Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 114-01. An FPRAS for Common Integer Polymatroid Bases with Binary Capacities
Manuscript map · lines 4675–4684
OpenAI@2026-10-07#rem:oai-p-114-01
Authors: OpenAI. Family 114.
Title: An FPRAS for Common Integer Polymatroid Bases with Binary Capacities.
Abstract: We give a fully polynomial randomized approximation scheme for counting common integer bases of two polymatroids with the same total rank, supplied by exact rank-value oracles. The total rank and capacities are encoded in binary, and each integer vector is counted once. On every execution, the number of oracle calls and the bit work outside the oracles are bounded by a fixed polynomial in the ground-set size, the binary input length, the inverse relative-error tolerance, and the logarithm of the inverse failure probability. The algorithm handles binary capacities directly, without expanding them into labelled copies.
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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