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When $k=4$, we show the bounds $91/240\\le \\lambda_3\\le 11/28$. For odd prime $k$, we analyse the binary case $q=2$ via a phase reduction on rotation orbits. For $k=11,13,17$ this yields compact orbit-marker certificates for optimal constructions. 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When $k=4$, we show the bounds $91/240\\le \\lambda_3\\le 11/28$. For odd prime $k$, we analyse the binary case $q=2$ via a phase reduction on rotation orbits. For $k=11,13,17$ this yields compact orbit-marker certificates for optimal constructions. Combined with a lifting theorem by Lichiardopol, these certificates give exact formulas for $\\"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive the asymptotic formula α(k,q)=λ_{k-1}q^k+o(q^k), where λ_{k-1} is a constant arising from a variational problem on the unit (k-1)-dimensional cube. ... For k=11 and k=13 this yields certified optimal constructions, which combined with a lifting theorem by Lichiardopol give exact formulas for α(11,q) and α(13,q) for all q≥2.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The variational problem on the (k-1)-cube correctly captures the asymptotic density of maximum independent sets, and the phase-reduction constructions for odd-prime k are optimal in the binary case so that the cited lifting theorem extends them exactly to all q.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"α(k,q) = λ_{k-1} q^k + o(q^k) where λ_{k-1} arises from a variational problem on the (k-1)-cube; exact formulas hold for k=11,13 via phase reduction and lifting, with bounds 91/240 ≤ λ_3 ≤ 11/28 for k=4.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The independence number of the de Bruijn graph B(k,q) equals λ_{k-1} q^k plus a smaller term, where λ_{k-1} is the value of a variational problem on the unit (k-1)-cube.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"92c13cf0069f61e3c4215f223f17f5cd7733f28efe2f4203f82860a42046b3e0"},"source":{"id":"2604.14671","kind":"arxiv","version":2},"verdict":{"id":"5774d9a3-b8e5-4081-afce-5f747c6a8621","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T11:22:28.857098Z","strongest_claim":"We derive the asymptotic formula α(k,q)=λ_{k-1}q^k+o(q^k), where λ_{k-1} is a constant arising from a variational problem on the unit (k-1)-dimensional cube. ... 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