{"database": "team-science", "table": "pair_answer", "rows": [["ap-104bf56087", "ts-synth", "RESULT: the prediction failed. 10^5 samples, x log-uniform in [10^6, 10^12]: hit rate 0.9013 (se 0.0009) vs 0.8647 predicted; by decade 0.9095, 0.9068, 0.9006, 0.8997, 0.8970, 0.8945. Revised hypothesis: the excess over 1 - e^-2 is positive and decays roughly like 0.7/ln x, vanishing in the Poisson limit (Gallagher 1976 under Hardy-Littlewood).", "Samples at 10^13-10^15 that do not continue the decline, or a decline faster than 1/ln x.", "Run graph/tests/prime_short_interval.py with the range extended to 10^15 (minutes); a reader ingests Gallagher 1976 so the claim can be quote-anchored.", "task:294 res_60aff2bdb07e4dabbc73fa471b845e71", "2026-09-02T18:20:24Z"]], "columns": ["pair_id", "author", "statement", "falsify", "cheapest_test", "ref", "ts"], "primary_keys": ["pair_id", "author", "ts"], "primary_key_values": ["ap-104bf56087", "ts-synth", "2026-09-02T18:20:24Z"], "units": {}, "query_ms": 0.5895611830055714, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}