F-SIDE DISTINCTIVENESS MAP

Status: BUILDER-SUPPORT PROBE. Not a verdict. Moves no P-level, changes no frozen verdict, creates no claim. It answers one question: which components of the F-side motor stack are evidence, and which are architecture?

Scope: the constrained F-side observational projection as implemented in hierarchical-aif/src/motor_stack_aif/ and scored by compare.py on the frozen derived_eligible_1_to_8 cohort (Wadhwa 2022, E. coli, 80 train motors / 793 train events, 19 holdout motors / 233 holdout events). Duration-only. Held-out nextStateN / direction / jump were not read by this probe (D5 firewall; events.load_events(mode='duration_only') is the module default and compare.project_event allow-lists the duration fields).

Builder rule applied throughout: if a component does not create a new testable prediction on data this repository holds, it is architecture, not evidence.

1. The headline the map has to explain

The frozen record says the F-side candidate reproduces M7 to numerical precision:

0.042 / 2.506984e-07 = 167531.98265325985 — the resolved separation sits about 1.7e5 times below the corrected motor-equal resolution floor. D10 is the reading: the paired motor-cluster bootstrap resolves a difference of any magnitude when its sign is consistent across motors, so RESOLVED_ABOVE here is a statement about sign consistency, not about scientific material. This is a design signal about the model, treated as such below.

This is a re-derivation of M7, not an independent competitor, at the level of the fitted predictive density. The parameterisations coincide exactly on paper:

frozen M7 :  k_m = k * exp(tau * z_m),  z_m ~ N(0,1)   =>  log k_m = log k + tau * z_m
F-side    :  k_m = exp(eta_m),  eta_m ~ N(mu, tau^2)   =>  log k_m = mu     + tau * x

with mu <-> log k and tau <-> tau. The residual ~1e-6 is optimiser placement, not model structure.

What would have to differ for the F-side model to be a distinct model

None of these is currently implemented. Each is a structural change, not a retune:

1. A different latent link. eta_m on log-shape reproduces M7 by construction. A latent on the scale (with shape shared), or a joint (shape, scale) latent, is a different marginal.
2. A latent that is not exchangeable across motors — e.g. indexed by stateN, load, or occupancy — so the population prior carries structure M7 has no slot for.
3. A prior that is not Gaussian in log-shape (mixture, heavy-tailed, or bounded), which changes the marginal even at matched mean and variance.
4. A likelihood M7 does not have — the censoring branch actually exercised on censored observations (see component C4).
5. A reported quantity M7 cannot produce, scored against something. posterior_motor_shape is such a quantity, and it is currently scored against nothing (component C5).
6. A second observation channel. M7 is a duration model. Everything the F-side stack currently does is also a duration model. Distinctiveness on durations alone is bounded by how much of p(y) the two parameterisations can disagree about — measured below as [B], max 3.8437083222930823e-05 nats per event over a 6-decade y grid.

2. Component map

is_testable_current_data = does this component generate a prediction that the frozen cohort can put a CI around, today, without new data?

3. Evidence vs architecture — the verdict of the builder rule

Components that currently produce a testable prediction on data this repository holds (EVIDENCE):

• C1 the (mu, tau) population prior. It is the only component with a scored held-out number and CI-bound contrasts. Its two RESOLVED_ABOVE results are against M0 and M5; against M1, M2, M3 and M8 the result is NOT_ESTABLISHED — which is not equivalence and not "no difference". Underpowered is not equivalence.
• C7 / C8 as the measurement instrument and the interval rule. They are evidence about the scoring, not about the motor. The independent-oracle residual of exactly 0.0 is a real receipt about C7.

Components that are ARCHITECTURE — correct, tested, and currently producing no new testable prediction: C2, C3, C6, C9, C10, C11, C12.

Components that are ARCHITECTURE TODAY but are one bounded experiment away from evidence:

• C5 posterior_motor_shape — needs a scoring rule, not new data. This is the highest information-gain-per-cost item in the map.
• C4 the censoring branch — needs data the frozen cohort deliberately excludes. Transfer or cohort re-derivation required; no amount of modelling on derived_eligible_1_to_8 can exercise it.

4. What the numbers say about how much room there is at all

Measured on a synthetic log-spaced y grid over [1e-4, 1e2], 2001 points — no dataset was loaded for this probe:

| comparison | max |dlogp| | median |dlogp| | reading | |---|---|---|---| | [A] F-side 33-node vs M7 129-node, IDENTICAL params | 6.453021228480793e-09 | 8.881784197001252e-16 | the quadrature choice is not a modelling choice here | | [B] F-side vs M7, EACH AT ITS OWN fitted params | 3.8437083222930823e-05 | 1.7188155483349732e-06 | the entire pointwise disagreement between the two fitted models | | [C] F-side vs frozen M1 (k = 0.6250888335850175) | 6.818525730561962 | 0.06875493217032691 | the hierarchy is pointwise FAR from M1 | | [D] F-side at tau = TAU_MIN = 1e-4 vs plain mean-one Weibull at k = exp(mu) | 1.7051171770532392e-05 | — | the tau -> 0 collapse to M1-form is real and numerically clean | | [E] F-side at fitted tau vs its own tau -> 0 limit, same mu | 9.747243324446924 | 0.055692754431005076 | tau is the whole of what the hierarchy adds over a single shared shape |

The adverse reading, retained. [C] and [E] say the F-side density differs from M1 by a median of 0.0557–0.0688 nats per event on this grid — yet the frozen held-out contrast against M1 is +0.000615 [-0.010881, +0.011304] NOT_ESTABLISHED, and the leaderboard gap is 0.0006145101324697144 nats. Two honest readings, both retained: (i) the log-spaced grid weights tails the observed durations barely populate, so pointwise divergence overstates scored divergence; (ii) with 19 holdout motors the scoring rule cannot separate them regardless. The probe cannot distinguish these without an observed-y-weighted divergence, which would be a holdout computation and is NOT_RUN — COMPUTE_BUDGET / SCOPE. The grid is synthetic and the divergence numbers are therefore a property of the two densities, never an observation about motors.

5. Limitations of this map

• Every number in §1 that is not from probe output is read from frozen records; nothing here was refitted or rescored.
• §4 is computed on a synthetic y grid. It is a numerical property of two functions. It is not observation and carries no predictive claim.
• No held-out score was recomputed. No bootstrap was re-run. The C11/C01 corrected runs in flight were not touched, and none of their live counters was read or used.
• This probe read no held-out mark field. Any question here that would need nextStateN, direction or jump is NOT_CHECKED — would require holdout access.
• The map judges DISTINCTIVENESS, not correctness. Every component listed as architecture is, as far as its tests go, correct.
• P-ladder unchanged: P8 FULL_PARITY = false, first unsatisfied level P4 transfer. This probe moves nothing.

NEXT_ACT = Draft hierarchical-aif/protocols/C5-POSTERIOR-MOTOR-SHAPE-SCORING-PREDICTION.md pre-registering a leave-one-event-out-within-motor scoring rule for posterior_motor_shape, contrasted against the marginal per-event score on the SAME 19 holdout motors with the frozen seed 20260717 / nRep 2000 motor-cluster bootstrap — the one component in this map that can move from architecture to evidence without new data.