AI Proof WatchKeep up with AI contributions

Ten Advances in Mathematics and Theoretical Computer Science

OpenAI

For every relative binary distance 0<δ<1/2, Chapter 2 gives an asymptotic rate bound strictly below the classical MRRW bound. Companion spherical-code bounds improve the localized linear-programming hierarchy for 0<s<1.

Sources for this record

What was already known

MRRW and Delsarte linear-programming bounds were the longstanding binary and spherical baselines.

AI involvement AI-led

OpenAI attributes the argument and Lean formalization to Astra. Humans chose the problem and prepared the manuscript.

OpenAI’s original disclosure assigns the argument and subsequent Lean formalization to Astra; human manuscript preparation is separately credited.

Importance Notable

Improves upper bounds across fixed code parameters.

Limitations

These are asymptotic bounds, not exact finite-length maxima. The binary and spherical Lean targets are separate; human reviewers flagged representation-theoretic and compactness steps for further explanation.

Technical verification Formal (Lean 4.32.0 with Mathlib and Comparator + human)

The project reports a complete Lean certificate for the stated formal theorem. Human assessments have narrower scope; semantic matching and any manuscript gaps remain separately noted.

Independent checking

chapter-specific mathematical review of the published argument, with the limited coverage summarized in the audit. Table 1; Chapter 2 discussion

Checker
Chapter 2 human reviewers in the Sienicki et al. review corpus
Scope
binary and spherical bound structure and selected numerical claims
Basis
Reported by the linked checker
Evidence source

Formal checking

Lean 4.32.0 formal certificate in MetricCodes.lean; comparator target for MetricCodes.Johnson.binaryRate_lt_mrrw; manifest reports zero sorry and only standard axioms. main_results entry MetricCodes.Johnson.binaryRate_lt_mrrw; status and axioms

Checker
OpenAI ten-proofs project, Lean kernel and Comparator configuration
Scope
binary rate below MRRW and strict spherical hierarchy
Basis
Reported by the linked checker
Evidence source

Checking a formal statement does not establish that it matches the original problem.

Human understanding Partial

Human reviews examine numerical and structural claims, while representation-theoretic and compactness interfaces are singled out for further specialist explanation and checking.

Correction and publication history