Exact Certification and Guaranteed Termination for Two-Item Resource-Constrained Joint Replenishment

Abstract

Status: unrefereed candidate computer-assisted result offered for scrutiny. This release gives an exact proof oracle for two-item continuous-time joint replenishment with nonnegative linear average-rate resource constraints. It includes a resource-aware tail theorem and guaranteed finite termination for the stated two-item model, a real-coefficient cap-reduction lemma, and a certified algebraic family proving a relaxation-gap lower bound of approximately 1.11188959394. The archive passed producer-side fresh-extraction replay using solver-independent verifiers, mutation and fail-closed controls, 16 tests, and deterministic paper/figure rebuilding. These checks do not establish independent reproduction, formal verification, human peer review, field validation, novelty, priority, or operational benefit. The exact global gap, multi-item alignment and rounding, column-sparsity frontier, three-item oracle, robust uncertainty, calendar extensions, and 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.