family_wall: run manifests

id: family_wall-2026-08-23-analytic-limit
hunt: family_wall
started: 2026-08-23T15:40-05:00
finished: 2026-08-23T19:10-05:00
ran:
  - .venv/bin/python hunts/family_wall/verify_chain.py
  - .venv/bin/python hunts/family_wall/structure.py
  - .venv/bin/python hunts/family_wall/witness_bound.py
  - .venv/bin/python hunts/family_wall/envelope_bound.py
  - .venv/bin/python hunts/family_wall/tiled_cover.py
  - .venv/bin/modal run hunts/family_wall/modal_family_limit.py
  - .venv/bin/python hunts/family_wall/compare_modal.py
outcome: the family saturates; its limit is H exactly and its supremum over all n is bounded by 0.6751676, short of the configuration ceiling by more than 0.0068, and the pressure-crossover lead was confirmed with a floor-defect correction of order 1e-6
artifacts:
  - hunts/family_wall/FAMILY-LIMIT.md
  - hunts/family_wall/artifacts/family-limit-modal.json
  - hunts/family_wall/artifacts/witness.json
  - hunts/family_wall/artifacts/compare.json
  - hunts/family_wall/artifacts/tiled-cover.json
  - hunts/family_wall/artifacts/periodic-energy-curve.json

id: family_wall-2026-08-23-independent-audit
hunt: family_wall
started: 2026-08-23
finished: 2026-08-23
ran:
  - an independent adversarial audit by a different model, in an isolated directory outside this repository, from the brief now at hunts/family_wall/audit/BRIEF.md
  - .venv/bin/python hunts/family_wall/chain_repair_check.py
  - .venv/bin/python hunts/family_wall/period37_check.py
  - .venv/bin/python hunts/family_wall/f7_point_check.py
  - .venv/bin/python hunts/family_wall/audit/periodic_certificate.py
  - .venv/bin/python scripts/71_contribution_check.py hunts/family_wall
  - .venv/bin/python scripts/make_context.py --check
outcome: the audit broke two steps of the inequality chain as written, supplied a case split that repairs them, replaced the tiled-witness coverage with an explicit period-37 word valid for every n, and sharpened the supremum to 0.675142509660254; the three checks above reproduce its counterexamples, its witness values and its constants here
artifacts:
  - hunts/family_wall/audit/PROVENANCE.md
  - hunts/family_wall/audit/results/REPORT.md
  - hunts/family_wall/artifacts/period37-check.json
  - hunts/family_wall/RESULTS.md

Notes

• The audit is the reason this hunt's argument changed. It ran with no access to this repository, from a brief committed before any work began (audit/PROVENANCE.md). It was asked to refute, and it refuted the argument, steps (A) and the move to the cap, both with admissible counterexamples, while failing to refute the claim. The repair and the new coverage are in FAMILY-LIMIT.md sections 2.1a and 2.3a. Everything under audit/ is the audit's own work; the only edit is one lexical substitution forced by this repository's reserved-vocabulary gate, listed exhaustively in audit/PROVENANCE.md.
• The 2.0e-13 in the n=7, p=3000 control is not a disagreement. 0.0038262312115073 is an Arb evaluation at a six-decimal argmin, so an upper bound on the infimum, and both independent minimisers correctly land below it. FAMILY-LIMIT.md section 3 has the three-point comparison; MISSION.md carries the correction to its own required_oracles wording.
• The Modal job's n = 20 cells missed basins that the analytic witness ladder reaches directly: at four pressures the ladder returned a lower functional value than the multistart search. The raw Phi_20 = 0.6731391381 from that job is therefore built on a value that is not a floor and is not a valid certificate number. Section 3 of FAMILY-LIMIT.md records the correction (0.6730928938). Anyone rerunning the Modal job at k >= 16 should enumerate more of the two-letter word space per shard than the 16000 used here, or seed from the ladder.
• The n = 10 .. 16 sweep running in parallel is a separate measurement; nothing here duplicates it, and its peaks are a further check against the section 2.3 bounds.
• Nothing in this hunt was run in exact arithmetic. Section 4 of FAMILY-LIMIT.md states which direction each float error can move a claim and which numbers would need Arb if the barrier is ever leaned on formally.