{ "status": "Numerical exploration, not an exact certificate.", "scope": "r=1,...,15; fixed factorial normalization and absolute-value profile.", "exact_single_value_scope": "endpoints.py proves every other integer r cannot improve a<=18m.", "results": [ { "B": 1, "best_in_scan": { "r": 2, "limiting_a_over_m": 17.57225289992264, "limiting_endpoint_slope": 18.57225289992264, "stationary_y": 0.004075478608682487 }, "scan": [ { "r": 1, "limiting_a_over_m": 21.88673088194184, "limiting_endpoint_slope": 22.88673088194184, "stationary_y": 7.736820860672428e-07 }, { "r": 2, "limiting_a_over_m": 17.57225289992264, "limiting_endpoint_slope": 18.57225289992264, "stationary_y": 0.004075478608682487 }, { "r": 3, "limiting_a_over_m": 19.49166984406955, "limiting_endpoint_slope": 20.49166984406955, "stationary_y": 0.026937403273106755 }, { "r": 4, "limiting_a_over_m": 22.18231068852095, "limiting_endpoint_slope": 23.18231068852095, "stationary_y": 0.06930359308394175 }, { "r": 5, 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