Exact Two-Item Resource-Constrained Joint Replenishment and Its Independent-Cap Relaxation Gap

Abstract

Status: unrefereed candidate computer-assisted result offered for scrutiny. This additive v1.2.0 release gives an exact proof oracle for two-item continuous-time joint replenishment with nonnegative linear average-rate resource constraints and determines the exact real-coefficient two-item independent-cap relaxation gap. It proves Gamma_(2,box) = gamma, where 1.111889593939396 < gamma < 1.111889593940297 and gamma is the relevant real root of 262 g^4 - 916 g^3 + 863 g^2 + 150 g - 375 = 0. The matching upper argument uses a symbolic critical interval and a complete 212-cell rational outer certificate; a separate 2,829-cell certificate provides a coarser cross-check. The tagged archive passed producer-side fresh-extraction replay: exact 92-entry manifest coverage, 17 tests, deterministic certificate and paper rebuilding, ordinary and optimized release gates, and re-hashed semantic mutation controls. These checks do not establish independent reproduction, formal verification, specialist human review, peer review, field validation, novelty, priority, or operational benefit. The unrestricted multi-item gap, alignment-aware multi-item relaxation and rounding, the column-sparsity frontier, a three-item oracle, and operational field validation remain open. Licence scope: software is MIT; original non-software contents are dedicated under CC0-1.0 to the extent the publisher holds the relevant rights. See LICENSE_SCOPE.md in the archive.