Verification record · AUDIT-DS-STABLE-MARGINS-COMPILE
Publication-grade audit of DS16 stable margins and the compile verdict
Verification recordpublication: internalno direct precedent found
Statement
Independent audit verdict: DS-STABLE-MARGINS-PRICE, DS-PROFILED-COMPILE-CERTIFICATE, and DS-STABLE-STATE-SELECTION are all hardened. PRICE/FUNNEL/FLOOR survive after replacing a pointwise SLLN at a data-dependent centroid limit with a compact tilt-codebook uniform strong law, making the all-labelings event pathwise and measurable, distinguishing v*+(kappa) from v*(kappa), and fixing the raw-label/exact-centering convention. The compile verdict is restricted to the only currently established unconditional registry path; DS14 applies to certified sequences, not one finite diagnostic, and certificate-branch inhabitation remains open. Independent Fraction arithmetic reproduced both fixtures and four exact census instances; an N=100 public-library run reproduced the centered nuisance collapse and non-centered retention. The census range is corrected to 5-944, and 0.004-0.046 is qualified as an aggregate researcher summary rather than a per-run bound. Primary-source search found codebook-rigidity prior art but no direct combined theorem, so search_gap remains a claim-specific conclusion, not novelty.
Assumptions
the audit session did not produce DS16 and froze source commit 1b58518
the exact audit harness is pure stdlib Fraction code and does not import py/ds_stable_margins.py or reuse its classification logic
the theorem verdict is restricted to d_psi = d_lambda = 1, K >= 3, equal weights, exact scores, class (L)+(S), raw fixed-rule labels and centered empirical moments
the measured verdict does not assert an asymptotic basin-selection theorem
Closest prior work
- Rakhlin, Caponnetto (2006)Stability of K-Means Clustering
- Telgarsky, Vattani (2010)Hartigan's Method: k-means Clustering without Voronoi
- Blanchard, Jaffe, Zhivotovskiy (2025)Consistency and inconsistency in k-means clustering
- Silvey (1978)Optimal design measures with singular information matrices
- Alsing, Wandelt (2019)Nuisance Hardened Data Compression for Fast Likelihood-Free Inference
Why each source is not this result: the search records
Nearest sources, checked 30 August 2026
Relationships
Evidence references
Reviewed inputs and supporting evidence; these are not proof prerequisites.
- Margin price and value funnel at arbitrary finite Ds labelingsDS-STABLE-MARGINS-PRICE
- Profiled compile verdict is selected by an observable certificate stateDS-PROFILED-COMPILE-CERTIFICATE
- Exchange-stable Ds states span both margin regimes; ascent selects the funnel at scaleDS-STABLE-STATE-SELECTION
- Variational form of the profiled objectiveDS-PROFILED-VARIATIONAL
- Scalar efficient-score upper problem is exactly solvable by dynamic programmingDS-SCALAR-EFFICIENT-DP
- Conditional finite-to-population Ds bridgeOPEN-DS-FINITE-POP-BRIDGE
- Margins dichotomy at global finite Ds optima (conditionally centered laws, scalar nuisance)OPEN-DS-MARGINS-AT-OPTIMA