This run used the repository virtual environment. Its reported backends were python-flint, with both mpmath.iv and python-flint available. The script reconstructs exact rational prime-log vectors first, then evaluates them through both directed interval routes at 35 and 70 requested digits.
The five selected supports were 12,18,48,95,192, giving local limits 12,32,48,97,192. Ordinary-composite retention failures, prime-power retention failures, and cap-equality failures were all zero in every case. The saturated repair equals the exact Mangoldt repair on each local range, so saturation_repair_residual is the empty exact vector. Separately, the exact positive surplus is S = sum_{d<=N} Lambda(d)(W_d-1)_+: it is nonzero, and the current full total remains factorial + P_Lambda = psi(N) + S.
id: paid-shortfall-saturation-2026-09-13-check-001
hunt: paid_shortfall_saturation
started: 2026-09-13T22:28:03-05:00
finished: 2026-09-13T22:28:14-05:00
ran:
- .venv/bin/python hunts/paid_shortfall_saturation/saturation.py --output hunts/paid_shortfall_saturation/results.json
artifacts:
- hunts/paid_shortfall_saturation/results.json
outcome: Five finite selected-prefix cases passed exact saturation and surplus identities with two-backend interval overlap checks