What was already known
Earlier constructions gave linear-size lower bounds; the paper compares with Reading’s n−1+floor((n−2)/2) bound.
What changed and why it matters
Improves a linear construction scale to n log n and connects Bruhat order with low-discrepancy permutations and representation-theoretic applications.
The AI contribution
AlphaEvolve suggested promising permutations; the named mathematicians recognized the digitwise structure and supplied the theorem and its applications.
Limitations
The displayed exact construction is for powers of two and does not determine every exact maximum. Humans identified, generalized and proved the pattern; this is not an autonomous AI proof. AIProofWatch has not audited the argument.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
The source reports this precise contribution; statement review does not establish a proof audit.
Accessible artifact / proof
Accessible supporting proof or code; not compiled or reproduced by AIProofWatch.
Correction and publication history
Public-discussion audit found this substantive scoped contribution missing. Source statement, baseline, attribution and importance reviewed; no full proof audit. Historical addition without subscriber alerts.
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