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2026-06-09Add MNIST real-data validation of e0 theorem and estimatorYurenHao0426
New script validates both no-fit claims on MNIST-subset MLPs. e0 theorem: 16 configs, hidden share 0.39-0.82, measured E_B[e0] within 0.0001-0.0089 of prediction (512 real-backward draws each). Estimator: 96 trajectories, velocity MAE 0.00196 (3.9% of mean gap), bias -0.0006, beating fixed K(0) everywhere; kernels computed via a layerwise gram identity self-tested against autograd at machine precision. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-09Record evidence ledger and wrap-up correctionsYurenHao0426
Note 36 consolidates the full evidence chain (numbers, figure sources, negative results, claim discipline) as the paper-writing base; note 37 records the two audit fixes; superseded banners on notes 00/03; README index updated. Superseded alignment_recovery_dynamics probe removed. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-09Add closed-form soft-ramp theorem and matched comparisonYurenHao0426
Closed-form gap law note (34) + consolidated snapshot (35), with the comparison script reading the dense run's config/gaps from its output dir and evaluating the closed form on matched data and init seed plus a multi-init band. Corrected headline: corr(log,log) 0.933 matched / 0.982 five-init geometric mean; lam_min ensemble corr 0.987. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-06-07Add complete markdown draftYurenHao0426
2026-06-05Validate exact initial FA erosion distributionYurenHao0426
2026-06-05Test first order FA tangent hierarchyYurenHao0426
2026-06-05Review methods for FA operator dynamicsYurenHao0426
2026-06-05Derive actual FA initial operator momentYurenHao0426
2026-06-05Clarify proof and estimator statusYurenHao0426
2026-06-05Position Song Xu Lafferty related workYurenHao0426
2026-06-05Separate estimator from nonzero cost theoremYurenHao0426
2026-06-05Compare soft erosion theory distributionsYurenHao0426
2026-06-05Add effective capacity literature and gap theory noteYurenHao0426
2026-06-05Clarify soft erosion scaling claimYurenHao0426
2026-06-05Revise capacity theory to soft erosionYurenHao0426
2026-06-05Record dense soft capacity transitionYurenHao0426
2026-06-05Add phase transition trajectory zoom analysisYurenHao0426
2026-06-05Analyze phase transition training timeYurenHao0426
2026-06-05Add contribution roadmap and phase transition plotYurenHao0426
2026-06-05Record systematic low bias analysisYurenHao0426
2026-06-05Stress test early-kernel operator predictorYurenHao0426
2026-06-03Add early-kernel operator predictorYurenHao0426
2026-06-03Check directional predictor across NYurenHao0426
2026-06-03Probe early kernel predictorsYurenHao0426
2026-06-03Add time-varying kernel diagnosticYurenHao0426
2026-06-03Investigate finite-T kernel errorsYurenHao0426
2026-06-02Plan finite-time tangent extensionYurenHao0426
2026-06-02Record T5 local tangent validationYurenHao0426
2026-06-02Record fixed-width capacity probeYurenHao0426
2026-06-02Record short SGD tangent validationYurenHao0426
2026-06-02Replace transition theory with tangent capacityYurenHao0426
2026-06-02Add BP-calibrated transition theoryYurenHao0426
2026-06-02Record 256-trajectory transition analysisYurenHao0426
2026-06-01Add downstream capacity threshold validationYurenHao0426
2026-05-29Add trajectory gap distribution bridgeYurenHao0426
2026-05-29Add initialization coverage distribution matchingYurenHao0426
2026-05-29Add multilayer capacity distribution matchingYurenHao0426
2026-05-29Add large empirical capacity validationYurenHao0426
2026-05-28Add trajectory ensemble validationYurenHao0426
2026-05-28Add hidden gradient alignment metricYurenHao0426
2026-05-28Add synthetic FA trajectory validationYurenHao0426
2026-05-28Add functional capacity overlap simulationYurenHao0426
2026-05-28Add prior-free minimax initialization simulationYurenHao0426
2026-05-28Add capacity scaling calculationsYurenHao0426
2026-05-28Add static alignment beta validationYurenHao0426
2026-05-28Initialize project notesYurenHao0426
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