Verification software for A Split-Graph Counterexample to a Roman–Double Roman Candidate Inequality

Abstract

Offline, standard-library-only verification software accompanying Seth Christopher's preprint “A Split-Graph Counterexample to a Roman–Double Roman Candidate Inequality”. Version 1.0.0; source-only publication revision figshare.1. This item contains Roman_Double_Roman_Verification_Software_v1.0.0.zip, including the byte-preserved mathematical modules and original standalone verifier, a new strict-JSON wrapper, a new public process adapter, a bounded sequential replay instrument, and a separate LaTeX build driver. The software and its software-use documentation are offered under MIT to the extent applicable rights are held. The original full archives did not have a blanket MIT grant and are not redistributed here. Required companion inputsThe manuscript, exact inputs and research evidence are in the companion Preprint “A Split-Graph Counterexample to a Roman–Double Roman Candidate Inequality”, file Roman_Double_Roman_Manuscript_Source_and_Evidence_v1.0.0.zip, under CC BY 4.0. Merge the two extracted archives into their common Roman_Double_Roman_v1.0.0 directory. Their file paths do not overlap. ReproductionFrom the assembled directory run: python3 -I -S -B verification/check.py inputs/certificate.jsonFor the full bounded replay run: python3 -I -S -B reproduce.py --out ../roman_double_roman_replayUse a new external output directory. Expected replay status: SOURCE_ONLY_ROMAN_REPLAY_PASS. Full replay requires Linux and Python 3.10+; each serial child defaults to 60 wall seconds and 4 GiB address space. No network or model call is required. ScopeFresh public-source replay completed 15 bounded serial processes. The standalone check accepted the exact 15-vertex certificate, verified its upper witnesses and chordality, and exhausted all 42,129 Roman assignments of weight below seven and all 1,076,624 double Roman assignments of weight below ten. The original differential suite passed 1,323,108 assertions across 1,098 labeled graphs on two through five vertices, with 24 relabelings and nine deliberately invalid or unsupported certificates rejected by both production checkers. Additional protocol and strict-JSON rejections passed. These checks share authorship and are not independent peer review. No global priority, minimum-order counterexample, or proof-assistant-kernel certification is claimed. The public source generation is distinct from the original private-runtime generation. The host Python interpreter is not included in the protocol-generation hash. This source-only publication does not reproduce the private sandbox or claim confidential-read isolation. AI assistance: ChatGPT provided substantial assistance with question selection, the graph construction and proofs, source research, verification software, test execution, and manuscript preparation. Aurelia performed bounded candidate search; Selene checked adjacency-set and reduced-label obligations; Mica checked the full original label alphabets and freshly rechecked use. These are computational roles, not coauthors or independent peer reviewers. Seth Christopher initiated and directed the research programme and is the sole author responsible for the submitted content.