B70 (prototype): Does the dependence probe discriminate at an alphabet that is not saturated?

[NGL321]

Part of #532. Cut by B66 (#642) on the user's own answer: "cut a ticket for significantly more complex data if results are not evident, because I think 8 is insufficient here." The results were not evident.

Question

Does the sensorimotor dependence probe discriminate at all, once its injected content is complex enough to matter — and what counts as "complex enough" when the read is as wide as it is ever going to get?

Why this is sharp now

B66 ruled that I(P; Δ) > 0 is a gate, not a ranking: it is a transmission reading, B42 (#605) derived the flat bundle as the arrangement where a message survives a loop unchanged, so a transmission reading is maximised by it and no reference can separate them. That ruling stands and this ticket does not reopen it.

What it left open is the user's own account of the 2×: the probe's task is too small for specialisation to pay. B66 tested that on the only difficulty knob available for free — B63's nested alphabet, k' = 2, 4, 8 — and the answer was not evident:

reduction | decoder	margin flat − trained, k=2 / 4 / 8	as a share of the ceiling
peak | centroid	+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

In bits the margin grows; as a share of the ceiling it falls; the two decoders disagree on the k=4 → k=8 leg; and on the trace reduction — the one B63 showed carries most of the content — both arms sit exactly at the ceiling at k = 2 and k = 4, with the sign flipping with the decoder at k = 8. The probe saturates at every alphabet available to it.

What it must settle

1. What "significantly more complex" means here, and this is the decision the ticket exists for. At least three shapes, and choosing among them is the answer: more patterns (k far past 8 — patch is 12288-dimensional and orthonormal at k = 8 with max |cos| 0.0000, so k = 64 or 256 is available); structured patterns, where the alphabet is compositional rather than a flat list, so that a room routing parts to specialists could in principle beat a room that does not; or patterns that vary over the window rather than one fixed-norm injection, which is the axis B63's trace/peak contrast already showed carries most of the content.

2. Whether more patterns can even be read. After the direction normalisation the terminus is 2-dimensional. Separating 256 classes from a 2-dimensional feature with 24 examples each is not a decoding problem that gets better with more classes — it gets worse. The alphabet and the terminus are the same constraint from two ends, which is why this ticket waits on B67: Is the world-read boundary's 3-wide commanded block the binding constraint on dependence? #643.

3. What a non-result means. If the margin still does not move, that is not a refutation of the project's bet. It says the probe cannot see the effect, and the honest finding is then that dependence is a gate whose discriminating power is exhausted, with the bet untested on any surface this map may build. That is a real outcome and it should be stated rather than dressed up.

What it must not do

It must not enrich the sandbox. That is out of scope on #532 and is minted as #641. The probe is not the sandbox — B43's injected content is an instrument, and enlarging an instrument is in scope. Whether the deeper form of the user's bet is testable at all without a richer world is a fair thing to conclude, and not a licence to go build one.

It must not reopen the gate ruling. B66 settled that dependence does not rank architectures and that differentiation may not be attached to it as a scoring column — a rule that fails the flat bundle on differentiation disqualifies by identity rather than discriminating. Differentiation stays where B52 (#622) put it: a guard on a candidate's training path.

It must not quote a threshold. B43 refused one on ADR-0021's k = 1 discipline; B63 did not reopen it and neither did B66.

Standing constraints this inherits

Quote patch, and report the other two strata as saturated (B66 §3, §5). Proprioceptive and touch read the ceiling exactly at k = 2, 4 and 8 — saturation is bijectivity to the terminus, not an artifact of choosing 8, and raising k cannot fix it. Patch is also the only stratum where the untrained arm fails under every reduction and both decoders.

Quote the untrained surface and the flat bundle (B63 (#637)), and name the reduction — B66 §4 found the untrained arm clears the null on the narrow strata under three of four reductions, so an unqualified "the untrained arm fails" is false.

Say which object (B49 (#616)) — node stalks here, lanes there, no number crosses.

A candidate may not argue dependence from gain (B43 §7) — P varies which pattern, never how hard.

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

Stamp your own horizon (B38 (#599)) — per run, not per arm.

Notes

The rig is built and the ladder is cheap to extend. prototypes/cold-start/T6/b63_dependence.py on branch worktree-b63-dependence-instrument-637; B66's b66_ladder.py and b66_untrained_check.py on worktree-b66-separates-642, with READOUT-642.md. B63 costs ~6 min per arm for 576 trials, so a larger alphabet scales roughly linearly in k — check the box's commit limit before launching and checkpoint, per B61 (#634)'s five lost arms.

C ≥ 16 is not negotiable — B63 found the vacuous conditioned form leaking back in below it, large enough to have carried a false pass.

--no-file has been lifted for the gate verdict by B66, subject to the float32 finding recorded there; that does not extend to anything this ticket reads.