{ "what": "The lambda(5)/lambda(6) campaign record: Mercer's remaining conjectured values, lambda(5) = -L(1,2,4,5,6) and lambda(6) = -L(1,2,4,6,7,8), whose pair is the first non-monotonicity in the lambda sequence. Section-5 generic cases with exception families DISCOVERED by the symbolic inner product; family closures accumulate below.", "provenance": "Statement and strategy: Idris Mercer, INTEGERS 19 (2019) #A4 (arXiv:1709.06612). Engine: instruments/lambda4 (n-generic), calibrated at every run by re-deriving the lambda(4) generic case before any lambda(5)/(6) claim is computed.", "stages": { "calibration-lambda4-generic": { "ok": true, "base": "0", "dip": "-8/5", "exceptions": 14, "positive": 9, "extremizerActive": [ "2b = d", "2c = b+d", "a+c = d", "b+2c = 2d" ], "ms": 3 }, "targets": { "ok": true, "L4": { "A": [ 1, 2, 3, 4 ], "lo": "-855435038691829/562949953421312", "hi": "-6843480309534631/4503599627370496" }, "L5": { "A": [ 1, 2, 4, 5, 6 ], "lo": "-1832357810512957/1125899906842624", "hi": "-7329431242051827/4503599627370496" }, "L6": { "A": [ 1, 2, 4, 6, 7, 8 ], "lo": "-112015241955925/70368744177664", "hi": "-7168975485179199/4503599627370496" }, "initialSegments": { "seg5": { "A": [ 1, 2, 3, 4, 5 ], "lo": "-7785679854625841/4503599627370496", "hi": "-486604990914115/281474976710656" }, "seg6": { "A": [ 1, 2, 3, 4, 5, 6 ], "lo": "-273113652316289/140737488355328", "hi": 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