Variance attribution with an uncertain policy reaction
Scientific algebra supplement, 6 November 2026

Requirements: Python 3.8 or newer; standard library only.
Run from any directory:
    python3 verify_algebra.py
The script writes algebra_checks.json beside itself and prints the report.
A successful run reports all_passed: true and exits with status 0.

The 29 checks use exact rational arithmetic. Rate moments are independently
expanded by the multinomial theorem and independent Gaussian moments; they are
not obtained by differentiating the article's moment-generating formula.
Further checks cover coefficient duality, inverse identities, posterior
projection algebra, covariance-construction coefficients, and finite balances
used by the regular-crossing argument.

The output is an algebra check, not simulated or empirical data. It does not
mechanically prove the analytic uniformity and tail lemmas, identify an explicit
numerical posterior-crossing witness, check literature novelty, or establish
finite-sample performance. The self-contained analytical arguments are in the
accompanying article, especially Appendix A.

Files:
    verify_algebra.py       portable exact-arithmetic checker
    algebra_checks.json    expected reproducible result
    README.txt             these instructions and scope limits

No network access, external data, credentials, or machine-specific paths are
required. No external paper text is included.
