Closure Order Stress Tests in Cosmological Inference A minimal protocol with toy models and BAO summary data

This record presents a minimal, reproducible protocol for testing the sensitivity of cosmological inference results to the order of inferential closure (e.g., fitting before aggregation versus aggregation before fitting). The work focuses exclusively on methodological robustness and does not propose new physical models, parameter extensions, or resolutions of cosmological tensions. Using progressively structured toy models, the protocol demonstrates that closure-order sensitivity can emerge when covariance, weighting, and artificial aggregation are simultaneously present. The same stress tests are then applied to publicly available BAO summary statistics (dzd_zdz) from 6dFGS, SDSS, WiggleZ, and BOSS. No detectable dependence on closure order is found for these distilled observables, indicating that BAO summary data are robust under closure stress tests. All analyses are intentionally restricted to fully open and transparently accessible data. No proprietary likelihood packages, paywalled supplemental materials, or restricted-access datasets are used. The record includes both a technical note (PDF) and a fully executed Jupyter notebook, enabling direct inspection and reproduction of all results. This work is intended as a lightweight diagnostic tool for pipeline-level validation and as a methodological reference for assessing procedural robustness prior to physical interpretation.