C2OGate: Externally Checkable Joint Stopping-Time Certification for Cost-Dominant Continuations

Abstract

C2OGate is a research software and reproducibility archive for certifying whether a proposed optimization continuation is cost-dominant relative to an unchanged baseline continuation. Conditioned on one observed first-order transcript, the method retains the joint dependence of the two continuations’ first-hitting times and enumerates their attainable stopping-time cells. Every cost-violating cell is reduced to a dimension-free Gram semidefinite program. The workflow deliberately separates numerical discovery from acceptance. An untrusted producer searches for dual exclusion certificates; an independent consumer reconstructs every cell model from semantic parameters in exact rational arithmetic and checks multiplier signs, stationarity, the dual objective identity, and positive rational LDL^T pivots. Solver status and producer-generated coefficient matrices are not trusted. The public decision is three-valued: accept, reject, or uncertified. Missing, invalid, or unresolved evidence fails closed to uncertified. Version 0.9.2 is the frozen software, certificate, data, manuscript, and supplementary-material snapshot prepared for submission to Optimization Methods and Software. It contains: • the C2OGate Python implementation and tests;• exact rational semidefinite-programming certificate payloads;• standard-library and independent SymPy consumers;• frozen, hash-bound computational and empirical records;• a nonselective 123-date SPY options audit using ThetaData quotes and independently sourced WRDS underlying quotes;• redistributable benchmark data and a synthetic market-data transformation fixture;• complete Taylor & Francis manuscript and supplementary source; and• submission-ready manuscript and supplementary PDFs. The principal infinite-class experiment has certified horizon H=6. It excludes all 28 cost-violating cells with 28 exact rational dual certificates and 448 positive rational pivots, while sharp separately conditioned marginal bounds reject. A horizon-H=10 proof-production suite verifies all 66 bad cells and 1,584 pivots. The 123-date SPY audit verifies every date after all declared costs, with median and worst all-in cost ratios of 0.806 and 0.979. Certificate discovery remains a heuristic success-or-fail procedure; exact verification and fail-closed aggregation are the guaranteed components. Raw ThetaData and WRDS subscription rows are not redistributed. The archive contains the hash-bound derived replay inputs, rational matrices, stopping records, and cost ledgers used in the manuscript, together with a redistributable synthetic fixture exercising the same transformation path. Recommended verification commands: python -m pip install -e ".[pep,certificates,dev]"make smokemake checkmake verify Public repository: https://github.com/LiGentle/C2OGate Version DOI: https://doi.org/10.5281/zenodo.22872788Persistent all-versions DOI: https://doi.org/10.5281/zenodo.21964073