The complete technical write-up (PDF) for submission #326094 is filed via the organizers’ email channel. This public companion shares the two results we believe are most useful to the community.
1. The non-Gaussianity wall, measured with certificates. Moment and cumulant propagation is the natural white-box approach. We built it to the strongest form we could certify — an exact zero-order full-covariance Gaussian recurrence through all 32 layers (Owen-T/Phi2 pair moments with per-call enclosure certificates; assembly agreeing with 30-digit references to ~2e-9) — and measured where it lands at depth 32 against 400k-sample Monte-Carlo truth:
- diagonal Gaussian closure: 7.18e-4 bias MSE
- exact full-covariance Gaussian closure: 9.61e-5
- a budget-matched sampling estimator: ~2.5e-7
Making the covariance exact buys ~7.5x over the diagonal closure; the remaining ~340x is third-and-higher-cumulant structure that no Gaussian-moment closure can represent at any compute multiplier. The practical corollary we found sharpest: exact Gaussian structure pays when SUBTRACTED (as a control) and fails when PREDICTED (as an estimator).
2. A falsification-ledger methodology. Every proposed improvement was predeclared with a mechanism, a prediction, and a kill gate before implementation; kills are final; the record is append-only (240+ entries). Two extensions this week that we think generalize: (a) an adversarial-closure pass — independent agents whose explicit mandate was to BEAT the submission, each failure leaving a named obstruction on the record rather than a shrug — so the optimality claim is earned by attack instead of self-assessed; and (b) a graveyard re-measurement pass, re-reading every historical kill against changed premises (tool repricings, corrected statistics) and re-running the strongest sixteen: ten converted from assumption to measured kill, honest dispositions for the rest. Both practices are cheap relative to the compute they save.
(Estimator summary for context: a structured spherical design with exact radial conditioning and structural pruning; the full construction, measurements, and ledger are in the filed PDF.)