| median 5.0, q90 21.0). B39's §2 conditional falls; its struck quantifiers stand. A candidate may not argue a τ̂ from its return gain — the return is not what sets the decay. And the retention lever is not unpressured: σ(used) sits on the band's upper face from the first tick on all 150 cells, so above it ρ(used) = ρ(K)/σ(K) exactly — retention is K's departure from normality — and one-step prediction error buys its accuracy with transient growth, exactly as ADR-0015's norms predicted in writing. τ falls ∞ → 344 → 65 → 52.9 over 2,000 ticks, passing ADR-0026's recorded λ = 0.99 → τ ≈ 99.5 on the way down. Standing constraint: a candidate objective term aimed at retention states its case against the prediction term as an adversary, not as a lever nobody is pressing.

Earned agreement is a diagnostic, never a bar, and the scoring rule is joint. B48: the trained architecture's entire H⁰ is the privacy reserve — earned 0 against the flat bundle's 88 — but earned is retired as a candidate bar on composed rank's own terms. It reads the transport operator (B17: never touches a stalk), and it is exact: earned > generic is rank-deficiency of δ relative to its own sparsity pattern, hence measure zero, hence reachable only by objectives whose optimum is exact rank deficiency — and B42 showed those optimise to collapsed lanes. Constructible, never learnable. Its replacement must be graded and read on node stalks, and B52 has specified it: the traffic's own agreement spectrum — a soft count N(θ) over the traffic covariance's directions at normalised disagreement level θ, reported as a profile and as an excess over a matched-generic null, guarded by a scramble test at frozen maps. It is not clamped by the construction mask and is ceilinged at 1.002 by the traffic's effective rank, so B53 is what moves it; first reading on B57 (#629). B52 amended its own item 3: the statistic is not required to fail the flat bundle alone — fusing differentiation into one number is B49's struck move — so the joint rule below is what carries the null, and it is unchanged. Standing constraint: any agreement statistic is reported alongside audience differentiation at a cell and the exposure it cost, and a candidate must show agreement rising while differentiation stays nonzero — the flat bundle's 88 at differentiation 0.0000, bought with 5.2 dimensions of exposure per cell, is the null it must fail. And the destination's bar must not be satisfiable at zero earned agreement: a necessary-condition check carried alongside the bar, the shape of B39's world_loop cost, not a second destination.

Holonomy is suspended, not struck. The user's own amendment on B48, and B41's rule applied to a ruling rather than an edge — a suspension is a reallocation, never a deletion, and the warrant for reviving it stays readable. It rests on two separable premises, and either falling revives it: B32's flatness attains the maximum of dim H⁰ is an imported analogy here, not a theorem — every quantitative result there assumes O(d) or invertible maps and ADR-0032 yields rectangular partial isometries — and B42's collapse is an argument about exact path-independence (S_out S_inᵀ is an exact identity only on shared rows), so a graded term may live at nonzero audience differentiation where an exact one provably cannot. Lifted narrowly by B54, onto a different term than the one suspended. Premise 2 gave: the escape is a sub-bundle distinction, not a magnitude one. B33's full-stalk term stays suspended; what re-enters is two-sided — drive channel_return toward 1, hold identification away from 0 — whose second clause makes collapsed lanes the term's worst point and is the measured guard against drift to global (both cycle bases reported). Premise 1 stays open and no longer load-bearing: the channel form never appeals to it, and Dong et al.'s Theorem 5 runs with the two-sided term. Trained by B56 (#628), and the suspension does not return — but the guard does. Clause 1 is a real lever on a trained surface: channel_return 0.2006 → 0.7899 against baseline's own drift to 0.3223, both cycle bases agreeing, at zero exposure cost (rank-measured k_v 20.0 on every arm at every rung). The named risk did not fire, on the user's ruling: the full-stalk form's optimum is differentiation 0.0000 by construction, where clause 1 costs 7% of differentiation relative for a 3.9× rise — different in kind, and premise 2's sub-bundle escape confirmed on a trained surface rather than at construction. Clause 2, however, is inoperative in both forms: the hinge is bit-identical to clause 1 alone (ident_loss exactly 0.0 at all seven rungs, GAMMA = 0.6075 read off a construction sweep and lying below the trained surface's entire operating range), and the unbounded form pushes identification past chance to 1.0412 while leaving differentiation at 0.3117 against clause 1's 0.3122. So B42's standing constraint returns to un-discharged — clause 1 survives as a live candidate and may not be argued as guarded. Answered by B59 (#631): the guard is a parameterisation, not a term, and it is not yet evidenced. Clause 1's optimum is a degenerate family it cannot rank — B56's own stagger table carries channel_return 1.0000 at audience differentiation 0.0000 (stagger 0, B48's null) and at 0.7321 (stagger 19), scored identically, ten exact staggers of twenty seed-invariantly — so B42's collapse is one point of the optimum rather than the optimum, and breaking the tie is a selection problem. The mask does not break it: b42_stagger.distinctness reads the learned row subspaces, so m_e fixes how many rows an edge takes and never which subspace they span, and a k_v pinned at 20 is the window collapse lives in rather than a barrier to it. Per ADR-0015's own template line — the right template for a stability constraint is a direct parameterisation rather than a penalty — the guard is a differentiation-selecting initialisation (B58 (#630)'s staggered frame) and never a second penalty, which is what clause 2 was. Standing constraint, the admission criterion: a candidate reports the differentiation exchange rate — differentiation given up per unit channel_return gained, both as excess over a matched baseline arm at the same rung and seed, at adjacent rung pairs and not end-to-end — and passes only if it is flat or falling. An absolute floor is refused: baseline drifts 0.3683 → 0.3354 with no term at all, so any constant either never fires or fires on the untreated control, which is clause 2's failure in a new costume. Unaided clause 1 fails it — segment-wise 0.0000 → 0.0247 → 0.0755, tripling while channel_return is still only 0.7899 — and is refused, staying live only in composition with such an initialisation. B42's constraint is therefore un-discharged in fact: shape decided on #631, evidence owed by #630, where the falsifier is pre-registered — a staggered start that relaxes back toward stagger 0 under training means the tie cannot be broken by parameterisation either, and the suspension returns. One clause rides along: a differentiation reading taken while k_v moves unreported is void — dormant on main, live the day the mask ruling lands. Amended on B58 (#630), which crossed #631 by one minute. Three corrections, none of them reversing the answer — the guard is a construction and #630 confirms it. (i) The falsifier is replaced. #631 pre-registered relaxes back toward stagger 0 and it did not fire (stagger 19 at 0.5317 against stagger 0's 0.0803, a gap of 0.45), but convergence to the null was never the risk that mattered: the drift has no measured floor. Corrected falsifier: the staggered frame's differentiation settles above collapse, over a horizon long enough to show the drift decaying rather than linear — one seed at 2,000 ticks cannot separate a slow settle from a slow slide, and the two have opposite consequences. So B42's constraint stays un-discharged in fact: a guard must hold at the optimum, and what is measured is a start that decays. Answered by B61 (#634), and the corrected falsifier does not fire. Run to 30,000 ticks the staggered frame's differentiation settles: 0.4071 → 0.3921 → 0.3921 → 0.3912 across the last 12,000 ticks, with the decay rate falling two orders of magnitude to the noise floor (−0.0251 per 1k at #630's last pair, −0.00014 at the end) and channel_return still 0.9819 under the shipped rule with no term. #630's extrapolation — the flat bundle's neighbourhood inside ~15,000 ticks — is falsified by measurement. So what is measured is no longer a start that decays but a start that decays to a nonzero settle, which is the shape the falsifier asked for. It is still not a discharge, on three counts stated at the reading: the settle is on one seed (seed 43 replicates the decaying rate to 9,000 and stops short of the flat region); every rung past 100 is drift under a frozen stimulus, and these arms are the shipped transport rule, which does not qualify for B56's exemption; and the gap to the null keeps narrowing even so — not because the candidate falls but because the null climbs, which is B69 (#646). Do not quote the settle as discharging B42's constraint, and do not quote the narrowing gap as the staggered frame decaying. (ii) The exchange rate is scoped to term-side candidates. On a staggered start channel_return begins at 1.0000 and moves −0.0011, so the rate's denominator vanishes and it is undefined — it was written against terms and does not reach a construction. The initialisation-side form is: drift flat or decaying against the same matched control, which the staggered frame does not yet pass. (iii) The void clause reads participation, not rank. #630's frame buys +4.9 to +5.5 participation dimensions while rank k_v recovers to 20.0 by tick 50 — so a reading that watches the rank sees the clamp and misses the exposure, and the quantity the clause requires reported is the participation ratio. Do not strike holonomy on B32's authority, do not revive B33's term on B54's, do not quote B54's discharge of B42's constraint — it was measured and it failed — and do not quote clause 1 as a candidate on its own.

The stall stamp itself is mis-read on a long run, and three of four runs mis-stamp. B61 (#634): b56_analyse.horizon returns the last rung clearing MOVING = 1e-2, which over 2,000 ticks is the same as when did the body stop — the body stops once and stays stopped. Over a long run the world sporadically re-crosses the threshold after it has died, and the last-above rule latches onto the re-crossing: s19 seed 42 falls to 8.3e-05 after tick 150 and reads 3.91e-02 at 30,000, stamping the run live to its end when the honest stamp is 100. Same on s19 seed 43 (5.48e-01 at 9,000) and s0 seed 42 (4.90e-02 at 6,000, so it is not an artifact of ending the run); only p8 stamps correctly. Standing constraint: a long-horizon reading stamps its stall with b61_analyse.stall_diagnostic, which reports both rules and the re-crossings, and never with b56_analyse.horizon alone — read through it a long arm reports drift rungs as live, which is the precise thing B38 (#599)'s rule exists to prevent. An instrument defect, not a finding about the architecture.

A term whose gradient never reads a stalk may be read past the stall stamp. B56 (#628), on the user's ruling. Clause 1 of the channel term is computed from the maps alone and B17 established the transport operator never touches a stalk, so this class of term trains on a motionless body by construction — its gain and its cost are both computed from the maps and neither is an artifact of the stall. This is narrower than B38 (#599)'s constraint and does not touch it: the stamp still bounds what may be said about the shipped rule, which past the horizon is drift under a frozen stimulus rather than learning, and B33's practice of reading the verdict at the last live rung stands for everything dynamical. Stamp your own horizon regardless — it is per-run, not per-arm.

Two construction-time clamps absorb what training moves — inference, two instances, not yet a mechanism claim. B22 measured every rank-derived number invariant to the integer over 20k ticks, on three arms, because project() re-applies the construction-fixed mask — while composed ER on the identical arm moved 1.149 → 1.330 → 1.002. B44 measured ρ(K) moving on 149 of 150 cells while the band pins σ(used) at exactly 1.000, so none of it reaches the operator the cell computes with. The trained parameter moves and the quantity the architecture reads does not. B56 (#628) is the third instance: rank-measured k_v read 20.0 on every arm at every rung while channel_return moved 3.9× and audience differentiation moved 0.056, so the differentiation a holonomy term spends is a reallocation inside a window whose size never moves. So it is a finding, not an inference — and the constraint stands as written: a candidate that proposes to train a quantity states which clamp stands between the parameter and the reading.

Clause 1's gain is quoted against its initialisation, or it is not quoted. B58 (#630): a staggered initialisation reaches channel_return 0.9984 at 2,000 under the shipped transport rule with no holonomy term, and adding B56's clause 1 to it moves channel_return by +0.0001 and differentiation by +0.0034. So clause 1's 3.9× rise is buying back what a construction gives for free, and B50 (#618)'s saturation confound — which B56 §5 netted out with "a saturated quantity cannot be moved 3.9×" — returns on the trained surface: that argument is right about B56's own arm and does not establish that the quantity must start unsaturated. Standing constraint: a candidate arguing a gain from a holonomy term states the initialisation it was measured from, and reports the same term on a frame that already has the quantity. Two readings ride with it: exposure can be bought — the staggered frame carries +4.9 to +5.5 participation dimensions over the shipped init — and B61 (#634) has since read it at horizon, where it is a start that decays on the same shape as the differentiation: participation runs 13.6 → 10.7 → 9.40 by 30,000, rate decaying −0.81 → −0.03 per 1k. The +4.9 may not be quoted at horizon, and not because it shrinks: B56's random-init comparator was never run past 2,000, so setting 9.40 beside 8.7 is a 30,000-tick reading against a 2,000-tick one. Against the flat bundle run to the same horizon the advantage does persist — 10.66 against 6.76 at 9,000, the null's participation flat at ~6.8 from tick 500. k_v rank reads 20.0 at every rung on every arm, a fifth instance of B22's clamp, so differentiation is not always a reallocation inside a fixed window (B22's clamp still holds the rank, which recovers to 20.0 by tick 50 — a fourth instance) — and the exact stagger family is arithmetic, the random frame cancelling exactly out of F_out · F_inᵀ, so its ceiling is predictable at any p without building a surface.

Detectability's re-indexing is an endpoint information reading, and the path quantifier is gone without a successor. B43 (#609): sensorimotor dependence is I(P; Δ) — traditional Shannon mutual information between a content-varying sensory perturbation at fixed norm and the paired-counterfactual response at the world-read boundary, with the situation marginalised. ADR-0021 keeps its fork, its A₀ = 1 convention and its per-edge language; the statistic, the terminus and the reference are what re-index, and the bottleneck ratio is kept and demoted on #383's precedent because ½·log(1 + Δ²/σ²) contains it. Three standing constraints ride out of it. max-over-paths-of-min needs no replacement — information only decreases along a route, so the terminus has already suffered every constriction on every route, and B39's suspicion that the widest-path form was a dome artifact is upheld; a reading may not reintroduce a path quantifier to strengthen a dependence claim. Amplitude is not the alphabet — B43 (#607) showed a topological candidate clears the amplitude clause by construction, so P varies which pattern, never how hard, and a candidate may not argue dependence from gain. And the situation is the noise, not a nuisance to condition out: the sandbox is deterministic, so the conditioned form reads its ceiling by construction and is vacuous — the fork is the centring (B18/B19's error in information clothing), and the configuration sweep is the noise model rather than a robustness check. Instrument on B63 (#637).

Dependence passes, and the pass does not discriminate. B63 (#637) built B43 (#609)'s instrument and read it on three arms of one surface. I(P; Δ) > 0 clears on the trained surface across all three strata (patch 0.857 bits, proprioceptive and touch 3.000 at the ceiling, every p at the 400-permutation floor); it does not clear on the untrained one on any stratum — on ADR-0021's own peak | centroid reduction, which is the qualifier B66 (#642) found this claim needs: under three of four reductions the untrained construction does clear the null on proprioceptive and touch, up to 1.561 bits. So B58 (#630)'s a construction may supply the quantity free is discharged in the architecture's favour — on patch and only there, still the first time on this map that it has been. And it clears on the flat bundle too, B42's retained null, by nearly 2× on patch — the only stratum with headroom. B43 §5's above zero, above null can be cleared by a whisker is understated: on the widest stratum the null wins. Standing constraint: a dependence claim is quoted against the untrained surface and the flat bundle, or it is not quoted — the dual of B58's initialisation rule, and the reference doing the job B43 gave it rather than the reference failing. B43 refused a threshold on ADR-0021's k = 1 discipline and that refusal is not reopened; and B66 (#642) has answered what it is quoted against by striking the question: nothing separates them and nothing could, so the sought reference does not exist and B52's amended item 3 is not the precedent it looked like — see the next entry. Three readings ride with it. The sweep size is load-bearing and was nearly a false pass: at 4 configurations the untrained arm reads 0.87–1.30 bits against its own 0.20–0.28 at 24, so C ≤ 8 is not admissible and the vacuous conditioned form leaks back in below 16. The terminus is 3 components wide — spec.joints, the actuator's commanded block — so the profile currently orders by stratum dimension against terminus width rather than by transport quality, patch (12288-dim) reading lowest and touch (3-dim) saturating; that is a fifth instance of the construction clamp, and the first where the clamp sits on the bar rather than on a trained object (B67 (#643)). And ADR-0021's per-trial reduction is lossy: the peak tick reads 0.857 bits on patch where the whole window reads 2.810, so B43's reduced per trial exactly as ADR-0021 already prescribes is amended by advisory on #609 — the amplitude discipline is upheld (both variants read a direction), only the tick axis is restored.

The traffic's rank and its agreement are two levers, and the two shipped rules pull opposite ways on the first. B62 (#635): with both rules off past construction the traffic's uncentered effective rank does not move (2.7802 → 2.7825 over 20,000 ticks, B57's own horizon, on two independent arms), so the collapse is training's and neither the body's nor the sandbox's — and it is PredictionRule's alone, which reproduces it at zero cost in exposure or audience differentiation while TransportRule alone raises the rank to 3.1347 and buys the alignment (q 0.8832 → 0.0636) for 1.96 dimensions of exposure, raising differentiation (0.5307 → 0.5505) rather than spending it. Standing constraint: a candidate aimed at the traffic's rank names which rule it is aimed at, and may not argue a rank effect from the shipped pair — their prices differ in kind and the compromise costs a column (differentiation → 0.4826) that neither lever costs by itself. B52's instrument is vindicated and is not a second name for B60 (#633)'s object: N(θ) tracks alignment, the rank only setting how much of it can be counted, so the ledger's row 8 resolves to its first reading. Two riders. N(θ) is quoted with A(θ) or it is not a reading — it is a participation ratio inside the counted band and reads 1.0000 on a direction carrying 0.4% of the traffic; B57's own readings are untouched (A 0.9547 → 0.9977). And ker(G) = ker(δ_P) exactly, so exact agreement is unavailable to any visible direction by construction — a bar written on earned asks for a measure-zero event and an invisible one. What #633 inherits: the near-rank-one C it proposes to whiten is manufactured by the prediction rule, not by the transport rule whose update it would change; under TransportRule alone the traffic keeps effective rank 3.0. Whether that relocates the lever is #633's to rule.

Dependence is a gate, not a ranking, and differentiation may not be stapled to it. B66 (#642), on the user's own refusal of its ticket's premise. I(P; Δ) is a transmission reading and B42 derived the flat bundle as the arrangement in which a message survives a loop unchanged — so a transmission reading is maximised by it by construction, no reference can separate them, and B63's what is missing is a reference that separates is struck along with item 1 of its own successor. The bar is a necessary condition on the world loop, which many arrangements are supposed to pass; the flat bundle clearing it is only a scandal if the gate was expected to rank, and it never was. The joint rule is refused as the repair: audience differentiation is the definition of not-being-flat, so a rule of the form clear the null and have nonzero differentiation disqualifies the null by identity rather than discriminating, and would pass the architecture because it is the architecture. B52's precedent does not transfer — its clause guards a candidate's training path against buying its result by collapsing lanes, and does not disqualify a reference architecture from a reading; the agent carried it one object across and the user caught it. Standing constraint: a dependence claim is quoted on patch alone, on two independent grounds — proprioceptive and touch read the ceiling exactly at k = 2, 4 and 8, so their saturation is bijectivity to the terminus rather than an artifact of choosing 8 and no alphabet can fix it; and patch is the only stratum where the untrained arm fails under every reduction and both decoders. --no-file is lifted — a gate verdict is not required to discriminate — with #224's float32 finding recorded beside the verdict rather than holding it back. Two readings ride with it. The probe saturates at every alphabet it has: on the trace reduction both arms sit exactly at the ceiling at k = 2 and k = 4, and at k = 8 on patch the sign flips with the decoder (flat +0.058 on centroid, trained +0.296 on nn1), so the flat bundle's 2× is a peak-reduction fact and not a robust one — B70 (#648), blocked on B67 (#643) because the alphabet and the 2-dimensional terminus are the same constraint from two ends. And the user's own account of the 2× is untested, not refuted: that the probe's task is too small for specialisation to pay is a claim about a world this map may not enrich (out of scope, #641); the one reading pointing at its cells-are-constrained half is B42's flat-bundle k_v at 14.8 of 32 against the control's 20.0.

Decisions so far

• A1: Is ADR-0004's k < n what has to give? — No: k is not a term in the composed object and ADR-0004 is exonerated. The hops run through lanes (m in n), not charts; the composite is a product of principal-angle cosine matrices, driven by m/n and by ADR-0010's incoherence constant c — whose adoption pre-registered this exact failure and whose falsifier was closed against a proxy. The taper's timescale job is already gone (ADR-0028), so widening m costs capacity, not rate.

• B4: Does the interior lane width m have a derivation, or only a value? — Neither a derivation nor a vindicated value — but the bound is now exact, and m is not the lever. A hop is a truncated orthogonal matrix, so Forrester (2015) eq. (3.3) gives the composed spectrum in closed form. Generic lanes at today's widths predict composed rank median 1.011 against the record's 1.025 at construction: the collapse is what the dimensions alone produce, so it needs no pathology and indicts no ADR. Rank 2 needs m ≈ 10, but Σ_e m_e ≤ n − 1 caps the degree-9 cell at 3.4 — so only n to ~128, or degree to ~3, reach. The delay-embedding ceiling Prior art: dimensioning small predictors and bottleneck width #32 used has no literature standing for a shared object. — ceded

• B3: Read the pre-registered falsifier that #220 closed against a proxy — It fired, at 4.06x, and the instrument was never missing. Cross-edge alignment reads 3.49x / 3.50x taught (seeds 0/1, main 2bce07d, full dome, 30k, c = 2 in circuit) against the pre-registered 14.20x, while the untrained arm reads 4.04x / 4.08x against 3.66x and does not fire — so taught now sits below untrained and training removes alignment where it once multiplied it 3.88x. ADR-0022's "largely a thing training makes" is false on the live surface. The collapsed half is the receiver's contribution, 2.57x → 1.10x — which is #533's principal-angle mechanism read on a single hop: the falsifier firing and composed ER 1.000 are one fact through two instruments, and this one has a pre-registered baseline attached. Can disagreement alone buy the unspent 2.15x, without reading a neighbour's parameter? #184's unspent 2.15x re-sizes to 2.90x (its closure survives; ~1.7e3x compounded still leaves ~6.7e5x). c is indicted but not isolated — ADR-0032's floor moved the sender-side half, and the c-only control is B1's.

• B1: Read the principal angles, and whether c alone moves composed rank — c is not a lever at all; composed rank is a function of (m, k_v, hops) and nothing else. Redrawing every carried subspace as a Haar frame of the same shape reproduces the real ER distribution, tail included (median 1.0216 vs 1.0255, three seeds) — so no rearrangement inside fixed dimensions can move it. c is structurally dead: the 150 cells it governs are slack by 4.4x and the 4 at the cap are the wholly-pinned ones The actuator's c_v is 2 and nothing holds it there #228 puts beyond it, so the sweep over 1..12 is flat to six decimals at construction and at every checkpoint of both trained arms. Rank 1.000 is domination, not annihilation (full rank 3, median spectrum [1, 0.113, 0.002]). Training raises alignment while rank falls (leading cosine 0.568 -> 0.79/0.81), leaving the trained surface ~370x below generic — so any m must clear its bar with margin. Confirms B4 by measurement (both read 1.011 generic at today's widths, and n x4 at 2.047 against its 2.195) and falsifies A1: Is ADR-0004's k < n what has to give? #533 §4's ratio premise: n reaches. Three of the ticket's own premises were wrong and are corrected in the readout. — ceded

• B5: Five places the record contradicts itself on m, the piece's dimension, and what width can do — All five corrected; none declined, and no decision moved. ADR-0004's m = 4 margin reads ~1.05x, not ~1.4x (Which knob supplies L1's private floor: n, boundary_m, or one patch per cell? #474 took the delay-embedding ceiling from < 2 to < 1.5 against Must the chart be a per-domain number, and what does that cost the shared dictionary? #132's median d_corr 1.43). ADR-0004's pieces are manifolds and language's is a finite set: what does local flatness mean there? #440 is no longer cited as having re-opened the piece's box dimension — it closed ruling the piece is dimensioned, and what it left conditional is curvature, not the dimension. Must the chart be a per-domain number, and what does that cost the shared dictionary? #132's quartiles 1.26 / 1.43 / 1.53 now sit next to that ceiling for the first time, with both caveats intact (the lane carries the overlap; the ceiling is an analogy to Takens/Sauer, not a cited bound). Which knob supplies L1's private floor: n, boundary_m, or one patch per cell? #474's landing ~8h after ADR-0004's pieces are manifolds and language's is a finite set: what does local flatness mean there? #440 shut is recorded as provenance, not a re-ruling — B4 found nothing resting on the box dimension, and whether m moves is B2's anyway. Composed rim-to-apex transport carries one direction, and a per-map floor that succeeds per map does not spread it #497's @failure no longer says width is irrelevant: the construction invariant caps the degree-9 cell at m ≤ 3.4 where rank 2 needs m ≈ 10. Edits on PR #545, not yet on main; Composed rim-to-apex transport carries one direction, and a per-map floor that succeeds per map does not spread it #497's amendment is live on the tracker. — ceded

• B2: Which lever gives — c, the privacy invariant, or degree? — The privacy invariant gives, doubled to Σ_e m_e ≤ 2n − 1, and it is the third lever of four — not the first. A fourth nobody had named does a third of the work free: the invariant binds at exactly one of the six relay cells (L1 at slack 0; L3–L6 idle 13 of 31), yet m is one global constant per edge kind, so per-edge m_e alone takes composed ER 1.028 → 1.154 with no ADR on the ticket moved. And no lateral edge lies on any rim-to-apex chain (0 of 405), while laterals eat 12 of 31 at the binding cell — so the cheap half of "lower degree" is lateral width, at no hop cost. Stack: per-edge + laterals at m=1 + invariant doubled = 2.193. c is struck (0.000) and to be removed (B7); n is not a lever but a permission slip — m=10 at today's n reads 2.561 against n=128's 2.544, at 1/16 the parameters. Write #474's ruling: interior_m 4 to 3, boundary_m 8 to 4, and the invariant behind them #483 is superseded, not resumed: per-edge widths dissolve Which knob supplies L1's private floor: n, boundary_m, or one patch per cell? #474's (3,4)/(2,5)/(1,6) frontier. The bar is generic median ≥ 2.0; ADR-0009's 1.5 is discharged, not inherited — it is that ADR's own falsifier for induced activity and it has already fired. The whole stack is provisional on B6: training erodes the excess over one ~440x, read at one width only, and if that is a fraction rather than an amount every lever here fails and the transport rule is what must change. Corrected the same day: two arms that completed mid-session and were unread at resolution (100k baseline and winner) show c's cap saturating at horizon (Gram p90 0.25 -> 0.9998, all 153 governed cells over half), so c is not the dangling degenerate value the removal was premised on — loosening it is still worthless, but c = 1 is the only setting on the record whose advantage grows with training (1.0038/1.0079 at 100k against 1.0000026/1.0000150). c's disposition is back with the user on B7.

• B7: Does ADR-0010's c get removed, now that it is live at horizon? — Kept, unchanged, and marked — removal is struck, and so is the re-pin. The removal instruction's premise is dead twice over: the cap saturates in the tail under training (baseline Gram p90 0.25 -> 0.9998, cells at cap 4 -> 21, all 153 governed cells over half) while the median stays pinned at 0.2500 at every checkpoint of both arms — so the typical governed cell is as slack at 100k as at construction; and c has three readers, not one (_push_apart, tick.py::reconciliation_gain line 375, bias_selection.py's fold-margin nomination line 1160), so the ticket's checklist would have shipped a live gain change as a dead-code deletion. Re-pinning at c = 1 is struck too: its only evidence is sweep_c, a post-hoc re-projection of a surface trained at c = 2 that calls project() once and never touches the gain — and c = 1 doubles reconciliation_gain at exactly 150 cells (262 of 414 sit at 1 by pigeonhole or degree), which no arm has ever run. What survives is the signal: c = 1 falls to a floor at 10k and then reverses, 1.000202 -> 1.003835 (baseline) and 1.000147 -> 1.007930 (winner), p90 1.111 and max chain 1.914 against c >= 2's p90 1.00014 — the only setting on this map that recovers under training rather than eroding ~440x. It becomes a measurement on B9 (c = 1 in circuit, projection and gain, run to horizon ungated) and a mark on B10 (register row + ADR-0010 amendment, carrying #184's discharge — the row still names it an open cost after B3 fired it at 4.06x). #228's c_v = deg(v) is moot, not deferred: it survives because c does.

• B9: Does c = 1 hold its advantage in circuit, with the gain doubled at 150 cells? — No — it inverts it, and c is finished business in both directions. In circuit (projection and gain, ungated, 100k, both arms, seed 42) c = 1 reads excess over one of 1.31e-09 (baseline) and 5.20e-10 (winner) against c >= 2's 2.60e-06 and 1.50e-05 — ~1,990x and ~28,800x worse, where B7's sweep_c said ~1,474x and ~530x better. The re-projection overstated it by ~2.9e6x / ~1.5e7x; p90 1.111 and max chain 1.914 become 1.0000 and 1.0000, and the floor-then-recover shape is gone. The sign is structural: c is the incoherence cap, and #533's hop is the cosines of the principal angles between a relay cell's two carried subspaces, so pushing incident maps apart destroys the very material composed rank is made of (leading cosine 0.818/0.794 -> 0.353/0.370; s2/s1 down 44x). So c is slack when loosened (B1) and harmful when tightened — not a lever in either direction, GAUGE_C = 2 stands, and B10 is the last word. The surface stays admissible (zero non-finite, norms in band): c = 1 is admissible and useless, not inadmissible. Also found: a latent scaling bug in #502's re-derivation — overlap_target = g_v^2 c_v - pinned_count subtracts an absolute count from a budget c scales, so at c = 1 the drive-side apex cells' residual budget falls 7 -> 3 and the cap ratio reads 1.107–1.120. ADR-0010's own bound is not broken (lambda_max/g_v^2 c_v = 0.774–0.836, Put the incoherence term in the projection, and swap the gain's denominator in one edit #220's pairing intact). — ceded

• B10: Mark c in the register and amend ADR-0010, carrying #184's correction — Written — and the row says something stronger than the ticket asked, because the ticket's own instruction was stale by the time it was read. It wanted c = 1 named live and under measurement on B9; B9 landed first and inverted it, so writing that would have reproduced the exact fault this ticket exists to fix — a row pointing a reader at a question already answered. The row states the settled fact instead: c is not a lever in either direction — loosening worthless (flat to seven significant figures over c = 1..12 at every checkpoint of both 100k arms, B1), tightening harmful in circuit (~1,990x / ~28,800x worse, B9) — with #184's precondition discharged, pointing at B3's 4.06x rather than restating it, and the cap's saturation written only with its qualification: Gram p90 0.25 -> 0.9998 and all 153 governed cells over half, while the median stays pinned at 0.2500 at every checkpoint of both arms. The register is generated, so the write is at restriction.py:69's @flexibility annotation and docs/registers/architecture.md:71 regenerated from it — which is why the diff touches restriction.py at all (comment only; the value and all three readers are untouched). ADR-0010 amended, not deleted: it pre-registered this exact failure and the amendment records that the pre-registration was correct, the substance being the asymmetry it did not anticipate — it guarded a loosening while the direction that moved was tightening, having read c as a budget with slack rather than as a cap whose sign matters. Two smaller marks in the same pass: Why 2, and why not tighter's standing offer to tighten is superseded, and #502's partly-pinned derivation now records B9's latent scaling bug — recorded where the expression lives, not ruled on, since ADR-0010's own bound is intact and the shipped c = 2 is unaffected. #228's c_v = deg(v) left moot, not deferred. Documentation only, no re-run; register and restriction suites green (45 + 45). Edits on PR #554, not yet on main. — ceded (the departure above only)

• B6: Does training's erosion of composed rank scale with lane width? — Neither: it is not a fraction, not an amount, not a floor — it weakens sharply with lane width and then stops. B2's stack is not sunk and the transport rule is not forced. On domes genuinely rebuilt at each width (not T4's sweep_m, which holds k_v fixed), the erosion factor moves x437 (m=3) -> x269 (6) -> x18.0 (10) -> x4.1 (14) at a common 20k horizon, while the amount removed just tracks the construction excess (0.025 / 0.202 / 0.389 / 0.478) and the endpoints span 53,000x. The confound is closed rather than argued: at 20k the narrow arm was still falling, so m=14 was carried to the same 100k horizon — over the span in which m=3 loses a further 12.8x, m=14 moves 1.13x and not downward throughout. It erodes less, not slower. The mechanism is visible and is B1's: rank 1.000 is domination, so collapse means pulling the leading per-hop cosine off the rest, and the gap training manages to open falls +0.2269 / +0.1383 / +0.0317 / +0.0038 across the widths, tracking the erosion over three orders of magnitude — while the whole cosine distribution shifts a near-constant +0.034..+0.041. Training is not doing less work at width; it has no headroom left to concentrate. Two limits stated rather than papered over: uniform interior_m saturates (construction ER 1.4115 at m=10, 1.6158 at 14, 1.7772 at 20) and never reaches B2: Which lever gives — c, the privacy invariant, or degree? #540's 2.193, because k_v = min(n, sum_e m_e) caps at n = 32 — so these arms read the trend and cannot stand in for the per-edge stack; and the best trained composed rank anywhere on the record is now 1.186, against a bar of 2.0. Item 5 (c = 1 at width) is superseded by B9, which landed mid-session: those figures came from sweep_c, the re-projection B9 discredited, so the width series measured the artifact's size and not c — corrected on the ticket. The two agree on mechanism (B9's tightening destroys the same leading cosine that width protects) and B9's "erosion is universal" is now qualified: universal at m = 3, not across widths. — ceded

• B8: Write #540's ruling: per-edge m_e, lateral lanes at 1, and the invariant doubled — Two of the three written and shipped; the doubling is held, because the number and the reason B2: Which lever gives — c, the privacy invariant, or degree? #540 gave for keeping it cannot both stand. Interior lane width is no longer a value: graph.py::allocate_lane_widths gives each lane the largest width both endpoints can afford by max-min fair filling, laterals are pinned at 1, and widths come out 5–18 where a global constant gave 3 — under Σ_e m_e ≤ n − 1 unchanged, zero violations, build_graph raising if breached. interior_m is gone from DomeSpec and Which knob supplies L1's private floor: n, boundary_m, or one patch per cell? #474's frontier is dissolved rather than re-valued, so Write #474's ruling: interior_m 4 to 3, boundary_m 8 to 4, and the invariant behind them #483 stays superseded. The held row is the finding: at 2n − 1 the guaranteed private dimension max(0, n − Σ_e m_e) reads zero at 104 of 150 predicting cells and the dim H⁰ floor falls 914 → 54, reinstating the zero row #474 was opened to remove — while this ticket's own item 2 ordered the invariant's reason written down as new to the record (a cell needs more features for its own dynamics than it holds an authoritative position on network-wide), which the doubling contradicts. Shipping both would have been writing a contradiction, so the collision is measured and handed to the user on B12; DomeSpec.privacy_budget is a field, so the flip is one line. The shipped stack therefore reads 1.341 generic against the bar of 2.0 — B12 is on the critical path, not beside it. The reallocation is not free either: dim H⁰ falls 1278 → 914 with the floor of 1 held everywhere, and the gradient inverts (L1 vision 1 → 7–9, L4–L6 14 → 1–3), because idle budget was privacy. Also: Composed rim-to-apex transport carries one direction, and a per-map floor that succeeds per map does not spread it #497's @failure third pass — the m ≤ 3.4 cap was an artifact of one global constant, not of the invariant, which corrects B5 in the opposite direction; n refused on cost rather than on A1: Is ADR-0004's k < n what has to give? #533 §4's falsified ratio argument (2.561 at n=32 against n=128's 2.544, at 16× the parameters); and the delay-embedding margin relieved from ~1.05× to ~1.75× of Must the chart be a per-domain number, and what does that cost the shared dictionary? #132's median, both caveats intact. Recorded diagnostics moved: χ +2505 → +2323, worst cut 205:1 → 104:1. Suite 12 failed + 5 errors against a 13 + 5 baseline, all environment. Edits on PR #558, not yet on main. PR #557 is merged but landed nothing — it targeted worktree-cs-542, which had already merged to main 33 minutes earlier, so the work was stranded on a branch that had already landed; retargeting it would have deleted #541's research doc and reverted #554's ADR-0010 amendment. Allocate interior lanes per edge, laterals at 1, invariant held (#548, replaces #557) #558 is the same two commits replayed onto current main. — ceded (holding the doubling; max-min fairness as the reading of largest both endpoints can afford; not re-running the generic-chain instrument)

• B12: Does the doubled invariant give, or does the reason it exists? — Neither. They were never in contact, and unwelding them beats both horns on both axes at once. _assemble permits the same leading block on every incident edge, so Σ_e m_e ≤ n − 1 never enforced distinct lanes — it is a worst-case bound on the union's rank being used as the block size, welding privacy p_v to lane capacity by one line. Reserve p directly (permitted = n − p) and the guarantee holds exactly rather than as a tight worst case, on a one-line change that B1's law already reads, because k_v is a free argument of it. At budget 63: the doubling gives 2.073 generic with dim H⁰ 54 and 104 of 150 cells at zero, while reserve p = 8 gives 2.231 with a floor of 1200 and no zero cell — more privacy than the shipped stack's 914 and more rank than the doubling buys, at identical parameter count. The trade runs backwards once unwelded: raising p narrows k_v at fixed m, and rank is driven by m/k_v, so privacy and composed rank rise together — B2: Which lever gives — c, the privacy invariant, or degree? #540 had measured this (k_v 18 → 4 moving 1.010 → 1.215) without connecting it, because welded you could not move one alone. Σ_e m_e ≤ B survives as a capacity budget, not a privacy invariant, and DomeSpec.privacy_budget is misnamed on landing. The private-dimension gradient is retired as decoration: #548 already broke its monotonicity (rim 7–9 against L2–L6's 1–3) and #271 already measured its retention claim null (correlation −0.107..+0.047, smallest lift at the apex), so p is flat and chosen; if it ever returns it is a taper on p, designed, not a by-product of degree. One mechanical consequence ruled here: at budget 63 the water-fill emits two lanes of width 32 against k_v = 24, so allocate_lane_widths caps each lane at n − p — DomeSpec.drive_m's own reasoning, already in the spec, and applied in every figure above. B11 now builds both arms and compares — the user's own addition — rather than asserting the reserve's advantage from construction figures.

• B11: Does #540's per-edge stack, built and trained, hold rank above the bar? — Yes for the reserve arm, no for the doubling arm — and the reserve arm is the first thing on this map to raise composed rank and privacy together, the first arm anywhere on the record that training does not erode, and the new best trained composed rank. Both of B12's arms, built on the spec B8 shipped, two seeds, reserve carried to 100k: the doubling erodes x6.2 / x6.7 to 1.0936 / 1.0725 having stripped 104 of 150 cells of privacy, while reserve p = 8 erodes x0.9 — it sits above its construction value at every checkpoint from 10k on, holds the band 1.40–1.53 flat from 10k to 100k, and reads 1.4237 (p90 2.2791) with the dim H⁰ floor at 1200, above today's 914. That is a floor, not a rate, across the span in which m = 3 loses a further 12.8x, and it beats B6's 1.186. Neither arm clears the median bar of 2.0 (reserve delivers 42% of the required excess, doubling 9%) though reserve's p90 clears it. Two findings beyond the ask. B2: Which lever gives — c, the privacy invariant, or degree? #540's law survives its own falsifier: all three arms depart from the generic prediction at their own per-hop widths, and none of it is genericity — the carried subspaces are generic to within 1–3% and the whole gap is singular-value spread, the instrument's second idealisation. And a construction reading is the wrong number to rule on — ADR-0032's band is a training-time projection, sigma_min/sigma_max closes to 1.0000 by 100 ticks, and the two arms invert between construction and horizon (doubling leads at construction, 1.5757 to 1.3825, and is worse everywhere after 500 ticks). B2: Which lever gives — c, the privacy invariant, or degree? #540, B8: Write #540's ruling: per-edge m_e, lateral lanes at 1, and the invariant doubled #548 and B12: Does the doubled invariant give, or does the reason it exists? #556 each ruled on construction figures alone. B9's sign constraint holds in both arms — the Gram cap is flat at construction (4 of 414 at cap in all three) while alignment rises to 0.9784 — and the risk it named did not bite: the reserve arm presses the cap hardest (p90 0.9982 at 100k) and its leading cosine still ends higher than at 20k. c is untouched. — ceded (a second seed on both arms was run instead of a 100k doubling arm, so the doubling arm has no horizon reading; p = 8 was taken from B12: Does the doubled invariant give, or does the reason it exists? #556 and not swept)

• B13: What is p, and where does the reserve arm's floor peak? — p = 12, derived as p = k = CHART_DIM, and the floor does not peak — it climbs to a degenerate ceiling, so the boundary that matters is where lanes stop being different lanes. The construction curve and the trained curve run in opposite directions across the whole sweep: built ER peaks at p = 0 (1.54) and falls to 1.01, while trained ER rises 1.0845 (p=0) -> 1.1824 (4) -> 1.4386 (8) -> 2.1309 (12) -> 2.9171 (16) -> 4.0000 (20). p = 12 and p = 16 are the first arms on this map to clear B2's bar of 2.0 on a trained surface and hold at 100k (2.2127 and 2.9408, against a previous record of 1.4237) — so #540 §5's residual h <- (I+T)h is not forced. p is the dial on B6's headroom law: erosion tracks the construction cosine gap monotonically over two orders of magnitude (0.0547 -> x6.97 … 0.0000 -> x0.08), because narrowing k_v closes the gap training needs to concentrate. The price is priced: p buys rank by forcing incident lanes to share directions — 0% of the median lane at p <= 8, 33% at 12, 67% at 16, 100% at 20, where all 1,578 hops coincide and an interior edge selects nothing; a real cure for #533's collapse, but p >= 18 is refused as a different architecture rather than a setting of this one. B11's falsifier fires at p = 0 and p = 4, which fall below construction — the reserve arm does not erode is a property of p >= 8, not of the mask. The dim H⁰ floor is 150p exactly at every p, training-independent. p's derivation follows the invariant's own reason (#548) to the one constant the record already has for a cell's own dynamics, with both limits stated (a magnitude, not a subspace; k is itself stipulated). Reading on PR #563, not yet on main. — ceded (p = 12 over the higher-scoring p = 16, on the derivation rather than the number; refusing p >= 18 on selectivity; the sweep grid and horizons; reusing B11: Does #540's per-edge stack, built and trained, hold rank above the bar? #555's p = 8 runs)

• B14: Is a generic median the right bar, now that an arm survives training? — No — the bar is replaced, and the new one is already cleared, by p = 16 rather than by the arm this ticket was about. 2.0 was a demand for balance nobody argued for: effective rank is the participation ratio (Σσ²)²/Σσ⁴, so on a two-direction composite ER ≥ 2.0 is reachable only at exact equality of the two directions — where Map: transport whose composed rank exceeds one #532's own destination and ADR-0009 both state the condition as "carries more than one direction". Both of #540 §7's anchors were gone (the ~440x erosion is a narrow-lane effect per B6; 2.193 was a construction figure B11 broke), and §7 had marked 2.0 ceded with re-examination pre-registered "if B6 turns the map over". The test is now composed rim-to-apex ER, median over chains, at the training horizon, at or near what the surface's own (m, k_v, hops) predict — a ratio, arm-free by construction, which was the user's binding rule on re-deriving it. The reference is generic, not construction: B11's own "a construction reading is the wrong number to rule on" disqualifies the latter, which also ranks arms backwards (an arm flat at 1.05 would pass). Read on B13's sweep the ratio is 0.629 (p = 8), 0.910 (p = 12), 1.004 (p = 16) — so B13's ceded choice of 12 over 16 is reversed by the new bar, exactly as B13 said it would be by "a reader who weights the bar over the derivation". That goes to B17 with two things B14 could not settle: the threshold "at or near" leaves open (0.910 is where it bites — B14's own defect), and the forced-overlap price p = 16 spends (67% of the median hop against 33% at 12 and 0% at 8), which no document prices. B15 is blocked on B17 and no longer lands as "a measured improvement that does not reach the target". The fog on why training leaves generic graduates to B16 — not as the critical path, since p dials the decay away, but as the only route to ratio 1 that does not spend selectivity. — ceded (the residual/Kronecker ranking level behind B16; demoting rather than closing B16; routing the threshold and the p choice to B17 rather than ruling them — the test itself is the user's own answer)

• B16: Why does training seek concentration at all, and can the ratio reach one without forced overlap? — Because concentration is what the transport objective asks for — and the erosion is not in the principal angles at all, it is in the U-rotations between hops. Across p = 8's 100k run cos_product_er is flat at ~3.0 while composed ER halves, so the object B1 and #533 reasoned about barely moves; a parameter-free “top cosine saturates” predictor is exact at p = 16 (err −0.007) and p = 20 (+0.000) and wrong by +0.341 at p = 8. Two consecutive hops' U bases are the two ends of one shared lane, and the rule descends ‖F_v x_v − y_e‖ / (‖F_v x_v‖ + ‖y_e‖) — make the two ends agree — so bringing them into coherence, which is what makes seven contractions compound onto one direction, is the objective being met, not a pathology. Scrambling the junctions with random orthogonals, every hop left as trained, restores p = 8 to 2.2505 against a generic 2.2652 while the true surface sits at 1.4776: the collapse is entirely junction-carried. The cell's node-stalk traffic is rank one (1.002), so the rule has evidence about one direction — the leading junction coherence rises ~48% at p = 8 while the second stays at the random baseline, and r-coherent-direction synthetics bracket the measured ratio between r = 1 (0.487) and r = 2 (0.872). The ticket's own framing is corrected: at p = 16 the coherence never builds (0.227 → 0.193), so p does not merely deny the drive room — forced overlap makes agreement reachable without rotating the Us, which means forced overlap is not the only thing that could work. B6's law is a correlate (the drive is identical in both arms; at fixed k_v corr(traffic_er, cos_leading) = −0.45). Ratio 1 is purchasable two ways only, given a pure-product transport learned by an agreement objective: kill the contraction (what p does, priced in overlap) or add a path the drive cannot erode — which is the mechanism #540 §5's residual owed, since ∏(I+T_k) includes the unlearned empty product; the channel-heterogeneous candidate has neither and owes a cross-channel decorrelation mechanism. B17 is not relieved and should rule on the table it has. — ceded (20k not 100k, one seed, two arms; the residual/Kronecker ranking is argued from the mechanism and not measured; B6 ruled a correlate without re-running its sweep)

• B17: p = 12 or p = 16, and what counts as near the generic prediction? — Neither — the question is not answerable as posed, because the bar it adjudicates measures the transport operator and never the signal. composed_reads (T2/run.py:496-520) multiplies agent.sheaf.maps along a chain and never touches agent.sheaf.stalks, so every reading on this map — B1, B6, B11, B13, B14 — is a property of learned parameters, and the metric cannot tell a network composing many perspectives from a wide empty pipe (p = 20 reads exactly 4.0000 on an operator that is the identity on a 12-dim block). The mechanism the architecture's own account requires does not exist: restriction.py's mask "is set at construction, it closes and never re-opens", #556 found the same leading block on every incident edge, and the learned subspaces measure indistinguishable from Haar (B1) — so nothing looks for what two cells share, and p is a geometric substitute: it raises operator rank by shrinking the ambient until random slices must coincide, and at p = 16 B16's coherence never builds (0.227 → 0.193) while the number rises — the better-scoring candidate is the one where training does less. Three of the four deciding objects are unmeasured (verified by full-repo sweep): joint span across chains (every aggregator is an order statistic over per-chain scalars — so per-chain rank 1 as a working population code fits every number on this map and has never been tested); state rank against emitted rank; and regional consistency — dim_h0 exists only over the whole subcomplex, and its construction bound is exactly the private-dimension count, so every dim H⁰ this map has quoted is the trivial part and the 150p floor means p inflates precisely the uncoordinated half. And the premise underneath is an uncentred statistic: B16's traffic rank never subtracts the mean, so a settled belief varying richly reads 1.00 — B18 reproduces B16's uncentred figures exactly and reads centred 2.52 / 1.29 / 1.14 at 100/300/1000 ticks against uncentred 1.08/1.002/1.002, mean_share 0.9985: direction survives, magnitude wrong by 19–137×, early training unrecognisable. Corrections kept for the trail: "0% forced overlap at p ≤ 8" is a median artifact (564/1578 hops, mean share 0.133 at p = 8 — the record has spent this unpriced since B11); and on the axis B13's refusal of p ≥ 18 actually rested on — does an edge still select — p = 16 sits with p = 0 (edges clipped to m_e = k_v: 2/10/70/70 of 409 at p = 12/16/18/20; allocator distinct widths 9 through 16, then 8 → 2 → 1). p is deferred, not ruled; B15 re-blocked onto B27. Graduated nine parallel readings — B18 centred traffic, B19 state vs emitted rank, B20 joint span across chains, B21 the ripple test (reach and distinguishability), B22 coherent regions, B23 is the dome earning its constraint, B24/B25/B26 literature — into B27, an open grilling on whether the vision still holds and what the destination should be. — ceded (the nine tickets' composition and scoping; blocking B27 on all of them; keeping this ticket's title against the user's stated preference for retitling it)

• B18: Is a cell's own state really one-dimensional, or is that an uncentred statistic? — The artifact is real and larger than expected — centred excess over one runs 19–137× the uncentred — but B16's direction survives: the state is ~1.14–1.18 against an ambient of 24, not 1.002. The mean carries 99.6–99.9% of the energy past the first window, yet centred the state still falls 2.52 (100 ticks) → ~1.13 (3000) and holds — so "rank one" is wrong as stated and "concentrated" is right. The decisive number was not asked for: corr(er_uncentred, er_centred) = +0.213 (p=8) and +0.067 (p=16), so the uncentred reading is not a biased version of the intended one but a different measurement — it tracks the mean/variation ratio (corr with tr_cov +0.793 against +0.078 centred), which means B16's per-cell correlations rest on a quantity that does not track what they claim. That explains B16's tail: cells 272/311/332/340/… read 1.38–2.15 uncentred because their mean_share is 0.55–0.83 against 0.991 elsewhere — the least-corrupted cells, not the richest; two of them read 1.12 and 1.03 centred, below the median. Two findings beyond the ask. Centred richness by level is U-shaped, not monotone — p=16 reads 1.207 / 1.084 / 1.027 / 1.037 / 1.132 / 1.344 from rim to apex, falling through the middle of the dome and rising sharply at the top, invisible to the uncentred statistic (flat 1.001–1.014 at every level) — evidence for B23 that level structure exists and does not run the direction a hierarchy predicts. And p = 16 carries less state variation than p = 8 (1.1393 against 1.1785 at 20k, lower at levels 2–4) while its composed operator rank is roughly double — independent support from the state side for B17's finding that p buys operator rank without buying content. Does not settle the specialist-versus-bottleneck fork (B19's): 1.18 against ambient 24 fits both a narrow cell and a cell whose richness never reaches its edges. Limits: one seed, 20k not 100k, and replication is not bit-identical past ~3000 ticks (1.0069 against B16's 1.0054 at 10k) because the loop drops B16's EdgeRecorder. Instrument, data and READOUT-567.md on worktree-b18-centred-traffic-567. — ceded (dropping B16's angle/composed reads to make the instrument cheap; both arms at 20k rather than one to 100k; mean_share as the item-2 summary)

• B24 (research): Learned per-edge translation — what keeps long compositions from collapsing? — Seven-hop collapse at our widths is the predicted generic behaviour, and the one proven cure contradicts what a lane is. Newman (1986, CMP 103:121–126) gives the Lyapunov spectrum of products of i.i.d. Ginibre matrices in closed form: σ₂/σ₁ ~ exp(−k/2d), rank one at k ≈ 2d hops — seven hops sits right at that boundary for our lanes, and heterogeneity appears nowhere in the rate, which gives B4/B1's empirical generic prediction an analytic backing it never had. The central bet is challenged: the group that introduced learned sheaves replaced them with precomputed orthogonal maps on the premise that learning overfits, and a 2026 preprint finds learned sheaf geometry replaceable by resampled maps on 4 of 5 benchmarks — so "carried subspaces look random" is the normal reported outcome, not proof of a missing mechanism. A second collapse mechanism: Hansen & Ghrist — "if this sheaf has no nontrivial global sections, the only stable opinions will be everywhere zero" — so composition collapse (generic, visible at construction) and objective collapse (only at convergence) share one symptom and the current instrument cannot separate them. The only cure found is isometry (four names: orthogonal sheaves, connection Laplacians, dynamical isometry, holonomy-freedom) and it is in unresolved tension with the lane — an isometry preserves every direction because it discards nothing, and a lane is defined by what it discards; no source resolves it. Also: no GNN intervention restores rank, all are preventive; Alman & Song (2025) contradict the standard story that skip connections prevent rank collapse. §3's unnamed object has three names — Robinson's consistency radius/filtration, Praggastis's maximal consistent subcomplexes, and Abramsky–Brandenburger contextuality, whose local-sections-without-a-global-section is exactly the gait-cells-and-car-colour position, with a computable obstruction. On the dome: networks without a connection cost do not evolve hierarchy even when the task is hierarchical; with an explicit wiring cost they become modular and hierarchical (Mengistu et al. 2016) — so the sparsification bet is supported conditionally on a wiring-cost penalty, and "sparsify and hope" is not. Caveat that could overturn its own finding: a sheaf has gauge freedom, and "the maps look random" versus "determined only up to an arbitrary gauge" were not separated — cut as B28. Doc on research/573-heterogeneous-transport; five 2026 preprints load-bearing and unreviewed, Newman's original text and Praggastis's theorem not reached.

• B25 (research): Discovering what two views share, rather than allocating it — The architecture is a cellular sheaf and its objective is sheaf diffusion, whose optimum is the collapse — so the rule does not find a shared subspace, it reveals the one the maps already define and destroys the rest. Bodnar et al. (NeurIPS 2022): in the infinite-time limit each channel is projected into ker(Δ_F) ≅ H⁰. Corroborated independently from two-view SSL, where invariance alone has a constant optimum and the entire purpose of VICReg's variance floor and Barlow Twins' identity target is to exclude it. Verdict: disagreement descent, maps trained on it, no variance or rank floor is the configuration all three literatures call degenerate — and we have no floor of either kind. This is in direct tension with the user's own ruling that zero global sections would be fine: everything outside H⁰ is what the rule exists to destroy, so either the regime of interest is transient (and the seven-hop spectrum is the wrong instrument) or H⁰ must be deliberately enlarged — the opposite of what p does. Qualified by our rule not being pure diffusion (a prediction rule and a driven sandbox; driven systems do not relax to the harmonic). Most actionable single item, a third option between this map's poles: Grimaldi et al.'s flat bundle — one frame per node, edge map Rⱼᵀ Rᵢ, so the face stays per-cell while the lane is genuinely per-pair because two faces generate it, and flatness gives trivial holonomy, i.e. cycle-consistent by construction, at O(Bn²). Also: per-pair discovery from both endpoints is already published and needs no global allocator — and the global fair-division allocator has no counterpart in any literature searched. Over-wide lanes have a known signature (high-dimensional CCA finds spurious directions, perfect in-sample and noise out of sample) which is consistent with our "looks random" reading and is directly testable — folded into B28. The compression reference should not be built on: the only exact title match's bearing is inverted (order-insensitivity buys the expressivity gain; our path-composition is emphatically non-abelian); closest to the intended idea is Ma, Tsao & Shum. Genuinely open, and it is exactly this project's object: nothing found on whether a network of per-pair shared subspaces of differing dimensions can be made cycle-consistent. Doc on research/574-shared-subspace-discovery; no theorem numbers quoted from Hansen & Ghrist's opinion-dynamics paper because its text could not be corroborated.

• B26 (research): Populations of narrow specialists, and composing across mismatched abstraction — Rank-one specialists as a code are well founded; rank-one composed transport as a channel is a named capacity trap — and the "it was never a failure" reading conflates the two. Superposition, sparse population codes and VSA describe many nearly-orthogonal directions coexisting in one shared space — genuinely "how much of my thing is happening" — but none of it licenses a one-dimensional channel between modules, and the composed restriction map is the channel. A capacity bound in this project's own mathematics: dim H⁰ ≤ d, equality iff transport is path-independent, and separating C classes needs d ≥ C — so joint capacity is capped by stalk dimension, not chain count, which bounds the exact quantity the population-code defence claims capacity lives in. Two more against the framing: pure selectivity yields a lower-dimensional population geometry and fewer implementable readouts than mixed selectivity (Rigotti et al., Nature 2013 — the specialist hypothesis is the low-capacity end of the design space), and sharpening tuning raises Fisher information only below 2 dimensions, is neutral at 2 and reduces it at ≥3 (Zhang & Sejnowski 1999). But B20 is still the right measurement, for a better reason: "different sets of tuned neurons can induce the same geometry" (Kriegeskorte & Wei 2021) — per-unit tuning is not an invariant and neither the alarm nor the defence has measured the joint geometry. Also: a fixed shared mask is the trivial-sheaf regime that Oono–Suzuki and Dong et al. prove collapses — which, read against B24's "learned maps are replaceable", resolves to maps must differ per edge and be well-conditioned, not be learned — and our configuration has neither. Vocabulary the effort was missing: abstraction-is-a-lattice is settled since Cousot & Cousot (POPL 1977/1979) — Galois connections, incomparable abstract domains, reduced product — which is the G-as-exponent argument made rigorous; and "reach" has four names (over-squashing, dynamical isometry, Fisher memory curve, reachability/controllability, where Krylov rank is the composed-operator rank) sharing one instrument, the far-state Jacobian read as a full spectrum against hop count — the state-touching counterpart of composed_reads and what B21 should build. Negatives: no unified capacity theory for specialist populations as a class; no task-free criterion separating should be low-rank from failed to learn (the information-bottleneck route is refuted, best answer is task-relative sufficiency); MoE specialisation buys interpretability, not capacity. Doc on research/575-specialist-populations; six primaries unreachable, most claims tagged as search synthesis rather than fetched text.

• B20: How many distinct directions reach the apex across all chains, not per chain — Near one on the live surface — 1.03, a genuine collapse under every reading — but 4.3–7.2 on the trained p = 16/p = 24 arms, and the joint span moves with the per-chain median in p, not against it, so the bar and its candidate were never in conflict. Stacking the composed operators at each apex (T6/b20_joint.py, pullback A = FᵀC, checked against a native read) puts shipped at joint d_eff 1.029 with every cross-modality cosine 0.93–1.00 — actuator and touch arrive as the same vector — while p = 16 separates them (0.11–0.14). What the joint object adds is a bound the per-chain one cannot see: the lane ceiling falls with p (15 → 8 → 4), so p = 24 fills 89% of what its apexes can hold while per-chain ER reads a flat 4.0000 — the useful range for p ends between 16 and 24. And the premise itself is unavailable from the graph: six of eight apexes take all 16 of their chains through one shared three-hop tail, the two large ones take 83–84 through four, so “256 chains carry 256 directions” was never on offer. Still the operator, never the stalks — B17’s objection is re-posed on a bigger object, not settled.

• B19: What a cell knows against what it can say — state rank versus emitted rank — Both horns are wrong in the same place: transport cannot lose what a cell has, and the learned maps still stop reporting how much it has. State and emission on the same cell over the same window, the pairing the map had never made (T6/b19_state_emitted.py, three arms p = 8/12/16 at 20k, plus a null pass). The bottleneck horn is closed by construction: rank(interior_rowspace) = k_v at 150 of 150 cells in all three arms, so a cell's interior maps collectively span its entire exposed block and the stacked map is injective on everything the mask exposes — readable/state (same ambient, an orthogonal projector, the only honest loss measure here) reads 0.998, and that residue is the private block. So the specialist is right about the typical cell: centred state 1.318 of 32 ambient and 24 exposed, with 80% of the variance in the exposed block — the richness is exposed, not hidden, which closes the reading the ticket asked to separate. But a Haar control changed the verdict — per edge an independent random partial isometry of that edge's own m_e × k_v, same shape, same mask, ADR-0032's band exactly, on the same state stream: it emits 1.364 against the readable state's 1.369 (so a random isometry is neither lossy nor additive, which validates the instrument) and tracks state rank across cells at r = +0.974 (p=8) / +0.930 (p=16), while the learned maps track it at −0.046 / +0.052. Over state-rank quartiles the state doubles (1.054 → 2.167), the random map follows (1.059 → 2.003), the learned emission is flat (1.603 → 1.555). Levelling in both directions, not compression — training makes emission stop being a function of the state, the sender-side signature of B16's edge-agreement objective, which never asks the emission to remain a readout of its sender. The number for B27: across p = 8/12/16, B13's composed operator rank climbs 1.44 → 2.13 → 2.92 while state reads 1.318 / 1.353 / 1.254 and emission 1.433 / 1.398 / 1.324, neither monotone — p = 16 is an operator of rank 2.92 carrying a state of rank 1.25 — and the learned maps sit closest to random exactly where the operator scores best (learned/haar 1.108 at p=8, 1.050 at p=16), which is B17's the better-scoring candidate is the one where training does less on an instrument that touches the stalks. Independently reproduces B18 on a differently scoped population (2.589/1.340/1.143 against its 2.52/1.29/1.14) and agrees with its p=16-carries-less-state finding. Also, measured on traffic the apex is the poorest cell on the dome (1.062 against L3's 2.047; U-shaped, peaking in the middle) while emitting the most — beside the user's ruling that the apex is not privileged, the rim-to-apex chain runs toward the narrowest state in the graph. emitted/state is not a loss fraction and is not used as one (participation ratio is not a rank, and emission is over-complete at Σ_e m_e median 38.5 against k_v 24). Limits: one seed, 20k not 100k, null at two p settings not three, and every number is a per-cell order statistic — a median over 150 cells cannot see a population code, which is B20's. The one route back for the bottleneck is that injectivity is a property of the stacked map, while a single neighbour reads only m_e. Found in passing: the surface is not reproducible past ~3000 ticks — two passes identical in seed and schedule, differing only by a read-only diagnostic, split to 1.318 against 1.365 at 20k, so few-percent differences between arms here are not signal. Reading on PR #578, not yet on main. — ceded (the Haar control and its two variants, which were not asked for and are what changed the verdict; all 150 predicting cells rather than chain relay cells; WINDOW 1000 and the ladder; the three p settings and the 20k horizon; the null at two arms; readable/state as the loss measure over emitted/state)

• B21: The ripple test — how far does a perturbation reach, and does it stay distinguishable? — 2 to 3 hops, in a graph where every rim cell is within 9 of everything — and magnitude and distinguishability die together, not at different distances, so the gap the ticket predicted does not exist. The first state-touching reading on this map (B17's complement, and the far-state read B26 said to build): a yoked-world impulse (T6/b21_ripple.py) puts the world on a tape so the only difference between arms is the rock; the control replays bit-for-bit, and a full-size rock in ker(F) changes exactly nothing, anywhere, ever. Because that sham produces no round-off either, the floor comes from a six-decade rock-size ladder, and the criterion becomes linearity, not magnitude: the near field tracks the rock decade for decade, the far field is rock-independent across four decades — arithmetic, not signal — and a rock at 1e-6 of the cell's own state norm changes nothing at all, exactly zero, being under one ulp at the first hop. Attenuation is 20–50× per hop, so a 7-hop rim-to-apex chain costs 10–12 orders: the apex cannot hear anything, whatever the operator retains. The methodological warning for B27: past hop 3 the responses read d_eff 2–3 and mean |cos| ≈ 0.5 — rich diversity that belongs to the round-off; a distinguishability statistic read without a floor calls the empty far field informative. Where the rock does land, distinguishability is already poor and structurally so — the patch rim cell has stalk 48 through one lane of width 4, so 4 caps distinct rocks before a hop is taken and 2–3 are used; two orthogonal proprioceptive rocks reach the motor command with d_eff 1.000–1.007 of 2, i.e. the same vector — the bell, not the medium. The hierarchy does no work: reach is 3 hops up, lateral and down alike (lateral marginally longest), and apparent cross-modal influence is entirely graph distance — proprioceptive (2 hops) and touch (3) move the command genuinely, patch (6 hops) reads linearity ≈1 on every arm. p moves none of it at construction or 20k across shipped/p8/p16/p24, which answers B17's open value in the negative on both sides: p neither shortens reach nor buys any. Training makes the short reach louder and never makes the long reach exist (proprioceptive→command 0.018 → 0.729 over 20k; patch→command at the floor throughout, and no better distinguished at 20k than at construction). Not measured, and stated: one seed, one rim cell per modality, stalks not charts, a 32-tick window, an impulse rather than a held step, and the up/lateral/down table taken at construction only (B11's warning applies to it).

• B23: Is the dome earning its constraint, or is the hierarchy imposed and inert? — Imposed and inert: level predicts nothing the wager names, and the one strong stable correlation with depth runs the wrong way. Four trained arm-seeds (T6/b23_dome.py, reserve/shipped × seeds 42/43, 20k), putting what the dome fixes at construction against what training produces. The three trajectory-timescale statistics are negative in all four runs; centred state rank is weakly positive and tiny (+0.12..+0.30, ~2→3 against an ambient of 32); the decode of world state from a cell's own chart is flat once read against its null, whose excess is seed-unstable in sign (−0.114 / +0.072 / −0.066 / +0.359). The only strong, stable correlation is emission_gain at −0.84..−0.86 — reach falls with depth. tau_spectral's weak positive is not a ramp but a rise that breaks at the apex: apex retention over the graph median reads 0.35–0.50 at 100 ticks and 0.12–0.27 at 20k in every run, i.e. the apex is the fastest place in the graph and training drives it there — #271's 0.91-vs-0.99 on a second instrument. This is 05-timescales.md's own pre-registered falsifier ("learning produces the gradient or nothing does"), which Amend #230's diagnosis: the timescale gradient was never placed in any run #276 left standing unchecked because every earlier flat reading was taken where nothing was placed — read for the first time on a trained arm, and it fires. Two facts from the code: no per-cell rate exists (ClockDivisor is held by nothing; the live path reads no level, column or apex) and nothing sparsifies anywhere in src/, so the wager's stated referent — a dense net sparsifying toward semi-hierarchy — has no mechanism at all. Also found: the reserve arm has no private-dimension gradient, p_v = 8 at every cell, so B8: Write #540's ruling: per-edge m_e, lateral lanes at 1, and the invariant doubled #548's inversion is the shipped arm's story and every reserve reading on this map inherits a flat one. Dome-free scoping: the running surface is already shape-agnostic; what must be written is a connectivity rule, an allocator not keyed on levels, a drive attachment point, and a sparsification mechanism that does not exist — against ADR-0026/0027/0021/0009/0024 and the loss of rim_chains and every composed reading defined on it. Above its pay grade, and routed to #517: the body stalls by 2,000 ticks in all four runs and is still stalled at 10,000 (one recovers by 20k) — corroborated by T0: Mechanism reads on the live surface, before any intervention #518's own travel_window, 8.43 then ~0.001 — so most trained readings on this map are taken against a motionless world. — ceded

• B22: Coherent structures - the largest region over which a direction stays consistent — The earned part of dim H⁰ is exactly the dimension-counting prediction on all eight arms (+0), so what the split separates out is slack, not coordination — shipped's 1409 "earned" sections are 2477 rows against 3886 non-private columns, and the 150p trivial floor is exact. Regionally positive where regions are finite: at p = 8 sizes spread (median 27 cells, 5 of 7 levels) and spanning levels costs nothing — a cross-level region carrying 8-9× the constraints per cell holds as many directions as a within-level one, 100% at par to p = 12, failing at p = 16-20. Raising p fragments the regions while inflating the floor (median region 150→27→7→1, levels 7→5→3→1); at p = 16 the median direction is consistent over one cell. Training moves none of it — 3 arms × 9 checkpoints, every number invariant, while B20 reads the same arm's composed ER moving 1.149→1.002; restriction.py's mask closes at construction and project() re-applies it so learning cannot re-open it. — ceded

• B29: Is the sheaf flat? Holonomy, path-independence, and whether composition is order-invariant — Not flat anywhere it has room to be, flat exactly where it carries one dimension, and flatness is not the rank lever. B8's allocation makes the split a construction fact: every width-1 edge is a lateral and every wider edge cross-level (215/194 of 409), so 250 of the 260 basis cycles are rank-1 before a map is drawn and the whole-operator question survives only on the 45 cross-level cycles. There identification sits at chance on every arm from construction to horizon (0.93–0.98 vs Haar ~1.00; untrained baseline 0.998–1.007 ± 0.01 over 7 arms × 8 seeds) and the polar commutator never leaves chance either — not flat and not abelian. On the 250 rank-1 lateral loops the share returning positive climbs from exactly 0.500 at construction to 0.69–0.81 by 2,000 ticks (Haar null measured 0.487–0.502). Holonomy does not predict composed rank: Spearman flips sign across arms and across checkpoints within every arm. And p trades one against the other — channel-return-over-null 3.06 / 4.01 / 1.08 / 1.35 as per-chain ER runs 1.00 / 1.46 / 2.90 / 4.00, an exact inverse, so p's gains are not flatness gains but their price. The ticket's ladder is refuted, not inherited: trivial holonomy fixes d directions, but a generic abelian one fixes 0 in even d and 1 in odd d (not “partial capacity” — the inference slid from an eigenbasis over ℂ to surviving directions over ℝ) and a generic non-abelian one fixes 0, not 1; a sheaf flat by construction reads composed ER 12.000 over seven hops against generic lanes' 2.817, so “non-abelian holonomy” and “composed rank 1” are not the same fact. Part 5's tension does not break, it sharpens: H = I separates into two orthogonal failures (subspace angle moves sigma_max alone, frame angle moves identification alone), so trivial holonomy requires every edge at a cell to expose the same block — B12's degeneracy and B13's ceiling. A flat sheaf here is one whose lanes have stopped being lanes; what the surface reaches is contextual flatness, which is B22 from the other side — and B22's “raising p fragments the regions” is this reading's inverse in the same numbers. Trained arms are one seed at 20k and the world stalls by 2k, so every claim is quoted at 2,000 ticks beside the horizon. — ceded

• B28: Is "the learned subspaces look random" real, a gauge artifact, or overfitting? — Neither — and the sentence both horns aimed at is the thing that breaks. The gauge here is orthogonal, not GL (ADR-0032's co-isometry, the Frobenius band and the Euclidean disagreement norm each break the general-linear freedom B24 named), and both maps of a hop are held by the same relay cell, so O_v cancels inside every hop: composed ER and the principal angles are exact gauge invariants — measured on the orbit at 9.1e-07, energy 5.3e-09. So a learned sheaf here is identified up to O(k_v) x O(m_e) and everything this map records is invariant under it; B1, B11, B13/B20 all stand, and item 3's gauge search is provably empty. Overfitting is struck too, on a live world (the in-process test is vacuous — the body stalls and reset() does not restore the arm's pose, so std_max reads 7e-08 in every window; the trained maps are transplanted into a fresh body instead): the centred agreement between an edge's two ends is 0.0006 (reserve_p16) and 0.0098 (shipped) after 20k, and the four rungs — the exact worlds trained on, unseen worlds, both held-out slices — are indistinguishable. There is no in-sample fit to lose. But "indistinguishable from Haar" is false on the shipped arm — a cell's lanes end 2.05 SD more mutually aligned than Haar, climbing monotonically while composed ER falls 1.330 -> 1.001 — so what training finds is a cell's lanes agreeing to carry one direction, which is the collapse, and it accumulates only after the world goes quiet. B17's conclusion is better supported than before and its wording needs correcting.

• B27: Is the vision still sound, and what is the next step toward it? — The vision is sound and, in five of its six points, unbuilt — so the destination is replaced, the map widened to cover the training rule, and the next step is the objective. Point 3 is refuted as built and is the sharpest fact on the map: a random map of the learned maps' exact shape, mask and band reports a cell's richness at corr = +0.97; the learned maps read −0.05, lifting the poorest quartile 1.054 → 1.603 and pressing the richest 2.167 → 1.555 to a constant near 1.5 carrying no information about the cell (B19) — training does not compress the cell's voice, it levels it. Point 2 is unbuilt (B22: training moves none of it), point 4's criterion is right and its achievement absent (B21), point 5's wager is lost (B23), and point 6 survives only in the coherent-region form — the ticket asked for inference 3 to be broken and it could not be, but it survives as a price list: p trades composed rank against channel return one-for-one, so every unit of rank this map bought was paid for in the property the vision names as the requirement. The objective is indicted rather than the parameterisation (B25: the rule's own optimum is the collapse, and ADR-0032's band is a floor on each map, never on the representation). p held at 12, p = 16/24 off the live candidates, B15 unblocked with its rank claim demoted. Opens B30–B35.

• B32 (research): Path-independence and coherent structure in graphs and sheaves — Nothing says the approach is known to fail, but global flatness is the worthless maximum, and the guard B33 was built around does not close the known failure. Bodnar's Lemma 6 equality means a path-independent sheaf has its entire stalk as global sections — cohomologically the constant sheaf — while Dong et al.'s Theorem 5 requires holonomy non-trivial on the full stalk before a large harmonic space counts as genuine: so flatness attains max dim H⁰ and that maximum is empty. B27's local scoping survives this and is promoted from preference to hard constraint — the term must be unable to drift global. Cycle consistency is confirmed to be the same object (Nguyen et al., SGP 2011, optimising for maps "independent of the path chosen in the network"), and its documented end-to-end failure is CycleGAN steganography — the loop closes on a side-channel the task never reads, which a width floor does not close, so B33's floor answers one degeneracy and not the other. Holonomy has never been used as a training signal (Grover & Bourgerie 2026 only measure and ablate: "nonzero rotation is not sufficient"). The clean positive: prune-by-cycle-agreement is standard in structure-from-motion (Zach et al., CVPR 2010; "CCI") and absent from ML sparsification, so B34's criterion has a literature to inherit — and in SfM the relations are estimated independently of the criterion, which argues for a schedule over a joint objective. Binding caveat, unclosed: every quantitative result assumes O(d)/invertible maps, so on ADR-0032's rectangular partial isometries Lemma 6 is an analogy, not a theorem — which qualifies the dim H⁰ ≤ d bound inherited via B26. Verified in passing: both of #396's citations are sound at source. Branch research/b32-path-independence, docs/research/591-path-independence-coherent-structure.md.

• B31 (research): Abstraction as neighbourhood breadth rather than hierarchical depth — Breadth is real and published, but not instead of depth — and the strongest form of the proposal is the one that was pre-registered and failed. For it: Gollo et al. (2015) obtain a dynamical hierarchy from in-degree alone, with identical units, and Chaudhuri et al. (2015) name the dissociation in both directions (area 8m shallow but core-connected and slow; TEpd deep but peripheral and fast). Against it: Li & Wang (PNAS 2022) prove long-range connections delocalize eigenvectors and break the timescale hierarchy while the depth-aligned local-excitation gradient protects it, and Chaudhuri's lesions make both necessary and neither sufficient. Decisively, the one pre-registered empirical test (Lurie, Pappas & D'Esposito 2024) registered the hypothesis in two forms and the across-communities form — precisely "abstract concepts connect broad networks of disparate abstract concepts" — failed in both datasets, the authors concluding long timescales reflect topologically local rather than global integration. That is a third instrument landing on the same radius as ADR-0011's locality bound and B21's 2–3 hop conduction. And it vindicates B23 at source: Lurie et al. independently report that regions atop canonical hierarchies show some of the shortest timescales in cortex, so the fast apex is a published fact about real cortex and not a rig artefact — the imposed gradient was the wrong model, not a broken implementation. Learned variable-radius neighbourhoods do exist in graph learning (JK-Nets per-node; ADC continuous per-layer/per-channel; APPNP's teleport term as the locality mechanism) and nothing of the kind exists in sheaf learning. Proxy gap flagged: Gollo measures synchrony stability/persistence and never a per-node autocorrelation τ, so it may not be cited as degree predicts τ. Branch research/b31-neighbourhood-abstraction, docs/research/590-neighbourhood-abstraction.md.

• B30: Where does the drive attach, now that the apex is not privileged? — By conduction to the actuator, under a span floor — and abstract by attachment point is struck, not rewritten. The criterion is two legs stated separately, the outbound one binding, because world_loop hides that at 1 actuator against 262 sensory cells it mostly reports the outbound leg, and the dome confounds the two. Read structurally at construction (sheaf effective resistance), never on a trained surface — no drive, no action, no surface. The floor is a condition on the set (not clearable by one joint), which is what the apex was silently supplying. ADR-0009 is superseded, not amended — its title is the claim — and the blast radius is eight sites, not the three the ticket named. The rim keeps its locus. Attachment count ceded.

• B36 (research): Is perceptual error cleared by acting? Rao, Friston, and the sensory row — Yes, and more strongly than the objection put it — but the ticket's two named authors disagree, and the drive's own shape is absent from the corpus. For Friston action has no other job: "action must suppress sensory prediction errors", descending the same ε̃_s perception descends, and not only proprioceptive ones. Rao is the opposite: Rao & Ballard (1999) has no action variable at all, and APC trains its action networks by reinforcement learning. Two principled lines exist and neither is who-clears — precision (a continuous, learned, modality-shared dial, not a kind) and the reflex arc (anatomical, explicitly not computational). The write/read replacement is supported by the Markov blanket, but the same table defines sensory states as a mapping from action, and the partition is global rather than per-edge (against What must a hop reach? #155's second precondition is still open, and the units do not line up #181). Ask 4 is [ABSENT] structurally: every externally-written motivational object in the corpus is read on every step and defined over outcomes, never actions — the corpus's drive rides the sensory row, and a state nothing reads is not a blanket state by construction.

• B37: Does ADR-0003's taxonomy sort, and which row is the drive in? — It does not sort, and the drive is on the written side — so ADR-0009's motor edge half falls too, and nothing of its title sentence survives. Who-clears is retired: Friston has action discharging the same ε̃_s perception discharges, and spec/04 §388 — the one place the record claims to derive the motor-edge signature rather than stipulate it — is satisfied by the sensory row verbatim, since external writes are the tick's last word for every boundary cell. The replacement is ADR-0016's axis, but it could not be adopted as the ticket phrased it: that ADR's own consequences say the actuator is "read and written by the world" (the efference copy), so literal write/read puts it in the very both bucket the ban forbids. Repaired to authorship — who authors the value the graph must accept — which admits the efference copy as an echo of the cell's own command, leaves ADR-0025 standing (it was already using this axis unnamed), and answers B36's Table-1 and per-edge objections without importing the blanket. Stated as two axes (which seam × which direction), whose collapse into one row is ADR-0003's whole defect; the fourth cell — internal rim, read from outside — is empty and deliberately unnamed. The drive lands sensory-side on three independent grounds, including ADR-0009's own dark-room argument, which took Friston's prior horn and then tabulated the motor side in the same document. What forces action is irrevisability, not motor-ness: the drive's author never revises (ADR-0016's tick order is Da Costa's infinite precision), so a sensory edge has two exits and a drive edge one. ADR-0003 is amended, not superseded — its title holds on its merits and only the sort criterion inside it falls. The cost, one step past B30's: a drive is not action at all, but an unrevisable expectation the graph can only satisfy by acting. B30's Q9 scoping is corrected — the floor binds what is written from outside by an author that does not revise. Nine amendment sites, §388 and ADR-0025 new to the record; none written.

• B33: Can a representation floor and a local holonomy term coexist? — They coexist — and the premise fails twice over: the floor as written cannot be built, and the one that can earns nothing. Neither term has the other's collapse: the local holonomy term takes wide-cycle identification 0.9697 → 0.8591 and channel return 0.322 → 0.745 at unchanged sigma_max — so Chu et al.'s steganographic optimum does not appear — and reaches the same effect with a floor present (0.8622), replicated at seed 43. But an absolute variance floor is unreachable under ADR-0032: the band pins map singular values at median 0.302 and forbids buying variance with gain, so only a rotation is available and it cannot raise a variance whose scale is set by a stalk that barely fluctuates — live-lane emitted std is median 0.019 with 0.32% reaching the target. Restated on the participation ratio it is reachable and subsumes VICReg's decorrelation term, but then contributes exactly nothing once the holonomy term is present (2.48 vs 2.48 at seed 43). Two costs are unavoidable and unpriced: the floor needs state ADR-0031 forbids, and the term satisfies ADR-0011 only in its weak form. The bar was not read, deliberately — reserve_p12's world dies at tick ~125, not the 1,000–2,000 the map inherited, so every trained checkpoint is motionless and every separation between arms is post-stall. Rig question minted as B38.

• B38: What surface can this map take a dynamical reading on? — The surface was never the blocker, and the bar — read at last — FAILS both ways: conduction 0.433 rim→apex (short 2.31x), 0.133 apex→rim (short 7.5x), both inside The retention instrument drops the stalk relay: re-read the chart loop's rho on a driven rig #274's band. B33 withheld the reading because detectability is dynamical and the world was dead; the premise is false. benchmarks/detectability.py holds the world by construction — its own branch() says "Nothing is stepped: this is the hold" — because the paired fork requires both branches to receive identical world input, and world_loop(c) is enumerated from the mask. A moving world would break the measurement, not enable it. What the stall corrupts is the training underneath the bar — and a 150x contrast shows that training was not buying the bar anyway: 30,000 ticks move the per-edge bottleneck ratio 456x and 1,427x and move the conduction ratio not at all, because ADR-0026's bar is a ratio of times (τ̂_c / world_loop(c)) and training moves amplitudes. So the rule that trains transport does not act on the quantity this map's bar measures — minted as B39, and it cuts at B27's widening of the destination. The stall horizon is not a per-arm number and nothing about it is inheritable: across four arms x two seeds it spans 60–1450 ticks, varying 13x between seeds of one arm and a further 11x with the measurement window, so it belongs to a run-at-a-timescale; the record's 1,000–2,000 was the wrong mark (last flicker of numerical motion, not the window where the world moves, which is ≤250 ticks on six of eight cells). EVAL_TICKS and every other constant are retired in favour of B28's per-row motion stamp. arms.py is ported to Write #556's reserve mask: k_v = n - p, and the bound it supersedes (#562) #597's surface — the reserve arms are now src/ verbatim, the rig's allocator deleted rather than repaired, reserve_p12 proven identical to build_graph(DomeSpec()), all 37 T6 instruments importing — and the transplant route is adopted for readings that need a moving world, carrying sheaf.maps only. — ceded

• B34: What criterion carves a topology by sparsity? — A per-edge width allocation that counts rather than scores: m_e is the number of directions whose principal-angle cosine clears threshold on the short local cycles through e, floored at 1, capped by min of the two endpoints' warrants, rationed by Σ_e m_e ≤ B. Pruning is the m_e = 0 case, not a second mechanism, and Grilling: four failures named in session transcripts and never captured #311's anti-hub objection becomes arithmetic. One criterion, not two — the same holonomy as B33's term, read as a per-direction spectrum where the term is a scalar residual. The width-1 degenerate optimum dissolves under a count (a width-1 edge scores the minimum), so no representation floor is needed — which is as well, since B33 established there is none to have and B32 that a width floor would not close the side-channel anyway. The bootstrap is deliberately undecided, on the user's ruling that there is no preference to exercise: routes go to B40. Two record corrections: B12 killed #320's second rejection ground (privacy is reserved directly, so density no longer starves it), and its surviving one is about the node-stalk dimension mask, not Edge.m. — the criterion's form and the endpoint rule ceded

• B40 (prototype): Which training route buys earned cycle closure — and does the flat bundle end the criterion? — No route wins because the count never leaves the floor, and the flat bundle does not end B34 — it is exactly flat, and the privacy reserve is what breaks it. On the trained surface the raw count is 0 on all 194 wide edges at every checkpoint at threshold 0.9 and 0.95; at 0.8, over 500 ticks, at most 12 edges gain one direction and none ever gains a second — so every route allocates m_e = 1 everywhere, which is B34's own §4 tree with the floor in place rather than absent. control, split and phased read identification 0.978 / 0.985 / 0.979 at 150: indistinguishable, and not because they are equally good. Arm 2's terminator (the count's own drift < 0.05, chosen because B29 forbids one on identification) fires at tick 50 with drift exactly 0.0 — nothing to wait for. The named risk does not fire: enumerated rather than read off B29's basis there are 190 local cycles, median 3 per edge, 104 edges with ≥2 — but 90 of 194 wide edges are true bridges (Tarjan; 0 stranded by radius, so ADR-0011 is exonerated), so on 46% the criterion counts over an empty set whatever the route does. Three of its four clauses are inert — allocated exceeds raw by exactly 90 every time and raw max = alloc max throughout, so cap and ration never clip; only the floor acts, and the floor leaks by construction: floored-lane gain 1/√3 against kept 1/√3.75, ratio √1.25 = 1.118 unmoved across seeds and checkpoints, because the band spreads norm over m directions and at m = 1 it all sits on one. Arm 4 falsified the ticket's prediction for it — the count still spreads (std 1.3, 7 distinct) — and against the scale-matched haar null (independent isometries: chance, sigma_max 1.1e-07) the advantage is flatness, not isometry. Unprojected the construction reads identification 0.0000, channel_return 1.0000, sigma_max 1.000 at m_e < n; the dimension mask takes it to 0.6123 and ADR-0032's band repairs it to 0.0386 at three orders of amplitude. It is 0.62× the parameters of the per-edge scheme and strictly more local. sigma_max is an amplitude and says nothing about ADR-0026's ratio of times; B39 is untouched. — the surrogate for a multi-cycle count, the threshold, and the 500-tick horizon ceded

• B35: Variable-radius neighbourhoods, and relays between regions — The radius does not grow — the width does, and abstraction is neither: it is redefined to community membership, how many distinct communities a cell belongs to. A community is a connected set of cells over which one direction stays consistent; a cell counts its own as the near-orthogonal direction-clusters among its incident edges. Strict Sum_e m_e is rejected — B40 pins it at the floor, so it reduces to plain deg(v). Radius is fixed at the 2-hop cycle neighbourhood on three converging instruments (B21's 2–3 hops, ADR-0011's weak form, and B31's pre-registered failure of breadth across disparate regions in Lurie et al.), so arm 1 was always B40's carve. §3's ADR-0011 lean is struck: ADR-0011 is gradient locality and no topology can violate it. The timescale objection is retired — the hierarchy is cellular (ADR-0005's bias selection, ADR-0028's per-cell lambda(K); built rather than found) and Does timescale become the spectrum of K? #143/Amend #230's diagnosis: the timescale gradient was never placed in any run #276/B23 left none to break, so Li & Wang has no object here; residue is an A_v re-read, since tau is measured off rho(K.(J_chart + J_stalk.A_v.D)). This answers Termination-driven abstract steps: ADR-0005's named escape hatch #322. Relays survive on a justification new to this map: they act on world_loop(c), the half of ADR-0026's bar B39 found training cannot reach — apex 15–16 to ~5–8 carries B38's 0.433 toward 1 with no training — which revives Relay cells: a long-distance node laid over the graph #312 on its stated condition with loop_length.py superseding its effective-resistance instrument. Adoption is a pre-registered conjunction, all three or nothing: world_loop falls, tau holds, and ADR-0021's bottleneck rises from 8.35e-10 — the anti-Goodhart clause, since loop length cannot touch an amplitude. Relay count is priced by Sum_e m_e <= B, Grilling: four failures named in session transcripts and never captured #311's anti-hub self-enforcing, B20's joint-span collapse the guarded end; a relay is budget-bearing and prediction-free. The wedge forces long-range agreement into the core, where slow state already lives #330's decided by nothing is answered — the warrant count sorts integrators from holders. Three CONTEXT.md sites named for the writing ticket (Sensorimotor rim, Level, Internal rim) plus a new Community entry, and coherent structure retired as misdescriptive (the object is architectural, and coherent is on Collectively's _Avoid_ list). Corrected after B40 landed concurrently: a relay edge is a bridge, and 90 of 194 wide edges already are, so a tree-shaped relay network pins every relay edge at the probe floor forever — the layout must carry two disjoint relay paths between any pair of regions.

• B39: ADR-0026's bar is a ratio of times — does the training rule act on it at all? — The ticket's premise was broken and correcting it is the answer: ADR-0026 splits, and the dome's demotion kills its predicate, not its quantity. τ̂_c / world_loop(c) appeals to no level — the ADR says so in terms ("|loop(c)| = 2 · level is a fact about this graph's wiring and not a licence to index by level"), What does ADR-0026's divisor become, now that the two loops differ at every cell? #383 replaced the depth-graded divisor for exactly that reason, and loop_length.world_loops is BFS from SENSORIMOTOR cells with by_level never called — so the divisor computes unchanged on a dense graph carved to sparsity. The quantifiers are pure dome and have been in breach of this map's no-level rule since B27: CONTEXT.md's inbound per-stratum count, its L1 outbound universal, and detectability.py's rim→apex / apex→rim enumeration are struck; ADR-0026 is amended, not superseded, and what it is booked for changes. So B38's §4 absolutes (0.433, 0.133) are readings of a retired predicate and may not be quoted — but its contrast is within-instrument and survives whole. On the surviving half, B38's arithmetic is stronger and narrower than it claimed: tau_hat reads peak-to-1/e, so a uniform rescale cancels exactly — the invariance needs neither the seed, the 24 trials nor Is the conduction ratio readable in the precision the architecture runs in? #224's gate — but it is conditional, because the returning contribution and the locally-decaying one are different terms whose ratio bends the shape, and B38's two arms sat 8–12 orders below unity where the return could bend nothing. So training is not barred from the numerator, and two levers exist that no candidate points at: K is already trained every tick at η_K = c·η with ADR-0015 keeping ρ(K) as "what timescale wants" and ADR-0026 already recording λ = 0.99 → τ ≈ 99.5 in-band — the lever is present and unpressured, since one-step error cannot prefer retention — and return gain, where B42's flat bundle reads channel_return 1.0000. B27's widening stands and is sharpened, not indicted: the rule can reach the bar, through retention or return gain; the hole is in the candidate list, since B33's floor and holonomy term, B16's edge agreement, B29's readings and B34/B41's criterion are every one a statement about the operator's geometry. Sensorimotor dependence attaches to ADR-0021, not ADR-0026 (the user's own answer) — dependence is content evaluated in context, which is detectability; ADR-0026 reduces to its necessary condition, preserving both ADRs' stated relationship. B27's Q2 answer text is nowhere on the tracker, only its provenance line, so the requirement binds the destination and has never been written down — B43. And carving raises the divisor: pruning can only lengthen shortest paths, so the map's own architecture spends against its own bar with no line item. Graduated B43 (what the dependence measure is) and B44 (does an O(1) return bend τ̂, does ρ(K) move — blocked by B42). Scope fence moved from redefining ADR-0026's bar to re-deriving ADR-0026's quantity.

• B43 (prototype): Do relays buy ADR-0026's bar without gaming it, and which width reading discriminates? — they buy it; the conjunction cannot show they bought it honestly. Clause 1 arrives free and on target (apex world_loop 14 → 5 at 16 relay sites, inside the predicted 5–8; cheapest is 16 edges at m = 1, none over budget). Clause 3 passes by nine orders — and so does an unaimed random relay set, by seven, because ADR-0021's bottleneck is a min over a path's edges and ADR-0026's divisor is a path length, so the anti-Goodhart clause is not independent of clause 1. Clause 2 fails on a seed: τ̂ falls (8 → 6; 9 → 5) and the ratio rises only because the divisor did. Two layout findings: B40's bridge constraint cannot fire (the dome is connected, so a relay is a chord — 0 relay bridges at every layout; what pins a relay is having no short local cycle), and a relay must anchor on both sides of ADR-0016's ban or the untouched leg bounds the min. Neither width reading discriminates: under B34's allocation Σ_e m_e is exactly deg(v) at 150/150 (B40's null confirmed) and community membership is also exactly degree at 150/150 at all three of B40's thresholds, moved by neither relays nor 500 ticks. Now B45 (#611).

• B41: What carves an acyclic edge, and what replaces the leaking floor? — The floor was two mechanisms under one name, and both are replaced. The criterion needs a witness — a short local cycle through the edge, which is all ADR-0011 lets a cell see — and an unwitnessed edge is now exempt: no witness, no action, it holds the width it last earned. Vacuous-full and a second use-based criterion were both rejected as self-rewarding (prune inside a cycle, the neighbours lose their witness and widen). A pruned edge goes to zero carried directions, with its warrant read without anything reaching the receiving stalk; the floor is dropped, and the two implementations of that requirement — a dormant out-of-lane map, or the user's gating — go to B46, because gating's whole advantage is killing a counterfactual that the flat bundle may already have removed. The count is normalised to a rate (a direction is warranted if it closes on a fraction q of the local cycles), at the price of q and of a kept direction being independent against a majority rather than against every route; cap and ration both stay, marked inert-with-binding-condition. The 46% bridge figure is a fact about the hand-laid dome, not about carving, whose target is a dense start where that class begins empty. — partly ceded

• B42: Is the flat bundle the transport architecture, and does the privacy reserve give? — No to the architecture, no to the reserve giving, and the reserve mask should stop being fixed at construction. B40's obstacle was frame placement, not p: the reserve mask is flat, so a frame built inside the permitted window telescopes exactly through the mask and ADR-0032's band — identification 0.0000, channel_return 1.0000, at the same sigma_max the band already charged. But the exactness is the collapse: a hop is S_out S_inᵀ, so closure holds only at audience differentiation 0.0000 (one notch of difference costs identification 0.0000→0.6075; three costs the channel), exposure falls 20→14.8 of 32, and it is worst locally — the shortest cycles run through one cell. Refused on the user's ground, not the dimension count: without varying degrees of abstraction the topology stops doing work, and what is left is a fancy mixture of experts. Retained as this map's null — it is the only construction on record that defeats A1: Is ADR-0004's k < n what has to give? #533's collapse at any hop count and the only one that earns any shared invariant (88 above control against the trained surface's 0). Two findings that are not about it: B40's arm-4 falsifier fired and was scored on a statistic blind to it (B47), and the trained architecture's entire H⁰ is the privacy reserve (B48). Also opened B49, ranked first by the user.

• B49: Is expressiveness-per-hop conserved against reach, or is there a third move? — Not conserved, because the trade was never one quantity. It welded two instruments on two objects: B21's 20–50x is a dynamical impulse read on node stalks through the tick, while A1: Is ADR-0004's k < n what has to give? #533's cosines are the transport operator, which B17 showed never touches the stalks — and #537 measured the leading cosine at 0.568 rising to 0.79–0.81, not 0.02–0.05. What is conserved is the budget Σ_e m_e ≤ n − 1, which is allocated rather than traded, and n reaches (ER 2.047 at n ≈ 128, B4's closed form agreeing at 2.195) against a premise A1: Is ADR-0004's k < n what has to give? #533 §4 and B2: Which lever gives — c, the privacy invariant, or degree? #540 both recorded as settled. The destination stands unrestated. A candidate third move — anisotropy, r directions per lane pair at gain 1 with a different block per neighbour — is argued and not adopted; it goes to B50 as a reading of the existing surface before anything is scored.

• B44: Does an O(1) return bend tau-hat, and does rho(K) move under the current objective? — No, and yes — the wrong way. The pre-registered falsifier fired: across channel_return 0.19 → 1.00 and five orders of bottleneck, paired per-cell τ̂ shifted by a median of −1/0/0/0 against control's own trial-to-trial null of |Δ| median 5.0, q90 21.0 — same verdict on Is the conduction ratio readable in the precision the architecture runs in? #224's gate — so the return is not what sets the decay and B39's §2 is wrong, its arithmetic intact and its conditional not. A 2×2 of {exact, chance} return × {unit, banded} gain on one trained surface discriminates neither axis. ρ(K) is not flat — 149 of 150 cells move >1e-3 off a uniform 1.000000 — but σ(used) is pinned at the band's upper face, so ρ(used) = ρ(K)/σ(K) and retention falls: τ ∞ → 52.9. The lever is present and pressured away from retention. — ceded

• B48: The room agrees on nothing it was not forced to — what would make it agree? — earned is a symptom, and the answer is not in the objective at all. Retired as a candidate bar on composed rank's terms, for two independent reasons: it reads the transport operator (B17), and earned > generic is an exact rank coincidence — measure zero, reachable only by objectives whose optimum is collapsed lanes, so constructible but never learnable. A second block stands regardless: rank statistics are properties of the construction-fixed mask, and B22 measured every rank-derived number invariant exactly over 20k ticks. The title question therefore resolves upstream to the traffic's effective rank — the node stalk reads ER 1.002, so the rule has evidence about one direction and makes exactly one direction coherent (B16's untried lever) — gated on B42's learned, gated mask. 88 is this map's null near its own ceiling, not a score to beat: flatness attains the maximum of dim H⁰ and buys it at audience differentiation 0.0000. Holonomy is suspended, not struck, on the user's amendment. Found in passing: CONTEXT.md defines H⁰ = private features, which holds iff earned = 0, so the vocabulary forecloses the question — B55. Opened B52, B53, B54 and B55.

• B54: Does a graded holonomy term live at nonzero audience differentiation? — Yes, and it was already measured — in B42's own raw file, in a column its published table omitted. 605-stagger-seed42.json carries channel_return 1.0000 at sigma_max 1.000 at audience differentiation 0.3000 (stagger 1) and 0.3333 (stagger 2). So B42's "there is no setting that gives both" is true of identification and false of channel_return, and the escape is a sub-bundle distinction, not a magnitude one — the ticket's own framing (small but nonzero) was wrong and the honest counter it named beats it on that axis. Full-stalk exactness costs all differentiation; exactness on the direction the loop actually carries costs none measured. This is B32's Dong et al. Theorem 5 running with the design — holonomy non-trivial on the full stalk — rather than against it. The suspension lifts narrowly: B33's full-stalk term stays suspended (its arm moved channel_return 0.322 → 0.745 while identification barely moved — most of what it bought was on the channel, and it was not aimed there); what re-enters is two-sided — drive channel_return to 1, hold identification away from 0. That second clause discharges B42's standing constraint by making collapsed lanes the term's worst point rather than a scoping rule, and is the measured anti-global guard (both wide and full bases, every reading). The side-channel is narrowed, not closed — B32's "ADR-0032's band limits the capacity" defence is refused rather than tested, and closure is B19's corr(state, emitted) under joint report. B32's invertibility caveat stays open and no longer load-bearing. B33's representation floor does not ship and is not settled — the channel form leaves m−1 directions unconstrained and nothing watches them, and identification may not stand in for a floor on the emitted representation (B49). Two caveats the ruling carries rather than buries: every number is a construction sweep, so under B49 none of it transfers to a trained surface; and stagger 6 (differentiation 0.5444 at perfect channel return and unit gain) is unexplained and unrelied-upon. Amended in place by B50 (#618), which landed mid-grilling and flagged this ticket by name: the forced intersection f = max(0, m_in + m_out − k_v) is an exactly-flat per-hop sub-bundle (identity exact at 395/395 hops, f ≈ 2.086 ≈ 85% of r@0.95), so a holonomy term reads through f for free and must net it out — clause 1 may otherwise be inert. f is stagger-invariant and so cannot explain the sweep's variation, and B50 independently confirms the sub-bundle reading; §1 goes from a measured yes to a measured yes with a named confound. Netting out f is a pass condition on B56, not a diagnostic. Opened B56 (#628). — Q5 ceded (that the term escapes B44: Does an O(1) return bend tau-hat, and does rho(K) move under the current objective? #610's adversary constraint), Q8 the user's own answer (run both arms, leaning hinge).

• B50 (prototype): Are the per-hop cosine spectra anisotropic, or interior? — The corner is occupied, and dimension counting put every direction there. Branch (C) fired and (B)'s first half fired without its second: corner mass >= 0.95 is 0.3553 at construction rising to 0.4172 / 0.4337 (baseline / winner) at 20k, while <= 0.05 never fills (0.011–0.020). But the whole of it is forced: two subspaces of dimensions m_in, m_out in one k_v mask must intersect in f = max(0, m_in + m_out - k_v) directions at cosine exactly 1, and the identity #{cos ~ 1} == f holds at 395 of 395 hops on three seeds, exactly. f averages 2.086 against a measured r@0.95 of 2.456 — 85% of r, 30.18% of every cosine — and is invariant under seed and tick. The per-hop shape is a flat top of exactly height f then an interior ramp; where f = 0 (two-thirds of hops) it is a pure interior ramp. So #616 §3's load-bearing "r ~ 1 is not what the geometry forces, it is what the objective buys" fails in both halves: geometry forces the bulk, and training buys more corner (r@0.95 2.456 → 2.997) while audience differentiation falls 0.5307 → 0.4540 — isotropy of the shared part, not concentration. r ~ 1 is a median only (mean 2.46–3.00, max 20). The third move is not an unvisited region: since #548, f already is the per-hop, route-specific, exactly-flat sub-bundle §3 asked for, so r is not a new knob — it is allocate_lane_widths read in a different basis, and the lever is one this map owns. Nothing scored, no candidate opened, per scope. Trajectory flagged to B54 (#624) with the caution that a holonomy term reads through f's directions for free and must net them out. And the ticket's inherited premise was stale — B1: Read the principal angles, and whether c alone moves composed rank #537's own instrument reads composed ER at construction 1.412 median / 2.869 max today against the filed 1.025 / 1.989, because B8: Write #540's ruling: per-edge m_e, lateral lanes at 1, and the invariant doubled #548 (lanes allocated per edge) and #562 (k_v = n - p = 20 everywhere) both post-date B1: Read the principal angles, and whether c alone moves composed rank #537's data; filed as row 8 on the surprise ledger (#520), amending its row 6, and not ruled here. t0.surface() had been dead on main since B8: Write #540's ruling: per-edge m_e, lateral lanes at 1, and the invariant doubled #548 and is repaired. — partly ceded

• B52: What replaces earned H⁰ — a graded agreement statistic on node stalks — The traffic's own agreement spectrum: a graded, traffic-weighted soft count of the directions the room agrees about — and the first quantity on this map that the construction mask does not clamp. Built on an instrument already on main (EdgeReading.energy, ‖F_u x_u − F_v x_v‖², and the δ WholeGraphReading already assembles): for each eigendirection u_i of the traffic covariance C with weight w_i, a normalised disagreement level q_i = u_iᵀLu_i / u_iᵀDu_i, an agreement profile A(θ) = Σ_{q_i ≤ θ} w_i, and a soft count N(θ) in ADR-0010's own participation-ratio form. Reported at three θ (B40's precedent — no constant invented), profile primary, headline never travelling alone (B49). A count and not an energy, because an energy ratio is maximised by the null and is the scalar B49 struck. Not earned with a tolerance bolted on: earned is a property of L alone, this of the pair (C, L) — and B17's correction is carried by a test, not a label: redraw the traffic at frozen maps and the number must move, pre-registered as an acceptance check earned provably fails. The null is a matched-generic one — same n, m_e, mask and C, phrasebooks redrawn — keeping earned's one good property (excess over generic) and netting out what dimension counting forces without importing B50's f, which B49 forbids anyway. On item 4, both halves: not clamped by the mask — confirmed against main at the user's ask (graph.py:666 builds permitted = min(n, Σ_e m_e) from widths alone; restriction.py:388's project() re-applies it first in its order; B42's learned, gated mask is a ruling and is not built) — but ceilinged at 1.002 by the traffic's own effective rank (B16), since N(θ) ≤ ER(C) by construction. A ceiling the architecture can lift, not a third clamp — which makes B53 (#623) the ticket that decides whether this instrument can ever read above one. And because permitted = min(n, Σ_e m_e), making the mask learned just is making the width allocation learned — B53's traffic-rank lever and B42's learned mask press one allocation from two ends, B50's “r is not a new knob” reached from the other side. The ticket's own item 3 is amended, not satisfied: the statistic stays clean and the flat bundle is failed by B48's joint rule, not by the statistic alone — fusing differentiation into one number is B49's struck move. Carried as a prediction rather than a guarantee: a flat room says one shared thing, so it agrees about one thing, and 88 may be a phrasebook fact with no page-side counterpart. No threshold is set, deliberately. Opened B57 (#629); B53 unblocks on specification rather than on a score. — Q4 and Q5 ceded

• B56 (prototype): Does the two-sided channel-return holonomy term hold agreement and differentiation up together? — Clause 1 is a real lever and clause 2 does nothing, so the term is one-sided in practice. channel_return 0.2006 → 0.7899 trained, both bases, at zero exposure cost; the hinge is bit-identical to clause 1 alone because GAMMA = 0.6075 was anchored on a construction sweep and lies below the trained surface's whole operating range, and the unbounded clause pushes identification past chance without moving differentiation. The named risk does not fire — 7% of differentiation for a 3.9× rise is different in kind from the full-stalk form's provable 0.0000 — but B42's discharge is un-discharged and becomes B59 (#631). The ceded B54 Q5 survives its first measurement: rho(used) and tau move less than baseline's own drift and not consistently in sign. Free finding, graduated to B58 (#630): stagger 6 is not an artifact and not about stagger 6 — the exact set {0,1,2,6,7,10,13,14,18,19} is seed-invariant and arithmetic in k_v = n − p, giving a priced curve from differentiation ceiling 0.8036 at p = 8 to 0.6061 at p = 16. Construction only.

• B53: Can the traffic's effective rank be raised, and does the learned mask carry it? — Yes, and the lever is the rule's input, not the mask — and the 1.002 ceiling is a reading taken about zero. TrafficRecorder accumulates np.outer(h, h), the second moment about zero, and B52 inherited it as C = (1/T) Σ_t x_t x_tᵀ under the name traffic covariance. The stalk is not centred there — encode is affine → ReLU → affine (body.py:392) and decode_output_bias exists because "any nonzero mean in its stalk is permanently unreachable error" — so a standing baseline puts a rank-one μμᵀ term in the reading, and the rule accumulates along it too (∂L/∂F_v = (∂L/∂o)·x_vᵀ takes the raw x_v). Instrument and rule share one omission. Decision: the transport rule learns from the deviation from a per-cell running mean — 32 numbers per cell, strictly cell-local, Permitted global signals still exactly one, no additive term on ΔK, no carve, no exposure bought, reversible. The price is ADR-0031's statelessness, which was a consequence of deleting the anneal and is defended by no ADR as a value; that note joins the ADR-writing hand-off. The mask is necessary and not the carrier, correcting this ticket's own framing and refining B52's line above: it fixes the room, and B16 measured the room a correlate — corr(traffic_er, cos_leading) −0.45 at fixed k_v, and identical traffic (1.006/1.006) and alignment across two arms where one eroded and one did not — while TrafficRecorder reads its 1.002 inside the mask already and B19 has 80% exposed and injective at 150/150. Opening the mask offers more room to a traffic not using the room it has. No clamp holds what this aims at: the mask clamps entries, the band clamps singular values, and the lever moves the U-rotations — angles.py's named free residue, flat cosines at ~3.0 while composed ER halved. Whitening (ΔF ∝ g·(C⁻¹x_v)ᵀ, ~1024 numbers per cell) is named as successor, not taken: B60 (#633), blocked on B57 (#629)'s centred-versus-uncentered reading, which is advised there and on B52: What replaces earned H⁰ — a graded agreement statistic on node stalks #622 and costs no new run. Under B49's rule this crosses from stalks to the operator only through the gradient's own factorisation, and carries a mechanism and no number.

• B59: What stops a channel-return holonomy term's optimum being collapsed lanes? — Nothing in the objective does, and that is the answer rather than a failure to find one: the guard is a parameterisation, not a term. Clause 1's optimum is a ten-member degenerate family it cannot rank — B56's own stagger table scores channel_return 1.0000 identically at differentiation 0.0000 (stagger 0, B48's null) and 0.7321 (stagger 19) — so B42's collapse is one point of the optimum, B54 §1's sub-bundle escape stated exactly, and worth less than it looked: an optimum you reach is not the same object as an optimum that exists. The clamp-as-guard answer was checked and killed: distinctness reads the learned row subspaces, so B56 §3.1's immobile k_v = 20.0 is the window collapse lives in, not a barrier — a third instance of the clamp constraint, this time killing a candidate guard before it was built. So the guard selects inside the optimum, which is ADR-0015's own template (parameterisation rather than a penalty) and lands on B58 (#630)'s staggered frame; a second penalty term is refused, being what clause 2 was. New standing constraint — the differentiation exchange rate: differentiation given up per unit channel_return gained, as excess over a matched baseline arm at the same rung and seed, reported at adjacent rung pairs and not end-to-end, passing only if flat or falling. An absolute floor is refused (baseline drifts 0.3683 → 0.3354 unaided, so most of the fall belongs to no term). Unaided clause 1 is refused on it — cumulative 0.0000 → 0.0221 → 0.0496, segment-wise 0.0000 → 0.0247 → 0.0755 — and stays live only in composition with a differentiation-selecting initialisation. B42's constraint is un-discharged in fact, a second unmeasured discharge being refused after B54's was measured and failed: shape here, evidence owed by B58 (prototype): Is the staggered frame the transport architecture, and what does the p-versus-differentiation curve cost? #630, falsifier pre-registered there (relax back toward stagger 0 and the suspension returns). The no-guard outcome does not fire — the optimum is the flat bundle is false as written. Rides along: a differentiation reading taken while k_v moves unreported is void, dormant on main. No new tickets and no fog graduated. ADR cost named and not written: ADR-0015 (its template promoted from a dense-K fallback trigger to this map's guard template), and ADR-0004/ADR-0032 territory if the staggered frame wins. Amended same-day on B58 (#630)'s advisory, which crossed it by a minute: the falsifier is replaced by a stricter one (differentiation settles, drift decaying), the exchange rate is scoped to term-side candidates with a drift form added for constructions, the void clause is moved from rank to participation, and — Q7's own consequence — clause 1 is inert on a staggered start, so the composition Q7 kept it alive for is the empty one. Not struck; whoever proposes it next owes a start on which it is not inert. The answer — the guard is a construction, not a term — is what B58 (prototype): Is the staggered frame the transport architecture, and what does the p-versus-differentiation curve cost? #630 confirms. — Q3 and Q7 ceded, and both amended by the agent on B58 (prototype): Is the staggered frame the transport architecture, and what does the p-versus-differentiation curve cost? #630's evidence, which the user has not seen

• B58 (prototype): Is the staggered frame the transport architecture, and what does the p-versus-differentiation curve cost? — Yes, and it is the first arm on this map to pass B48's joint rule at a live rung — with no objective term at all. A staggered initialisation on B56's own rig (only the initialisation patched) reads channel_return 0.9995 at audience differentiation 0.6310 and k_v participation 14.9 at rung 100, against B56 baseline's 0.2571 / 0.3585 / 9.1 — all three columns up, and exposure bought rather than spent (participation 13.6 / 14.2 at 2,000 against random init's 8.7 and the flat bundle's 6.9). The named risk does not fire: s0 runs 0.0000 → 0.0803 while s19 runs 0.7321 → 0.5317. And clause 1 is inert on a staggered start (+0.0001 channel_return, +0.0034 differentiation), so B50's saturation confound arrives on a trained surface where B56 §5 had netted it out. The exact stagger family is derived, not swept — the per-cell frame cancels exactly out of F_out · F_inᵀ, every hop is a partial permutation matrix and sigma_max is 1 or 0 with nothing between — reproducing B56's family on three widths and three seeds with no torch (exactness 20/20 against B56's measured sweep). Both prices on p point to 8: this ceiling saturates at 0.8036 there and B44 (#608)'s graded community band exists there alone; B44: What ambient p does the architecture want, now that community structure is what it buys? #608 still owns the decision. ADR cost: ADR-0010 primary (the stagger sets the arrangement c caps, which is the form that ADR asks for, and reaches #439), ADR-0032 one recorded sentence, ADR-0004 untouched. The decay has no measured floor — still falling ~0.035/1,000 ticks at 2,000 — which is B61 (#634). — ceded

• B57 (prototype): First reading of the graded agreement instrument — The instrument passes its acceptance check decisively, reads N ≈ 1, and the 1 is the standing mean. Item 1 does not fire: a traffic scramble at frozen maps moves N(0.25) 1.0000 → 0.0000 and q̄ 0.1796 → 0.9811 on every row of every arm in both forms, so the statistic is stalk-side by B17's own test and earned provably cannot follow it. δ_P is held against diagnostics.whole_graph's before anything is read (rank 3000, dim H⁰ 1800 of 4800, every arm). The window is T = 1,000 — T0/run.py's own, defended not asserted: traffic ER 2.7303 / 2.7564 / 2.7656 at T = 250 / 500 / 1000. It moves, and it is the map's first quantity that does: N(0.25) goes 0 → 1.000 between 500 and 1,000 taught ticks on all three arms, q̄ 0.9410 → 0.1796, so B22's clamp does not reach it exactly as B52 §4 argued. B53's advisory is discharged and its fork is neither branch: read both ways off the same window, uncentered the count is 1 and centred it is 0, on every arm at every checkpoint — the one thing the room agrees about is the standing mean, and the variety riding on it disagrees at the generic point. There is centred rank at construction that is not there at the horizon — 2.766 → 1.0045 uncentered and 24.912 → 1.611 centred on the baseline, 27.270 → 9.318 on the winner — so the rank is spent while the rule runs; but B57 could not attribute it for want of a rules-off arm, and amended itself on a post-resolution check: centred traffic ER grows monotonically with the window (13.014 / 18.465 / 24.912 at T = 250 / 500 / 1000) while the uncentered form is stable to the fourth decimal, so the centred column reports a direction and not a magnitude and B53's fork is answered only in that weak form. The count is untouched by this — centred N(θ) is 0.0000 at every θ at every window. B52 §5 is confirmed in its own words: the flat bundle at construction reads N(θ) 0.0000 at every θ at audience differentiation 0.0000 against its earned 88 — the page-side count is weaker than the prediction — while the trained flat arm reaches N(0.25) = 1.0000 like every other arm at differentiation risen to 0.2338, so training walks it off flatness and only the construction row is the flat bundle. The branch table's excess ≈ 0 clause fails: N_gen(θ) = 0.0000 at all 18 profile levels, three arms, nine checkpoints, both forms, three redraws — generic phrasebooks on the same traffic agree about nothing, so the excess is the whole count rather than the bookkeeping residue B52 expected. Filed as row 8 on the surprise ledger (#520) with the two readings it cannot separate, one of which makes the count a re-description of traffic rank. No threshold set, no candidate scored, one seed. Opens B62 (#635); B60 (#633) unblocks on this closing. — ceded

• B43: What is the sensorimotor dependence measure, as ADR-0021's re-indexing? — It is I(P; Δ): traditional mutual information between a content-varying, fixed-norm sensory perturbation and the paired-counterfactual response at the world-read boundary, with the situation marginalised — and it carries no path quantifier. ADR-0021 is amended, not superseded: its fork, its A₀ = 1 convention and its what fails is an edge language survive; the statistic, the terminus and the reference re-index, and the bottleneck ratio is kept and demoted because the replacement computes with it. The bar is I > 0 as an excess over a matched scramble null, per stratum as a profile, against three references and no invented constant — the ceiling log k, the flat bundle, and the untrained surface, added on B58 (#630)'s finding that a construction may supply the gain free. ADR-0003 is upheld rather than dented — the sides are world-written and world-read boundary cells, an edge property and ADR-0003's own location of the opposition, so sensory cells and action cells are refused as vocabulary (the user's recall located this; docs/research/026-action-boundary-citations.md carries Friston et al. 2010 on the primary text). Baudot & Bennequin is severed as a confounder, not a constraint, and a record-wide traditional / cohomological declaration standard graduates with it. Opened B63 (#637) and B64 (#638).

• B64 (task): Declare information-theoretic terms traditional or cohomological — Written as a CONTEXT.md term of its own, Information term, and the record's hand count is struck. Every information-theoretic term — H⁰, H¹, entropy, mutual information — declares itself traditional or cohomological, and a cohomological use names its site: this project's cellular sheaf on the graph, or Baudot & Bennequin's poset of partitions, with no functor and no comparison map between them. Placed immediately before Sheaf cohomology so the rule meets the reader before the terms it governs; a line inside that entry was refused because it scopes the standard to one of its two sites, which is the failure being fixed, and promoting docs/research/015's firewall section was refused because a citation pass records what was read and does not bind — the user's own answer on B43 was a standing standard, and CONTEXT.md is where standing vocabulary lives. The declaration may be inline or standing, which is what makes at each use satisfiable without the record-wide survey the ticket excludes: the two existing H¹ firewall sentences are kept rather than rewritten and named as the standing declaration for the sheaf side, so a bare H⁰ in a sheaf-side document is declared already and bare H⁰/H¹ are deliberately not banned. What does not survive is the counting — Free abelian's "this is the second H¹ sentence in the record" is struck, because the guard now reaches entropy and mutual information and a count over that class is not maintainable by hand. docs/research/015-information-cohomology.md §3 gains the forward pointer its own say which is meant rule earns, with the difference stated: the ancestor reached H¹ alone and only when both appeared together, which is exactly why nothing guarded B43's mutual information; §3 stays the evidence, the standard becomes the rule. Avoid gains sit on the new entry — bare mutual information, bare entropy, topological as the qualifier — and Sheaf cohomology's list is unchanged, since duplicating them there would re-scope them to the sheaf side. One site the writing passed is restated in the standard's words (benchmarks/holonomy_read.py's Boundaries docstring); no sweep was run and none is claimed. One word still stands open to overrule, unchanged from B43: the user's pair was traditional / topological, and cohomological is the session's substitution on Sheaf cohomology's existing Avoid line. Documentation only, nothing behavioural, no test reads the edited text; holonomy_read.py parses and ruff is clean. Edits on PR #640, not yet on main. — ceded (all four placement calls; the standard itself is the user's own answer on B43, written as decided)

• B63 (prototype): The sensorimotor dependence instrument, and its first reading — Built, and the first reading is taken. The estimator is a recovery problem, not a density one: a leave-one-out decoder plus the plug-in MI of its confusion table is a data-processing lower bound on I(P; Δ), so bias runs the safe way, and a matched scramble null runs the identical pipeline so whatever bias it carries is in the null too. k = 8 over each stratum's product space (cells × stalk), labels nested for a free k-ladder; 24 situations off one shared quiet fork, on a ladder because the sweep is the noise model. The conditioned form is verified vacuous rather than estimated — a re-run Δ is bit-identical, max|d| = 0.0, which is also the measurement behind #641's price the fork. Verdict: passes on trained, fails on untrained, passes on the flat bundle — see the Notes entry. #224's gate priced on one stratum: the patch response at the terminus clears eps_f32·‖state‖ on 0 of 192 trials on every arm, and training drives it 26× below construction and 16,000× below the flat bundle while the MI rises — the measure is invariant to an amplitude collapse the shipped runtime cannot represent, and EPS_F32's register row says precision is not a knob anyone may turn to fix it. Presence/absence collapses into that gate (the pairing makes the unperturbed Δ exactly zero) and is reported there instead. The per-edge lane profile runs: no extra trials and 0.1 min per stratum, because the balanced design makes the LOO centroid a closed form that vectorises across all 682 edges — 655/682 significant on patch, lane numbers, none comparable with the endpoint reading. The re-take is taken and still not filed: --no-file stays, because a CLEAR that this map's refused null also clears is the non-discriminating verdict detectability.py publishes the bottleneck ratio under ADR-0026's name, and two cutoffs read it #379 already cost this rig. Opened B66 (#642) and B67 (#643). — ceded (a HITL prototype ticket resolved AFK with no human in the loop: the estimator, k, the sweep size, the gate substituting for presence/absence, the lane profile running, --no-file, and Δ reduced to a direction are all the agent's calls)

• B62 (prototype): Does the rule spend the traffic's rank, and is the agreement count just rank in another basis? — The prediction rule spends the rank, the transport rule buys the agreement, and the two pull opposite ways; the count is not rank in another basis. A frozen arm past construction — teaching_read is patchworks.agent.run plus the two rule steps, so dropping them leaves the same world, dome, seed stream and stimulus — holds uncentered traffic ER 2.7802 → 2.7825 flat at every rung to B57's own 20,000-tick horizon — spread 0.0068, smaller than the same quantity's window-to-window spread, and replicated by a second frozen arm (2.7798 → 2.7812 to 5,000, spread 0.0069) — against B57's rules-on 2.9825 → 1.0967 between 500 and 1,000 and 1.0045 at 20,000, so the rank does not decay on its own. Split: PredictionRule alone reproduces the collapse (→ 1.0087 by 2,000) and buys no agreement (leading direction stalls at q 0.5495, A(0.25) 0.0039) at exactly zero cost in exposure or differentiation, both bit-identical to frozen, because it writes K and never touches a map; TransportRule alone never collapses and raises ER to 3.1347 while its leading direction reaches q 0.0636 — better than both rules together manage (0.1830) — and raises differentiation (0.5307 → 0.5505) while spending 1.96 dimensions of exposure per cell. The both-on arm's differentiation cost (→ 0.4826) is neither rule's own. Item 3 refuses the ledger's second reading in both directions: traffic of stated rank in bands of stated q reads N(0.25) 0.0000 at rank one when generic and 6.6410 at rank eight when low-q, so the band decides whether anything is counted and the rank decides how much — row 8 resolves to its first reading and B52's construction is vindicated on its own terms. B57's account is rebuilt from stated ingredients (a low-q mean under a mid-q variety gives unc ER 1.1423 / N 1.0000 and cen 6.8614 / N 0.0000) and holds N pinned at 1.0000 while unc ER runs 1.02 → 2.85. Three findings to the ledger (rows 9–11): the antagonism, ker(G) = ker(δ_P) exactly (δ_P on ker(G) at 1.75e-15 against ‖G‖ 1.4607 — exact agreement unavailable to anything visible, B48's earned = 0 proved operator-side), and N(θ)'s vacuous regime (1.0000 on a direction carrying 0.4% of the traffic). The split arms stop at 5,000 (all three arms do carry the matched-generic null, three redraws, N_gen 0.0000) — whether the antagonism survives the horizon is B68 (#645)'s pre-registered falsifier; one seed; no threshold set, no candidate scored. — ceded

• B61 (prototype): Does the staggered frame's differentiation settle above the flat bundle, or is 2,000 ticks too short? — It settles, and the corrected falsifier does not fire — but the gap keeps closing, because the null climbs. To 30,000 ticks the differentiation flattens to 0.3912 (0.3921 / 0.3921 / 0.3912 over the last 12,000) with the rate falling two orders to the noise floor and channel_return holding 0.9819; B58 (prototype): Is the staggered frame the transport architecture, and what does the p-versus-differentiation curve cost? #630's ~15,000-tick extrapolation to the flat bundle is falsified by measurement. The unasked finding is the null: s0 climbs 0.0000 → 0.1269 / 0.1511 at 9,000 on two seeds and is still rising, so the gap narrows 0.4558 → 0.3044 driven entirely by it — a crossing neither in evidence nor excluded, and B48's null, whose defining property is differentiation 0.0000, is revealed as a construction reading (B69 (#646)). p = 8 leads p = 12 at every shared rung on differentiation and participation, margin narrowed to ~+0.03 and noisy, holding channel_return worse — advisory to #608, which still owns p. B58 (prototype): Is the staggered frame the transport architecture, and what does the p-versus-differentiation curve cost? #630's exposure headline decays to 9.40 and its random-init comparator cannot be read at horizon. Every arm runs the shipped pair, so which rule drives the decay is B68 (#645)'s and not inferable here. Stall stamp 100; the settle is drift under a frozen stimulus and says nothing about a live agent. — ceded

• B66: What separates the trained surface from the flat bundle, when both clear I(P; Δ) > 0? — Nothing does, nothing can, and that was never the bar's job. The user struck the ticket's premise: I(P; Δ) is a transmission reading and B42's flat bundle is the arrangement in which a message survives a loop unchanged, so the reading is maximised by it by construction. Detectability is a gate — a necessary condition — not a ranking, and the reference list (untrained surface, flat bundle) is closed. The joint rule is refused: differentiation is not-being-flat, so attaching it disqualifies by identity rather than discriminating, and B52's clause stays a guard on a candidate's training path. --no-file lifted. The alphabet ladder was read off B63's nested labels with no re-run and the margin is not evident — growing in bits, falling as a share of the ceiling, the two decoders disagreeing, and both arms at the ceiling on trace at k = 2, 4 — so the probe saturates at every alphabet it has and a dependence claim is quoted on patch alone. Two corrections to this map ride with it: the untrained arm fails on every stratum only under peak | centroid, and B58's discharge is therefore scoped to patch. Opened B70 (#648).

Not yet specified

• Whether this map's collapse evidence survives B8: Write #540's ruling: per-edge m_e, lateral lanes at 1, and the invariant doubled #548 and B15: Write #556's reserve mask: k_v = n - p, and the bound it supersedes #562, and whether its central readings want re-taking. B50 measured the construction half and it moved a long way — composed ER 1.025 → 1.412 median, 1.989 → 2.869 max, on B1: Read the principal angles, and whether c alone moves composed rank #537's own unmodified instrument — because interior lanes are now allocated per edge and k_v is pinned at 20. The trained figures (1.000 ± 0.000 at 30k and 100k, both arms) have not been re-read and are not claimed stale. This is sharp enough to ticket and is deliberately not ticketed: it sits as row 8 on the surprise ledger (#520) awaiting the user's ruling, because B50 (prototype): Are the per-hop cosine spectra anisotropic, or interior? #618's table routes an off-table reading to the ledger and the ledger reserves the ruling column to the user. It bears on the map's "largely prior to learning" clause, which is the half B50 touched. A re-read is ~30 min per arm on the existing T4 rig.

• Whether the process failure B3: Read the pre-registered falsifier that #220 closed against a proxy #538 documents wants a register entry or a standing rule. Taken, and it is worse than first stated: the substitution was justified by an unavailability that was never checked and was false — the correct instrument (benchmarks/untrained_fixed_point.py attenuation) was named in #155's own falsification block, the very ticket Put the incoherence term in the projection, and swap the gain's denominator in one edit #220 inherited the condition from, and had been on main for three days — and the proxy pointed the opposite way (down 1.7%, judged small; actually down 4.06x). So the shape is not only an honest note died in a closed comment, it is a checkable claim of unavailability was never checked. Not this map's destination, but it was found here.

• Whether the cell's own dynamics can be made richer, and by what — now narrowed to what sits outside the objective. B19 closed the transport half: transport is injective on the whole exposed block at 150/150 cells and 80% of the variance is already exposed, so the narrowness is upstream of transport. Its second target — that emission stopped being a function of the state — graduated into B33 as the representation floor. What remains here is the tick, the sandbox and the prediction rule, and which of those to reach for is still not stateable. B62 (#635) makes one of the three stateable, and it is the prediction rule. Run alone past construction it collapses the traffic's uncentered effective rank 2.7798 → 1.0089 — the whole of the collapse, on the same interval as the shipped pair — at exactly zero cost in exposure or audience differentiation, because it writes K and never touches a restriction map, while TransportRule alone raises the rank to 3.1347. So the narrowness downstream of transport that B19 located upstream has a named author on this quantity. The patch does not graduate whole: what is ticketed is the mechanism and its horizon on B68 (#645), because B62 measured the antagonism without explaining it and read neither split arm past 5,000 ticks; whether the prediction rule is a lever this map may reach for is not stateable until that reports, and the tick and the sandbox are untouched by any of it. Related and equally open: whether any objective that is not edge-agreement is admissible at all, since B16's necessity argument is scoped to agreement objectives — B32 may bear on it.

• Whether the architecture wants a bound on forced lane overlap, and at what value. Graduated on 2026-09-09 by B35 and cleared from this section: its parking condition was "not a ticket until something says that distinction is measurable", and two things met it — B22 measured community sizes against p (median 150 / 27 / 7 / 1 at shipped / 8 / 12 / 16) and B35's community membership definition made the band load-bearing, since the measure only discriminates where communities are graded. Now B44 (#608), blocked on B43 (#607). The content half B22 could not settle — overlap genuinely shared versus overlap bought by shrinking the ambient — was B42's central risk and B42 has since made it concrete: an architecture can move effective p without anyone choosing it (the flat bundle reads 14.8 of 32 against the control's 20.0 on B22's own rank-measured k_v), and B42 pre-registers a prediction on B44 that the flat bundle lands at the undifferentiated end rather than the hermit end. Read effective exposure, not the spec field.

• What the ADR amendments actually say. B39 changed what two of them are booked for: ADR-0026 is amended for struck quantifiers, not for a re-index, and its CONTEXT.md Rim-core influence entry carries the per-stratum count and the L1 universal that go with them; ADR-0021 is amended to carry sensorimotor dependence, and B43 has decided its content — an endpoint I(P; Δ) reading with the path quantifier struck and no successor, the bottleneck ratio kept and demoted, and the Bottleneck ratio and Rim-to-core detectability glossary entries both changing; only the wording is still owed. B43 also names a site inside the ADR-0003 entry that nobody had: its final Consequence bullet has the opposition surviving as "a path through the graph (sensory rim → centre → motor rim, abstraction rising then falling)" — a level-shaped sentence on a map that forbids level, and abstraction rising then falling is what B35 displaces. B43's own measure does not inherit it. B27 named the cost — ADR-0021, ADR-0026, ADR-0003 and the two glossary entries, ADR-0011 — but the wording cannot be written until the architecture those amendments describe is decided. A writing ticket per the map's standing hand-off rule, once B33 and its dependents land. B30 enlarged and sharpened the drive-side half of this: eight sites carry attached deep or abstract by attachment point — ADR-0009 (superseded, not amended: its title is the claim), ADR-0003's amendment note, CONTEXT.md's Drive boundary cell and Internal rim, spec/04 §192 and §321–322, spec/06 §41 and §185–187, and spec/12 §159; ADR-0024 §53 is adjacent and untouched. B30 named them and wrote none. B37 enlarged it again to nine and changed what two of them must say: spec/04 §18–22 and §312–322 carry the retired who-clears tables, §388 carries a derivation of the motor-edge signature that the sensory row satisfies verbatim, and ADR-0025 cites ADR-0003's criterion by name — it survives but needs re-deriving on authorship. ADR-0003 is amended, not superseded, and ADR-0009's successor now drops the motor-edge clause B30 had it re-assert. B37 named them and wrote none. B35 adds three more and a fourth that is new rather than amended: CONTEXT.md's Sensorimotor rim ("Abstraction is hop distance from this rim"), Level ("abstraction is that distance") and Internal rim ("a faculty is abstract by attachment point") all fall to abstraction-as-community-membership, and a new Community entry has to be written — defined as a connected set of cells over which one direction stays consistent, explicitly disavowing graph learning's density-defined sense. B35 named them and wrote none.

• Whether the shallow dome can carry any reading for this map, or whether every reading must be full-dome. B38 has landed and it neither answers this nor blocks it any longer. The surface question is settled — the bar holds the world by construction, so it can be read on any dome, and a reading that does need motion must stamp its own horizon rather than inherit one (B38 found the horizon varies 13x between seeds of one arm). So which dome is now a question about cost and comparability — a shallow dome is cheaper and every figure on this map was taken on the full one — rather than about validity, and it is not sharp until something needs the cheaper surface. Map: the constant-evidence collapse and the variation famine at the cold start #517's guard 5 retired its shallow surface; this map has not stood one up. Now a rig question only — B27 demoted the dome from architecture to scaffold, so this decides what is measured on, not what is built.

• Whether A leak on the cell operator toward its prior, as the apex ladder's fallback rung #526's leak has any bearing here at all. R-A found K is not a factor in the composed object (composed_reads multiplies F_out·F_inᵀ hops only), so it may belong wholly to Map: the constant-evidence collapse and the variation famine at the cold start #517's ladder.

Graduated on 2026-09-08 by B27 and cleared from this section: what a lane should be — the discovery mechanism the vision requires and the architecture never contained — now lives as B33 (the objective's local holonomy term, which is what would discover it) and B34 (that term read per edge as a prune criterion).

• Whether the detectability read should be re-filed on the current surface. Settled on 2026-09-09 by B39 and cleared from this section: it stays unfiled, and for a harder reason than B38's own. B38 passed --no-file because filing a cutoff record on a surface it was simultaneously calling degenerately trained would put a disputed number on the tracker. That stands — and B39 has since struck the reading's path quantifier, so filing A prior computed at the apex cannot reach the rim it exists to modulate #341 CLEAR at 0.133; The gauge confines every prediction to one subspace, and nothing has checked the stalks reach it #325 and #329 SHUT at 0.133 would file a retired predicate. Not a separate decision: it follows from the split. The cutoff readings stay recorded in B38's readout and in B39's resolution; a filed read waited on B43 fixing what the predicate quantifies over, and it is fixed: the read is not re-filable, it is re-takeable. B43 moved the terminus and the statistic both, so those cutoffs are readings of the amplitude predicate at a place the predicate no longer ends — the re-take belongs to B63 (#637), which carries --no-file until it says otherwise.

• Whether Is the conduction ratio readable in the precision the architecture runs in? #224's gate deserves pricing. 85–95% of cells read as unreadable at runtime precision in B38's two reads, on both training horizons. It is the background condition of every reading this map takes and no ticket on Map: transport whose composed rank exceeds one #532 has costed it. Partly costed by B63 (#637), and it is worse than a background condition on one stratum: the patch response at the world-read boundary clears eps_f32·‖state‖ on 0 of 192 trials on the untrained, trained and flat arms, so that stratum's entire dependence reading exists only on the float64 cast — and the ratio falls 6.98e-14 → 2.74e-15 from construction to trained while the MI rises. What is still not stateable is what the architecture owes that: EPS_F32's register row rules precision not a design variable, so the lever is not the arithmetic, and whether the answer is the terminus width (B67 (#643)), the gain, or neither is not sharp yet. Proprioceptive and touch clear on 192 of 192, so this is not uniform across strata and a pooled figure would hide it.

• Whether carving is the right job for holonomy at all — graduated, and the falsifier did not fire as written. B40 built the flat bundle and found it closes cycles while the criterion still discriminates on it (std 1.2–1.5, 6–7 distinct values, two seeds), so the antecedent that would have ruled B34 out of scope is not met and B34 stands. What defeats the criterion is coverage, not schedule — 46% of wide edges are bridges with no cycle to close, cap and ration never clip, and the only clause that acts leaks at √1.25 by construction. Now B41 (a rule for acyclic edges, a replacement for the floor, and whether the count wants normalising by how many cycles it reads) and B42, now resolved and it reversed B40's reading: the reserve was never what broke exactness, the falsifier did fire, and the flat bundle is refused as architecture and retained as this map's null. What remains open from it is B47; B48 is resolved and opened B52, B53, B54 and B55; B49 is resolved and opened B50 and B51.

Cleared on 2026-09-08 by B40: the threshold and the split are both readings and both are taken. The split is arithmetically fine — enumerated per edge rather than off B29's basis there are 190 short local cycles, median 3 per edge, 104 edges with ≥2 — and the criterion is reported at 0.8, 0.9 and 0.95 so nothing rests on the value. B29's 40 of 45 was a basis count, and a basis is a BFS artifact. What the reading found instead is on B41: 90 of 194 wide edges are true bridges, cycle-less at any length, 0 stranded by the radius — so ADR-0011 is exonerated and the criterion is undefined there whatever the route.

• Making m_e a trained object. Edge.m is frozen, "fixed here and never changes", and the user's dynamism ruling (connectivity must track learning cells) requires it to move — which is #320's "masks close and never re-open" arriving as a build requirement rather than an objection. Out of scope while Plan, don't do stands. B40 moved it as far as a prototype may: b40_criterion.py allocates the width from a reading rather than a constant, and is the first thing on this map to do so. It allocates into a record, never into a built graph.

• Whether a retention term is admissible at all, now that B44 (#610) has measured one-step prediction error pressing ρ(used) down rather than leaving it alone. Not yet a ticket: the term's shape depends on what it would be an adversary of, and this map has not decided the objective — B48 (#615) has since asked it and pushed it upstream: no objective term on the current parameterisation can produce agreement, so the live question was B53 (#623) — now resolved: the rank lever is the transport rule's input (learn from the deviation from a per-cell running mean), it is not aimed at retention, so B44's adversary warning is not triggered directly and B56 (#628) has since read ρ(used) and τ alongside without finding a fight. The successor lever is B60 (#633). An adversarial-term shape was B54 (#624)'s — now answered and the adversary question is ceded, not settled: B54 ruled the revived holonomy term does not inherit B44: Does an O(1) return bend tau-hat, and does rho(K) move under the current objective? #610's constraint, on the argument that retention is temporal and on K while holonomy on the channel is spatial and on the transport operator. The user yielded that call rather than judging it, and B56 (#628) carries the check by name — it trains a holonomy term, so it is the cheap place to read ρ(used) and τ alongside and say whether the two terms compete. Related and equally open: whether any objective that is not edge-agreement is admissible, since B16's necessity argument is scoped to agreement objectives. #375 now has a number to be asked against: τ ≈ 52.9 ticks on reserve_p12 seed 42 at 2,000 ticks.

Out of scope

The apex retention ladder and the arm's untrained command (both stay on #517). Reward in any form beyond #517's standing ruling. Enriching the sandbox. Re-deriving ADR-0026's quantity — τ̂_c / world_loop(c) stays fenced. Moved on 2026-09-09 by B39, on the user's own answer: this line read Redefining ADR-0026's bar and was written while the dome was architecture. B23 fired, B27 called the wager lost, and the fence was then protecting a level-indexed predicate on a map that forbids level. Re-indexing ADR-0026's quantifiers off the retired dome is in scope; the ratio itself is not. Building the chosen architecture — that is the effort after this one. Attention. Named on B41 as the reason a gate is worth more than its local job; it is a use of that mechanism rather than a step toward this map's destination, so it returns as its own effort. Recorded so B46's design does not foreclose it. The sandbox's own determinism, which is the world half of the stochasticity question raised on B43 (#609) — out of scope under enriching the sandbox above, and now minted as an open problem, #641, uncut, rather than left as a consequence in a citation pass. docs/research/018-sandbox-citations.md §2.6 had stated it since it was written — a cell here can in principle drive its prediction error to zero; a cell in the real version of this world provably cannot — against CONTEXT.md's disagreement, never fully cleared. Its two remedies split cleanly and only one landed: position-dependent friction is now the Friction field, and per-reset() resampling, the half that buys irreducible error, was not adopted. The architecture half is in scope and is B65 (#639) — a stochastic element in the rule or the parameterisation, which is what B59's unrankable degeneracy points at. Whoever reaches for world noise prices the fork: bit-exact snapshot and restore is what ADR-0021's paired counterfactual and B43's measure both stand on.