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arXiv · 2609.34424

Construction-Reuse Trade-offs for Exact Certificates in Fixed-Rank Threshold Screening

Zisu Li·Jingyang Du
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Abstract

Repeated threshold queries may reuse selected identities without reusing stale reports, but cheaper certificates need not shorten the complete response. We study selected-lower, atomic-upper (SLA) certificates for fixed-rank conjunctive screening with explicit missing-information semantics. An endpoint characterization and a counterexample separate same-source containment from policy-dependent online behavior. The original 320-session experiment reduces summed construction medians by 31.18% against an exclusion-cover certificate, yet its Cover/SLA full-API geometric time ratio is 0.9682 (95% conditional blocked interval 0.9593-0.9769), and SLA takes 12.94% more summed time than uncached Bitmap. Three separately launched complete repeats preserve this adverse ordering, with Cover/SLA ratios of 0.9665-0.9718. An additional 720-configuration exploration varies catalogue size, construction period, requested count and query locality on empirically resampled tables. SLA is faster in 295 configurations against Cover and 271 against Bitmap, descriptive counts that do not establish universal superiority. Separately instrumented additive costs distinguish construction savings from retrieval and report costs. A plane-stress component case adds an independent analytical displacement check and 4,608 boundary-challenging queries: five implementations agree exactly, while medium- and fine-mesh selections differ at 459 positions. A state-stratified public bolt-record exercise preserves 185 incomplete positions among 1,479 requests. Raw timings, complete configuration results and a tested clean-environment package support reproducibility. The SLA construction was explored and refined through the self-evolving AI system ZiYor; the named authors specified, implemented and evaluated it. This is a bounded mechanics-to-query study, not physical joint qualification or universal speedup.

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Zisu Li, Jingyang Du. 2026-09-28. Construction-Reuse Trade-offs for Exact Certificates in Fixed-Rank Threshold Screening. https://arxiv.org/abs/2609.34424

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