Conditional mathematical models

Run from the repository root with Python 3.10+ (standard library only):

python3 -m unittest discover -s papers/07-release-packet/models/math -p 'test_*.py' -v
python3 papers/07-release-packet/models/math/run_experiments.py

Read math-foundations.md for definitions, proofs, caveats and a claim ledger. These are synthetic modeling primitives, not an operational protocol implementation. The adjacent agent simulator supplies the behavioral event trace; no authority or production interface is implied here.

• panel_distribution: exact declared-group panel probabilities; compare uniform group-first selection with uniform feasible representative selection.
• retry_summary: offered/completed selection, bounded IID retries, unresolved probability and resource costs.
• envelope, repair_bound: verify a supplied common positive witness and bound expected cumulative weighted repair under stated conditional assumptions.
• shared_capacity: add commitments across lanes for each person/epoch; no skill, deadline or legal feasibility is inferred.
• audit_interval, action_utilities: one-shot effort, participation and funded audit comparison; not a repeated-game or institutional equilibrium.

results/summary.json records hashes, seeds and all four Monte Carlo cases. CSV sweeps contain 12 panel, 20 retry, 42 repair and 41 audit rows (115 total). Twenty-one tests include independent finite enumeration oracles and explicit counterexamples. Monte Carlo intervals are pointwise nominal 95%; the Monte Carlo request count is 80,000. No intervals represent human-behavior uncertainty.

source-map.json distinguishes primary source verification from self-contained new derivations and prior dossier material. No remote source is fetched at run time.

Operational non-goals include identity verification, general feasible-panel construction, capacity scheduling, complete dependency discovery, currentness transport, authenticated authority, legal compliance and empirical validation. Positive finite scalar input validation does not certify all floating-point ranges; use the supplied toy range and fail explicitly on unsupported extensions.

RM-1 repair: audit_interval limits expected expenditure only; hard_audit_interval and blinded_audit_sample add a fixed-population identical-cost hard count cap. Concealment and actual audit delivery are external obligations.

Hard-audit endpoints use exact rational strings (maximum_audit_exact, minimum_audit_exact); supply these or Fraction inputs to the sampler. Decimal floats are interpreted through their printed decimal. The float upper display rounds down and is safe for the cap, but exact fields govern singleton feasibility.

Displaying exact audit intervals

Use the rational minimum_audit_exact and maximum_audit_exact fields for decisions and human-facing intervals. For a singleton [5/6, 5/6], convenience float endpoints can appear reversed because the upper display is rounded down. Do not infer feasibility by comparing those floats; the exact fields and returned feasibility result are authoritative, and the sampler accepts rational strings.