BAO Regularization in Paired H0/S8 Fits: A Source-Verified Clean-Core Audit

This technical note presents a source-verified clean-core audit of BAO insertion effects in four paired CosmoMC cosmological fits. The analysis is restricted to provenance-complete paired runs and reconstructs the BAO chi-square from official CosmoMC legacy BAO source files. Within the clean-core subset, BAO insertion is associated with a systematic decrease in H0 and increase in S8, with moderate corrected BAO chi-square and source-level reconstruction agreement at the ~0.003 chi-square level. The result is interpreted strictly as a local diagnostic audit and does not propose a new cosmological model or claim a resolution of the H0/S8 tensions. A supplementary public rerun helper has been added to facilitate independent verification of the clean-core audit from the published archive. It does not replace the frozen reproducibility package.