Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 111-01. One Sample Suffices for Matroid Prophet Inequalities against an Almighty Adversary
Manuscript map · lines 4635–4644
OpenAI@2026-10-07#rem:oai-p-111-01
Authors: OpenAI. Family 111.
Title: One Sample Suffices for Matroid Prophet Inequalities against an Almighty Adversary.
Abstract: We prove that one independent sample per element suffices for a constant-competitive prophet inequality on every finite matroid. The guarantee holds even when the arrival-order adversary observes all samples, all online values, and the algorithm's entire random seed. The rule needs no description of the value distributions and achieves the absolute competitive ratio $2{}{-310}$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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