f(n²,n) ≥ n + (1/√2 + o(1))√n and f(p²,p) ≤ 2p − (√(2/3) − o(1))√(p/log p) for large primes p.
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2 Pith papers cite this work. Polarity classification is still indexing.
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2026 2verdicts
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A witness-split and window-pruning SAT framework finds no 44-element 3-AP-free subset of [1,212] but leaves two resistant instances unsolved.
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Hitting Arithmetic Progressions at the Square-Root Scale
f(n²,n) ≥ n + (1/√2 + o(1))√n and f(p²,p) ≤ 2p − (√(2/3) − o(1))√(p/log p) for large primes p.
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Witness-split + window-cardinality refinement for $r_3(N)$: Architecture, empirical results, and a structural hard pocket
A witness-split and window-pruning SAT framework finds no 44-element 3-AP-free subset of [1,212] but leaves two resistant instances unsolved.