The Circularity Is a Property of the Criterion

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-16
DOI
https://doi.org/10.5281/zenodo.22786899
Primary Topic
Stochastic Gradient Optimization Techniques
Type
preprint
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preprint

The Circularity Is a Property of the Criterion

Ray David Crowell
Zenodo (CERN European Organization for Nuclear Research)
Stochastic Gradient Optimization Techniques
preprint

The Circularity Is a Property of the Criterion

Ray David Crowell
preprint en

Abstract

Been chasing a proof strategy for months and it feels like it should be working? Check whether your certificate is just your conclusion wearing a different vocabulary. Takes one minute. If you work on positivity, semidefinite programming, moment problems, or positive-definite functions in signal processing, you've probably been offered one of these: sum-of-squares, positive Cholesky, Bochner positive-definiteness, Carathéodory–Toeplitz, the Toeplitz symbol. All five are provably the same statement as the conclusion, so a search for any of them can never return "not found, keep looking" — the search is the test, and it terminates instantly. Ask one question: does the certificate exist exactly when the property holds? Yes means the route is dead before you start. And a warning if you test this numerically: we built a fake certificate that agreed with the truth on 100% of 20,000 random matrices and was wrong on thousands once we aime

Zenodo (CERN European Organization for Nuclear Research)
Cognitive Technologies (United States) (US), Cognitive Research (United States) (US)
Peace, Justice and strong institutions
Stochastic Gradient Optimization Techniques
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The Circularity Is a Property of the Criterion — Ray David Crowell · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS