Detectability of Non-Equilibrium Signatures in the Kinetochore Oscillation

Verification: Detectability of non-equilibrium signatures in the kinetochore DI oscillation

Session: 2026-06-10-scout-033 | Hypotheses: E2-H7 (broken-detailed-balance local probability-current curl certificate) and E2-H11 (trajectory-only entropy-production lower bound) | Verdict: INTERMEDIATE

What this verifies (and what it cannot)

E2-H7 and E2-H11 propose to detect and quantify the non-equilibrium drive of the mitotic

kinetochore directional-instability (DI) oscillation from tracking data, using stochastic-thermodynamics

estimators. The Quality Gate, GPT-5.5 Pro, and Gemini all agreed the load-bearing risk is detectability:

at the real experimental cadence (~2 s) with only a few oscillation cycles per cell and finite localization

noise, can these estimators actually resolve the signal? None of the three executed that test; the hypothesis

itself proposes a "synthetic-data power-analysis gate" as its mandatory first step. This verification IS that

gate. It is self-contained simulation: it establishes whether the method is mathematically sound and

statistically feasible in an idealized regime. It does NOT use real kinetochore data and therefore cannot

settle the real biological claim or the systematic-artifact risks that require real trajectories.

Model

A kinetochore-calibrated 2D rotational Ornstein-Uhlenbeck process (the canonical minimal non-equilibrium

steady state, same structure as Battle 2016 / Gladrow 2016): dx = -(kI + omegaJ)x dt + sqrt(2 D0) dW,

calibrated to period T = 100 s, per-coordinate amplitude R0 = 1000 nm, observation cadence dt = 2 s. The

entropy production rate is analytically known, sigma = 2 omega^2 / k (per cycle 4*pi*omega/k), and the

mean signed-area-rate circulation is -omega * R0^2; both vanish exactly at equilibrium (omega = 0), giving

a clean ground truth and a faithful equilibrium null.

Results

**Part A - the 1:2 Lissajous net-circulation cancellation (E2-H7 core identity): CONFIRMED to machine

precision.** When centromere stretch oscillates at twice the kinetochore frequency, the net signed

circulation of the trajectory is exactly zero (|net area| = 6e-15), while the 1:1 control matches the

analytic -pi*A*B*sin(delta) to 4e-8. This reproduces, and pins down numerically, the insight that a naive

net-circulation test would read "equilibrium-like" on a genuinely driven kinetochore - the reason the

hypothesis is forced onto the LOCAL curl instead. (Independently confirmed earlier by GPT-5.5 Pro and Gemini.)

Part A2 - local curl survives: CONFIRMED. The estimated local probability-current field of the simulated

NESS has a mean curl of -0.128 /s, matching the exact analytic value -2*omega = -0.1257 /s. The local curl is

nonzero everywhere even though the global moment can cancel - exactly E2-H7's claim.

Part B - statistical power: STRONGLY FAVORABLE (refutes the low-cycle-count pessimism). Detection

probability of the driven oscillation against an equilibrium twin is ~99-100% at every tested condition:

as few as 5 cycles, with localization noise up to 50 nm (5% of amplitude), down to entropy production as

low as ~3 k_BT/cycle. The reason is concrete and was missed in the qualitative worry: at 2 s cadence and a

~100 s period there are ~50 samples per cycle, so even 5 cycles is ~250 samples - ample for a pooled

circulation statistic. Handedness (powered-stroke sign) is recovered correctly in essentially all detected

cases. White localization noise averages out of the cross-product estimator in expectation and only mildly

inflates its variance.

Part C - slow-drift stress test: this particular nonstationarity is benign. An independent slow

random-walk drift (up to 300 nm RMS) added to each coordinate does NOT inflate the equilibrium false-positive

rate (stays at/below the nominal 5%) and does not degrade power, because an independent per-coordinate drift

carries no systematic cross-correlation and averages out of the signed-area statistic. Linear detrending is a

cheap, sufficient safeguard.

Interpretation and verdict: INTERMEDIATE

The mathematical core of E2-H7 (net cancellation + surviving local curl) is confirmed exactly, and the

statistical feasibility that all three validators flagged as the binding risk is, in the idealized regime,

not a problem at all - the method has ample power at realistic kinetochore sampling. This is a genuinely

useful, decision-relevant result: it removes the single most-cited reason to doubt the hypotheses.

It is graded INTERMEDIATE rather than CONFIRMED because the idealization does not stress the threats that a

clean rotational-OU model cannot represent and that GPT-5.5 Pro specifically flagged: (1) the (b, db/dt)

velocity embedding, where finite-difference velocity from noisy position can manufacture spurious

irreversibility; (2) correlated / phase-shifted nonstationarity (not the benign independent drift tested

here); (3) role-labeling by velocity sign baking the arrow of time into the statistic; (4) metaphase

nonstationarity of the oscillation amplitude and period. These are systematic, not statistical, and can only

be settled on the real Burroughs/McAinsh (PMID 26460545) or RPE1 lattice-light-sheet trajectories with proper

surrogate controls (time-reversal AND phase-randomized), which is the correct next step.

Bottom line for the hypotheses

• E2-H11 and E2-H7 are computationally sound and statistically feasible on data of the resolution that

already exists. The method is not hopeless at low cycle counts - the opposite.

• The remaining risk is implementation artifact control on real data, not detectability.
• This verification establishes method viability; it does not establish that the kinetochore IS measurably

irreversible (that needs the real tracks) nor anything about chromosome-segregation fidelity (which the

hypotheses correctly disclaim lies a factor ~10^4 away on the biochemical tier).