What was already known
Gruica, Bar-Lev, Ravagnani and Yaakobi posed the duality equivalence as Conjecture 1 in their random-access DNA-storage study.
AI involvement
The project credits OpenAI Codex with the complementary-recovery argument and Lean proof. A human directed the research, questioned scope and reviewed presentation.
The project credits Codex with the complementary-recovery argument and Lean proof. A human directed the question, challenged the scope and reviewed presentation. The credited mathematical work supports AI-led involvement.
Importance
Settles a stated coding-theory conjecture by a coordinatewise expectation identity.
Limitations
The coordinatewise sum uses recovery time zero for a coordinate known to be zero; an alternative one-read convention needs a correction. Sampling is uniform with replacement, and independent expert review remains open.
Technical verification
The pinned repository reports a successful Lean rebuild and standard-axiom audit. Its completed `codeRecoveryBalanced_dual_iff` theorem covers the duality equivalence under the stated time-zero, uniform-with-replacement convention. This is source-reported; AIProofWatch did not rerun it.
Formal checking
The repository reports a public Lean rebuild from commit 80e4dbf and a standard-axiom audit. The completed theorem codeRecoveryBalanced_dual_iff proves the exact duality under the stated expectation convention.
- Checker
- Lean kernel, as reported by MathIsEvenEasier
- Scope
- For every linear code of length n and encoded coordinate i, the expected uniform-with-replacement recovery reads satisfy a_i(C)+a_i(C⊥)=n under the time-zero convention; therefore C is recovery balanced exactly when its dual is.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. The sources describe human direction and presentation review but do not document a named person explaining the central proof. Few is the default from this evidence gap, not a finding that people cannot understand it.
Correction and publication history
Primary theorem, prior baseline, AI attribution and documented proof scope reviewed for non-notifying local inclusion.
Read this published revision