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The actual layered model fitted to real E. coli motors — every layer, every parameter, every score — read live from the result files, so this page cannot drift from them.
A population of motors, each motor its own latent shape drawn from that population, each dwell shaped by how many stators are engaged. Five layers built, two free parameters, eighty motors — the parameter count does not grow with the data because the per-motor layer is integrated out, not fitted.
Scored on nineteen motors it has never seen: … nats. Everything below is that model, opened up.
From the primary-source investigation (2026-08-19/20): our layers are strata of statistical pooling wearing biological names. Each row states the layer's mathematical identity, its biological counterpart, and the honest parity status. The naming ruling — rename the pooling layers, or build the maps that make the names true — is the operator's and is open.
| layer | what it IS, mathematically | biological counterpart | parity | what parity would require |
|---|---|---|---|---|
| Lmotor-5 | empirical-Bayes hyperparameters (μ, τ) of a Gaussian over log-shape — a POOLING level | between-motor heterogeneity (Wadhwa 2022) | MISNAMED | a per-motor covariate with units that CAUSES the heterogeneity, or an honest rename |
| Lmotor-4 | per-motor latent, integrated out by quadrature — pooling strength | a persistent per-motor property — NOT SOURCED that it is molecular | PARTIAL | an independent observable of the per-motor property |
| Lmotor-3 | frozen per-state normalisation divisor — cancels in every contrast, so the one biological variable here can influence NO verdict | stator occupancy N (the one anchored rung) | NEUTERED | N as an integer jump process with binding/unbinding rates in s⁻¹, calibrated on the held load→occupancy series; plus the state-pooled ablation (needs NO new data) |
| Lmotor-2 | not instantiated (identifiability refusal) | kinetic mode (D/L/T) | ABSENT | an independent observable of binding state |
| Lmotor-1 | mean-one Weibull hazard — a likelihood FORM | dwell survival; the D-L-T mixture is the mechanistic version and lives in a DIFFERENT implementation | PARTIAL | the hazard derived FROM the D-L-T kinetics rather than assumed |
| blanket | a = ∅ — "a partition without active states is not a full Markov blanket": a conditioning set | the MOTOR's blanket (PMF/torque sensing, engagement as action) — entirely unobserved in this dataset | ANALYST'S, NOT MOTOR'S | instantiate the motor's blanket and test μ ⊥ ψ | b — untestable today because ψ (load, PMF, temperature, CheY-P) was never recorded |
The units test decides it: the only units anywhere in this stack are seconds and counts — no torque, no load, no PMF, no temperature. A biological hierarchy is a composition of maps WITH units (ions/s → pN·nm → s⁻¹). Full statement and the eight-rung biological ladder: the classroom whiteboard.
Six layers named, five built. One deliberately left empty — and that refusal is the most disciplined thing in the model.
Two parameters for eighty motors. That is the whole design: a model with 80 free per-motor shapes would fit 80 numbers to a median of 7 events each and could not be scored honestly.
The flat curves below are not our models — they are the baselines a hierarchy must out-predict to earn its layers. Two fair ways to score, and they disagree about the ordering.
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Motor-equal gives every motor one vote, so a chatty motor cannot dominate — it is the honest unit, because the motor is the biological replicate. Event-pooled counts every dwell equally. The hierarchical model ranks 3rd on one and 5th on the other. The flat lognormal currently leads both — retained here because a baseline beating the mechanism is a result, not a blemish, and it is what the next layer has to overturn.
Each bar is one held-out motor's score under the hierarchical model. This is the reason every comparison says NOT_ESTABLISHED.
Our two-timescale mixture against the three models it must beat. A bar crossing the zero line means the comparison is undecided.
Positive = our mixture predicts better. Bars are 95% paired motor-cluster bootstrap intervals. Only the comparison against the memoryless null clears zero.
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One study, one species, one world process: E. coli stator dwell times from tethered-cell electrorotation-release, step-fitted at 0.02 s. The split is frozen by a hash of the motor id and never recomputed; any per-event mismatch halts the run.
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