# Scientific Fourier discretization audit

Family 371, source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. Selected-source addendum, 9 October 2026 Australia/Brisbane. All earlier editions are preserved.

## Current decision

Prototype exact finite aliasing controls; defer a source blowup solver. No buyer interview, paid pilot or profitability evidence has been obtained.

## Reviewed finding and application boundary

The source products are infinite Fourier convolutions. The new bounded rational sparse reference detects a phantom coefficient on an undersized circular grid and distinguishes central projection from full reconstruction. The twelve-dimensional blowup quantifier still selects arbitrarily large odd powers; a cubic fixture tests multiplication semantics only.

## Evidence extent

- [main.tex](../../../../../source/openai-math/preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026/build/main.tex): lines 1–190. Abstract, main twelve-dimensional selected-power blowup/open-set result, Gaussian corollary, probability boundary and selected methods; no full profile/spectral certificate verification.

[Source metadata](source.json), [individual definition observations](../../definition-hole-review-queue-2026-10-09-v3.json), [manuscript ledger](../../../../checkpoints/manuscript-ledger-2026-10-09-v4.json). Selected definition/body and challenge comparison found no intended-model mismatch; imported dependency semantics, complete proof, independent kernel and executable correspondence are not verified. Intentional challenge placeholders do not establish source proof failure.

## Next action

Develop finite controls where they answer a concrete modeling question, inspect quantitative construction constants separately, and compare business usefulness with an existing expert workflow. Preserve unknown hypotheses and source claims explicitly.