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ASkotch: a regime map and an exact instability mechanism

This package has two distinct results. Neither refutes JMLR Theorem 17.

  • Matched available-budget study: 18 synthetic regimes, five seeds each, 270 selected models. Released ASkotch has lower mean test MSE in 13 of 18 regimes; the inducing comparator wins the other five. The experiment gives every method 12 candidates and a four-second cap per candidate. It does not equalize consumed time: inducing PCG often stops early. See the corrected primary report.
  • Exact rank-100 mechanism: at the released recommended block fraction and rank, the actual ten-step randomized power estimate yields a mean-square instability in an explicitly highly ill-conditioned RBF family. Theorem and assumptions. A fixed relative step of one has an exact expected-error repair on the same family. Repair.

Primary regime map

The retained finite float64 runs all converged. Expectation instability does not imply every realization fails. The runs use the unchanged optimizer with a structured kernel adapter, rather than the untouched full large KeOps pipeline. Float32 exceptions and all finite checkpoints are retained. Finite-run report. The 140-case moderate-conditioning search did not find a case meeting its instability threshold; this negative result is preserved in its report.

Reproduce bounded checks

From the repository root, with Python 3.11+ and NumPy installed:

python kernel/verify.py

This independently checks the rational covariance/certificate algebra, saved fixed-step certificate, all 72 retained finite states, all 54 paired regime comparisons, and the complete negative moderate-conditioning grid. It works on temporary copies, preserving released artifacts. It does not launch a benchmark, search for a failing seed, or contact a cloud service.

Original benchmark configuration and driver are in regime_replicates/. They require the pinned upstream implementation and its GPU environment; the verification command above recomputes reported arithmetic, not timings. The upstream implementation is fast_krr at commit 61cdb69. Primary paper: Have ASkotch.

The source-bound analytic reviews are internal AI-assisted checks, not external expert review, formal verification, or novelty certification. PUBLIC_PROVENANCE.json records original and public artifact hashes, including explicit removal of local machine paths and the corresponding protocol-hash update. Scientific measurements and proof equations are unchanged. Historical source snapshots mentioned in older notes are not a vendored copy of upstream code.