{ "complete": true, "four_full_quotient_integrations": "finished", "support_and_pair_moment_integrations": "finished", "clean_extraction_verification": "passed", "verified_input_hashes": 1385, "all_finite_prime_and_pair_counts": "passed", "results": [ { "m": 2, "span": 19844, "Q_lower": 7.6199897108687304, "q_printed": "7.61991945321770", "C_printed": "1.986930449098e-5", "beta_printed": "0", "margin_printed_inputs": 8.646580023922447e-07, "margin_exact": 8.646580042009622e-07, "strict_margin": 8.646580041943538e-07, "normalization_compatible": true, "exact_physical_profiles_equal": true, "arithmetic_hypotheses": true, "trial_sha256": "7a84917a63303375f37ff0d970070256937b12a2bad4761170f78587e1c88a75" }, { "m": 3, "span": 1357780, "Q_lower": 11.428883231398524, "q_printed": "11.42888323139851", "C_printed": "2.185545128531e-8", "beta_printed": "0", "margin_printed_inputs": 3.046680646574499e-08, "margin_exact": 3.0466810220915626e-08, "strict_margin": 3.046681021100312e-08, "normalization_compatible": true, "exact_physical_profiles_equal": true, "arithmetic_hypotheses": true, "trial_sha256": "4430ce5cd58f1bd4a695b047d7263301c4541e8b6a000dc99691779d8ef61aa7" }, { "m": 4, "span": 82234788, "Q_lower": 15.238578705875785, "q_printed": "15.23857870587577", "C_printed": "1.945365350719e-11", "beta_printed": "0.00015523001241465", "margin_printed_inputs": 1.6832017428197047e-09, "margin_exact": 1.683205693726847e-09, "strict_margin": 1.683205680512183e-09, "normalization_compatible": true, "exact_physical_profiles_equal": true, "arithmetic_hypotheses": true, "trial_sha256": "acd55123c9ea5cd195b9316bb9bbd4b33ff512c1ff6930a789cf8f591f5c32d8" }, { "m": 5, "span": 4830355416, "Q_lower": 19.048047627456253, "q_printed": "19.04804762745624", "C_printed": "1.491020798040e-14", "beta_printed": "0.00014210693394371", "margin_printed_inputs": 2.094743164481457e-05, "margin_exact": 2.094743164822735e-05, "strict_margin": 2.094743164821083e-05, "normalization_compatible": true, "exact_physical_profiles_equal": true, "arithmetic_hypotheses": true, "trial_sha256": "e84db4db1193dc58df64e5fdb3138e608c0463e5f41ef012f5b9f3d2b11e01d0" } ], "log": "completed_logs/clean_package_checks_complete.log", "proof_pdf_sha256": "cb73d2497330feff1705e2947dd14a70ddcff7af4dd177b376f93ace22fe4794", "scope": "Computer-assisted proof using the cited distribution theorem, MPFR directed endpoint arithmetic, and the supplied mathematical error bounds; not a proof-assistant formalization." }