What was already known
A Simons workshop problem asked whether rerandomized subsampled trigonometric transforms could achieve O(r/ε²) embedding dimension; the conventional bound carried logarithmic factors.
AI involvement
Diar Heidary chose and directed the problem. AI agents developed substantive mathematical arguments and the Lean proof. A Claude critique prompted corrections aligning the report and formal statement; no independent human mathematical review is documented.
Agents are credited with substantive mathematical development and proofs within Heidary’s directed project; the evidence does not support autonomy.
Importance
Gives the sought row scaling for the specified Walsh-transform model at fixed confidence.
Limitations
It does not cover arbitrary trigonometric transforms or a constant uniform in δ. The Palomar submission was withdrawn during setup, though the source reports completed mechanical checks.
Technical verification
The source reports official mechanical verification and rendering on the identified September snapshot, with Lean and NanoDa replay; the Palomar submission was withdrawn during setup. This review did not rerun it.
Formal checking
Lean 4/Mathlib, Comparator and NanoDa
- Checker
- Palomar mechanical verifier, Lean and NanoDa
- Scope
- RerandomizedSTT.problem_5_6 with explicit Walsh law and row bound
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the finite-operator and sampling proof is documented; source-level model audits and AI critiques do not establish it.
Correction and publication history
Gives the sought row scaling for the specified Walsh-transform model at fixed confidence.
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