B66: What separates the trained surface from the flat bundle, when both clear I(P; Delta) > 0?

[NGL321]

Part of #532. Graduated by B63 (#637)'s first reading of the sensorimotor dependence instrument.

Question

Given that both the trained surface and the flat bundle clear I(P; Δ) > 0, what separates them — and what does the destination's bar become if nothing does?

B63 built B43 (#609)'s measure and took the first reading. The predicate passed, and so did this map's own retained null:

stratum	untrained	trained	flat	ceiling
patch	0.276 (p 0.070)	0.857 (p 0.0025)	1.645 (p 0.0025)	3.000
proprioceptive	0.257 (p 0.057)	3.000	3.000	3.000
touch	0.201 (p 0.304)	3.000	2.414	3.000

Bits, lower bound, against a matched scramble null of 400 permutations. On patch — the widest stratum, and the only one with headroom — the flat bundle reads nearly twice the trained surface.

What this ticket has to settle

1. Whether a reference that separates exists at all. B43 §5 named three: the ceiling log k, the flat bundle, and the untrained surface. The untrained one does separate — it fails on every stratum, which is B58's construction-supplies-it-free warning discharged in the architecture's favour for the first time on this map. The flat bundle does not. Whether a fourth reference is available, or whether the separation has to come from somewhere other than a reference, is the question.

2. Whether k = 8 is the reason two of the three strata cannot separate. Proprioceptive and touch saturate the ceiling exactly on the trained arm, and proprioceptive on the flat arm too, so there is no headroom in which to differ. But the strata are dimensionally bounded — touch's whole product space is 3-dimensional and cannot carry eight distinguishable patterns at fixed norm (max pairwise |cos| 0.9881) — so raising k there raises the ceiling without raising what can be injected under it. This may be unfixable on the narrow strata, which would itself be the answer.

3. Whether the separation is properly a job for the joint rule rather than for this statistic alone. B52's precedent is directly on point: it amended its own item 3 so the agreement statistic is not required to fail the flat bundle alone, because fusing differentiation into one number is B49's struck move — and the joint rule is what carries the null. Whether dependence takes the same shape, reported alongside audience differentiation and the exposure it cost, is the cheapest live candidate and should be priced before a fourth reference is invented.

What is not in scope

A threshold. B43 refused one on ADR-0021's own k = 1 discipline — every invented constant in this map's history has later been found to have none — and B63 did not reopen it. I(P; Δ) > 0 over a matched null stays the predicate; what is sought is what it is quoted against.

Re-opening the measure. B43 decided the statistic, the terminus, the two sides, the absence of a path quantifier and what content varies. A finding that the measure cannot be made to discriminate is a real result and belongs here, but it amends B43 by comment and ruling, not by quiet substitution (#532's standing practice).

Standing constraints this inherits

Quote the initialisation (B58 (#630)). A gain is quoted against the frame it was measured from, and the same term is reported on a frame that already has the quantity. B63's untrained arm is that reading for this measure and it is on the branch.

Say which object (B49). The endpoint measure is on node stalks; the per-edge profile is on the lane. No number crosses.

Stamp your own horizon (B38) — per run, not per arm.

traditional, declared at every use (B64 (#638)).

Notes

The rig is built and needs no rebuilding. prototypes/cold-start/T6/b63_dependence.py on branch worktree-b63-dependence-instrument-637, with b63_lanes.py for the per-edge profile and b63_table.py for the cross-sections. A full three-arm read is ~6 min per arm plus ~3 min of training; the estimator is seconds. READOUT-637.md carries what every number means.

--no-file until this ticket or its successor says otherwise — B63 kept it precisely because a non-discriminating CLEAR is what #379 cost this rig once already.

[NGL321]

Resolution — the premise was wrong, and the user struck it

This ticket asked "what separates the trained surface from the flat bundle". Nothing does, nothing can, and that was never the reading's job.

I(P; Δ) is a transmission reading. B42 (#605) derived the flat bundle as the one arrangement in which a message survives a loop unchanged — that is what flatness is. A transmission reading is therefore maximised by it, by construction and not by accident of B63's run. So B63's closing line — "what is missing is a reference that separates" — presupposes that the bar should rank architectures. It should not. No fourth reference could have separated them, because the quantity being measured is the one the flat bundle is optimal at.

The user's ruling, in their own words: "The flat room being superior in this, in the one category, in the one measurement, is not incorrect because there's only so much data moving through it right now, and the task we're asking of it is extremely minimal."

The agent's recommendation was wrong and is recorded as wrong

The first round of this ticket recommended item 3's joint rule — report I(P; Δ) alongside audience differentiation, and let the flat bundle fail on the differentiation column. The user refused it and the refusal is correct.

Audience differentiation is the definition of what makes a room not-flat. A rule of the form pass the dependence test, and also have nonzero differentiation says pass the test, and also do not be the flat bundle. The flat bundle cannot fail such a rule for a reason — it fails by identity. That is not a bar; it is the dependence test with the architectural choice stapled to it, and it would pass the architecture because it is the architecture. It disqualifies instead of discriminating.

B52 (#622)'s precedent does not transfer, and the agent carried it one object across. B52's differentiation clause guards a candidate's training path — do not buy agreement by collapsing lanes. It does not disqualify a reference architecture from a reading. Recorded explicitly because this session made the error once and the next reader should not repeat it.

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1. The bar is a gate, not a ranking (Q1, agreed)

Detectability is a necessary condition on the world loop. It says signal still gets across. Many arrangements should pass a necessary condition — that is what necessary conditions are for. The flat bundle passing is only a scandal if the gate was expected to rank, and it never was.

This strikes item 1 of this ticket's own question and amends B43 (#609) §5 by comment: its three named references are not a set from which a separating one is missing.

I(P; Δ) > 0 over a matched scramble null stays the predicate, exactly as B43 wrote it. B43's refusal of a threshold on ADR-0021's k = 1 discipline is not reopened.

2. Two references, and the list is closed (Q2, agreed)

The untrained surface discharges B58 (#630)'s a construction may supply the quantity free. The flat bundle is B42's retained null. Neither is failing at its job. Adding a third to make the numbers separate is inventing a threshold under a different name.

And two things are true together, which the record must hold: the flat bundle is refused as architecture on B42's own measured grounds, and it is not worse at transmission. The error was importing the first into the second as a scoring column.

3. Differentiation stays where B52 put it (Q3, agreed)

Not a column on this reading. A guard on a candidate's training path: a proposed rule may not buy its result by collapsing lanes.

4. The alphabet ladder, run here (Q4, the user's own answer)

#637 is closed, so this was read in-session off its existing files — B63's alphabet labels are nested, so k' = 2 and k' = 4 were already recorded. No runs. Full detail in READOUT-642.md on branch worktree-b66-separates-642, with b66_ladder.py and b66_untrained_check.py.

Patch — the only stratum with headroom. Margin is flat − trained; the ceiling is log k and moves with the rung, so only the share is comparable across rungs.

reduction | decoder	margin k=2 / 4 / 8	share of ceiling
peak | centroid (ADR-0021's own)	+0.393 / +0.565 / +0.788	0.393 / 0.282 / 0.263
peak | nn1	+0.461 / +0.430 / +0.709	0.461 / 0.215 / 0.236
trace | centroid	0.000 / 0.000 / +0.058	0.000 / 0.000 / 0.019
trace | nn1	0.000 / 0.000 / −0.296	0.000 / 0.000 / −0.099

The result is not evident, and that is the finding. In bits the margin grows; as a share of the ceiling it falls; the two decoders disagree on the k=4 → k=8 leg. On the trace reduction — which B63 showed carries most of the content — both arms sit exactly at the ceiling at k = 2 and k = 4, and at k = 8 the sign flips with the decoder (flat +0.058 on centroid, trained +0.296 on nn1). The flat bundle's advantage is large and consistent on peak, absent or reversed on trace.

The probe saturates at every alphabet available to it. k = 8 is insufficient, as the user said. → B70 (#648), blocked on B67 (#643), because after the direction normalisation the terminus is 2-dimensional and more classes is not a decoding problem that improves with more classes — the alphabet and the terminus are the same constraint from two ends.

Saturation is bijectivity, now measured rather than argued. The trained arm reads the ceiling exactly on proprioceptive and touch at k = 2, 4 and 8; patch never does. This settles item 2 in the negative: the saturation is not an artifact of choosing 8 and raising k cannot fix it. The one exception proves it — touch's flat arm reads 2.414 at k = 8 and the ceiling below it, because its 3-dimensional space cannot hold eight distinguishable patterns (max |cos| 0.9881), so crowding appears exactly where crowding starts.

5. A correction to a claim now on the map

Q1's ruling rests on the untrained surface failing the gate. It does — on ADR-0021's own peak | centroid reduction, and not generally.

Untrained arm, k = 8, p against its own 400-permutation null:

stratum	peak|centroid	peak|nn1	trace|centroid	trace|nn1
patch	0.0698	0.5337	0.1297	0.5387
proprioceptive	0.0574	0.0025	0.0025	0.0025
touch	0.3042	0.0150	0.1920	0.0025

On the narrow strata the untrained construction clears the null under three of four reductions, reading up to 1.561 bits (proprioceptive, trace|nn1, excess 1.208). So:

• The map's B63 entry — "it does not clear on the untrained one on any stratum" — needs the reduction named.
• B58's discharge is scoped to patch. The map records it as discharged in the architecture's favour "the first time on this map that it has been"; on the narrow strata, under the reduction carrying the content, the construction does supply it free. The discharge stands on patch and only there.

Patch is the only stratum carrying a verdict, on two independent grounds — headroom (§4) and teeth (§5). A dependence claim is quoted there; the other two are reported saturated.

6. --no-file is lifted (Q2 of the re-pitched round, agreed)

B63 withheld the CLEAR because the refused null passed too. Under §1 that reason is gone: a gate verdict is not supposed to discriminate. The verdict is filable, with B63's float32 finding recorded beside it — on patch, 0 of 192 trials clear eps_f32 · ‖state‖, so that stratum's reading lives only on the float64 cast. That is #224's gate, it remains fog on #532, and it is a caveat on the filing rather than a reason to keep withholding it.

7. What this does not show

It does not test the user's bet — that a parsed-up problem is solved better by specialists whose communication is tailored per neighbour, and that a flat sheaf constrains the cells themselves. A margin that does not move across three rungs of a saturated probe says the probe cannot see the effect, not that the effect is absent. The alphabet is a weak proxy for task difficulty, and the deeper form of the bet may not be testable without a richer world — which is out of scope on #532 and minted as #641.

One measurement does point at the cells-are-constrained half, and it is not this one: B42 read the flat bundle's rank-measured k_v at 14.8 of 32 against the control's 20.0. One reading, one surface — support, not proof.

It does not touch the terminus. B67 (#643) owns that, and §4's saturation is the strongest evidence yet for its item 1: the strata near-bijective to a 3-wide terminus saturate at every alphabet, and the wide one never does.

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Decision provenance. Q1 (the bar is a gate, not a ranking), Q2 (the reference list is closed) and Q3 (differentiation stays a guard on a candidate's training path) are AGREED. Q4 is the user's own answer — run the ladder in-session since #637 is closed, and cut a ticket for significantly more complex data if the result is not evident. The central ruling of this ticket is the user's own: they rejected the ticket's premise outright, on the argument that the flat bundle's advantage is a small-task artifact and that failing it on audience differentiation would be an injected term rather than a finding. Nothing here is ceded. The agent's own recommendation — the joint rule — was refused, and is recorded above as refused rather than quietly dropped.

[NGL321]

Resolved. The premise was struck by the user: nothing separates the two arms and nothing could, because I(P; Delta) is a transmission reading and the flat bundle maximises it by construction. Detectability is a gate, not a ranking. Ladder read in-session off B63's nested labels; result not evident, so B70 (#648) is cut and blocked on B67 (#643). Map updated, advisories on #637 and #643.