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Witness-split + window-cardinality refinement for $r_3(N)$: Architecture, empirical results, and a structural hard pocket
arXiv:2606.04016v1 Announce Type: new Abstract: We describe a reproducible computational framework for upper-bound searches on r_3(N), the maximum size of a 3-term-arithmetic-progression-free subset of [1,N]. The framework combines a verified lower-bound witness, endpoint forcing, depth-d witness-variable splitting, OEIS A003002 window-cardinality pruning, and recursive refinement of timed-out subproblems. Applied to the frontier case N = 212, K = 44, it found no feasible 44-set across...