{ "what": "The Fauzan/Calegari Hankel-determinant irrationality method, measured: the exact content-normalised polynomial P of each family member and log P(ξ)/h², the margin (negative = the family proves ξ irrational). Ported from frontier-apps/experiments/zeta-hankel on 2026-10-05 (instruments/zetahankel/PROVENANCE.json); every per-instance number below was re-run on this machine from the lifted engine.", "generatedBy": "instruments/zetahankel/rerun.py", "generatedOn": "2026-10-05", "env": { "python": "3.12.13", "flint": "0.9.0", "machine": "arm64", "system": "Darwin" }, "rule": { "margin": "log P(ξ) / h², P the primitive integer polynomial of Δ(X) = det(A + XB) (content stripped exactly)", "ball": "[logP_lo, logP_hi]: arb evaluation of P(ξ) with rad < 2^-60 · value, log taken in arb, endpoints rounded outward to doubles; margin_lo/hi the same divided by h², outward", "agree": "the lifted value lies in the ball widened by 1.86e-09 (the lifted engine stopped at rad < 2^-30 · value)", "bitIdentical": "the engine's own float output here equals the lifted record's, bit for bit, and so does log_content" }, "scope": "Per instance: exact (P and its content are exact integers/rationals) and ball-certified (log P(ξ)). The wall — \"the class stops between ζ(5) and ζ(7)\" — is a measurement across the lifted families, extrapolated; not a theorem. The race context is UNVERIFIED by cert-machine.", "headline": [ { "key": "zeta3", "constant": "ζ(3)", "k": 3, "family": "Z_k3_int_a4_b1_r4", "h": 39, "margin": -1.379680944401696, "margin_lo": -1.3796809444016966, "margin_hi": -1.3796809444016955, "liftedMargin": -1.379680944401696, "agree": true, "bitIdentical": true, "sign": "negative" }, { "key": "zeta5", "constant": "ζ(5)", "k": 5, "family": "Z_k5_int_a8_b1_r6", "h": 35, "margin": -0.18513270501974533, "margin_lo": -0.18513270501974538, "margin_hi": -0.18513270501974527, "liftedMargin": -0.18513270501974533, "agree": true, "bitIdentical": true, "sign": "negative" }, { "key": "zeta7", "constant": "ζ(7)", "k": 7, "family": "Z_k7_int_a8_b1_r4", "h": 35, "margin": 1.0157239176780057, "margin_lo": 1.0157239176780055, "margin_hi": 1.0157239176780062, "liftedMargin": 1.0157239176780057, "agree": true, "bitIdentical": true, "sign": "positive" }, { "key": "catalan", "constant": "G", "k": 2, "family": "E_k2_half_a8_b1_r1", "h": 35, "margin": 0.428375085443837, "margin_lo": 0.4283750854438369, "margin_hi": 0.4283750854438372, "liftedMargin": 0.428375085443837, "agree": true, "bitIdentical": true, "sign": "positive" } ], "families": { "zeta3": { "constant": "ζ(3)", "k": 3, "spec": [ "Z", 3, "int", 4, 1, 4 ], "name": "Z_k3_int_a4_b1_r4", "record": "certs/zeta-hankel/runs/scan3/Z_k3_int_a4_b1_r4.jsonl", "record_sha256": "0039fb3b66f1f1cf46b58f4fea87d9c9660c4b25a7c34e4652004072f7338e7c", "rows": [ { "h": 3, "deg": 3, "logP": -12.529922611959266, "logP_lo": -12.529922611959268, "logP_hi": -12.529922611959265, "margin": -1.3922136235510296, "margin_lo": -1.39221362355103, "margin_hi": -1.3922136235510292, "log_content": -6.396929655216146, "P_sha256": "0697357a28c307f494c89241f9b0a2e7e15c88f6969f0332e63cbc5f8f30cc0f", "content_sha256": "4b6381164a67bc88073fabeb83654576d233d98fca5b64bce65aaa1abe1d070d", "prec": 302, "secs": 0.008, "lifted": { "logP": -12.529922611959266, "log_content": -6.396929655216146, "h": 3 }, "bitIdentical": true, "agree": true, "m": 1 }, { "h": 6, "deg": 6, "logP": -55.22907444277261, "logP_lo": -55.229074442772614, "logP_hi": -55.2290744427726, "margin": -1.5341409567436834, "margin_lo": -1.534140956743684, "margin_hi": -1.534140956743683, "log_content": 3.513362274033206, "P_sha256": "6d6a27cbf8387f51ef5e6118528b92366e0c37c1a18a85d97aeffab54d584772", "content_sha256": "17181fe7834a53e6a3d07c1bea13f7b5a7ecd950f24250e5b176b8d78e938659", "prec": 450, "secs": 0.003, "lifted": { "logP": -55.22907444277261, "log_content": 3.513362274033206, "h": 6 }, "bitIdentical": true, "agree": true, "m": 2 }, { "h": 9, "deg": 9, "logP": -112.20694566573398, "logP_lo": -112.206945665734, "logP_hi": -112.20694566573397, "margin": -1.385270934144864, "margin_lo": -1.3852709341448644, "margin_hi": -1.3852709341448637, "log_content": 37.52887246944392, "P_sha256": "981a8f41eeb9408b3a44f22327baddd11f946aef636b153e1c3ca202ec4d8e9f", "content_sha256": "781b0ba1cf27718b21238b3153eeee95ee679956330fb4a296dad4fe10572cee", "prec": 721, "secs": 0.002, "lifted": { "logP": -112.20694566573398, "log_content": 37.52887246944392, "h": 9 }, "bitIdentical": true, "agree": true, "m": 3 }, { "h": 12, "deg": 12, "logP": -193.0241636888415, "logP_lo": -193.02416368884153, "logP_hi": -193.02416368884147, "margin": -1.3404455811725104, "margin_lo": -1.340445581172511, "margin_hi": -1.34044558117251, "log_content": 119.16184093976625, "P_sha256": "b648dbecb9faf18295165d8ef7dc9d164b92b9858cc556c0b707deafb6180d90", "content_sha256": "96ed0f8fae1e3ecfbf1c44e21f7714686f529df669107aefea654f6dc5f90820", "prec": 2206, "secs": 0.006, "lifted": { "logP": -193.0241636888415, "log_content": 119.16184093976625, "h": 12 }, "bitIdentical": true, "agree": true, "m": 4 }, { "h": 15, "deg": 15, "logP": -311.41763144646944, "logP_lo": -311.4176314464695, "logP_hi": -311.4176314464694, "margin": -1.3840783619843087, "margin_lo": -1.3840783619843091, "margin_hi": -1.3840783619843082, "log_content": 272.1341417372246, "P_sha256": "de523928229977839661c3e702e0822f9163831fd68ba3cfad297b7e5c6248f6", "content_sha256": "2d3ecfd5c0ce2fe242f98ef203ee2a0d4e782d5556a965cd622b2af1cb944383", "prec": 3148, "secs": 0.006, "lifted": { "logP": -311.41763144646944, "log_content": 272.1341417372246, "h": 15 }, "bitIdentical": true, "agree": true, "m": 5 }, { "h": 18, "deg": 18, "logP": -451.52125219998464, "logP_lo": -451.5212521999847, "logP_hi": -451.5212521999846, "margin": -1.3935841117283476, "margin_lo": -1.393584111728348, "margin_hi": -1.3935841117283472, "log_content": 488.37347421024265, "P_sha256": "9e047a8e766ebf3f253043f1e8853d08e8500ad62a7f4f0652c8ec70ca3cd55a", "content_sha256": "a5670660be35f28cdc68153b221b705b6b1adc9cf7697064f0efaba14dddd9d7", "prec": 4320, "secs": 0.01, "lifted": { "logP": -451.52125219998464, "log_content": 488.37347421024265, "h": 18 }, "bitIdentical": true, "agree": true, "m": 6 }, { "h": 21, "deg": 21, "logP": 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-808.0428102567118, "log_content": 1146.4548111219344, "h": 24 }, "bitIdentical": true, "agree": true, "m": 8 }, { "h": 27, "deg": 27, "logP": -1013.6184589161833, "logP_lo": -1013.6184589161834, "logP_hi": -1013.6184589161832, "margin": -1.3904231260852995, "margin_lo": -1.3904231260852997, "margin_hi": -1.390423126085299, "log_content": 1587.5946695566545, "P_sha256": "9615132cade41c0816163a2275be9bdbf83085555dcb677d20137d0c57aa5566", "content_sha256": "650e08dc83f85d92d0e632a695ab8ddcb18f2e1ccb8535f84170ee73fd5d77ca", "prec": 9156, "secs": 0.039, "lifted": { "logP": -1013.6184589161833, "log_content": 1587.5946695566545, "h": 27 }, "bitIdentical": true, "agree": true, "m": 9 }, { "h": 30, "deg": 30, "logP": -1247.012556093642, "logP_lo": -1247.0125560936422, "logP_hi": -1247.0125560936417, "margin": -1.3855695067707132, "margin_lo": -1.3855695067707137, "margin_hi": -1.3855695067707128, "log_content": 2118.8129528940917, "P_sha256": 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-1812.4821437049898, "margin": -1.398520172611875, "margin_lo": -1.3985201726118754, "margin_hi": -1.3985201726118746, "log_content": 3481.2910075104132, "P_sha256": "eaf6478a1d267efc64056b2b3bb84dc054c71f6839c758ef0dd685b50d89065b", "content_sha256": "2daa11013d344f36290e0f4532aa66f616ee7e3b6fd0dec683a463e3cf247c12", "prec": 15910, "secs": 0.151, "lifted": { "logP": -1812.48214370499, "log_content": 3481.2910075104132, "h": 36 }, "bitIdentical": true, "agree": true, "m": 12 }, { "h": 39, "deg": 39, "logP": -2098.4947164349796, "logP_lo": -2098.49471643498, "logP_hi": -2098.494716434979, "margin": -1.379680944401696, "margin_lo": -1.3796809444016966, "margin_hi": -1.3796809444016955, "log_content": 4272.9600444590415, "P_sha256": "f67d500245f13e0bb8d71c9b9ac1d9a239488a26d10cc036cf2f732f18be46e6", "content_sha256": "5e7d4d13666e417d80f3880dc61c0674ba6a6a94ac1c86d8dc416da0495e6454", "prec": 18684, "secs": 0.21, "lifted": { "logP": -2098.4947164349796, "log_content": 4272.9600444590415, "h": 39 }, "bitIdentical": true, "agree": true, "m": 13 } ], "secs": 0.66 }, "zeta5": { "constant": "ζ(5)", "k": 5, "spec": [ "Z", 5, "int", 8, 1, 6 ], "name": "Z_k5_int_a8_b1_r6", "record": "certs/zeta-hankel/runs/scan3/Z_k5_int_a8_b1_r6.jsonl", "record_sha256": "d81897d485e38f3e45b38555001f398c5b3d34a77b55a3cc7914231ba8f850e3", "rows": [ { "h": 7, "deg": 7, "logP": -16.301195949060475, "logP_lo": -16.301195949060478, "logP_hi": -16.30119594906047, "margin": -0.33267746834817297, "margin_lo": -0.3326774683481731, "margin_hi": -0.3326774683481728, "log_content": -49.85058416233227, "P_sha256": "fa597172bb0a86eb6f7310636ed553b6c3127bcb1cafcb790664a509ed9ab947", "content_sha256": "c73ae300fefccaa0b9076ad1c68bee599a6309b3f12701294795dfa4129c3f87", "prec": 544, "secs": 0.001, "lifted": { "logP": -16.301195949060475, "log_content": -49.85058416233227, "h": 7 }, "bitIdentical": true, "agree": true, "m": 1 }, { "h": 14, "deg": 14, "logP": -55.04260477830346, "logP_lo": -55.04260477830347, "logP_hi": -55.042604778303456, "margin": -0.280829616215834, "margin_lo": -0.2808296162158341, "margin_hi": -0.2808296162158339, "log_content": -113.14971468960476, "P_sha256": "45cd82cf49a0e0bf7654d7684c51dbde38b7c714d4c26258169582907596030e", "content_sha256": "8f62d197b3dfbf2a6810f9787a707ead82b4b578b8edd759fdce35b43a1b6962", "prec": 1456, "secs": 0.005, "lifted": { "logP": -55.04260477830346, "log_content": -113.14971468960476, "h": 14 }, "bitIdentical": true, "agree": true, "m": 2 }, { "h": 21, "deg": 21, "logP": -105.30801772504276, "logP_lo": -105.30801772504277, "logP_hi": -105.30801772504275, "margin": -0.23879369098649153, "margin_lo": -0.23879369098649159, "margin_hi": -0.23879369098649145, "log_content": -111.60283157924874, "P_sha256": "36b987ddc9c53e8a9e09ffd36150070dc3abb3012bf8a963777ee8c22e5ab8af", "content_sha256": "0b475d0ab2b50ab9ed86c2036b79ffef48996a66c97d833302fad84463664307", "prec": 3008, "secs": 0.04, "lifted": { "logP": -105.30801772504276, "log_content": -111.60283157924874, "h": 21 }, "bitIdentical": true, "agree": true, "m": 3 }, { "h": 28, "deg": 28, "logP": -139.14749127238355, "logP_lo": -139.14749127238358, "logP_hi": -139.14749127238352, "margin": -0.17748404499028514, "margin_lo": -0.1774840449902852, "margin_hi": -0.17748404499028508, "log_content": -19.795340274714476, "P_sha256": "a73cb33aa8546764f0ab5fb2d82a38adb7d994080deb30703d3a4cfe6adc51c8", "content_sha256": "60d14bd980a946695612f1abca895b402175032e51eee011a7d4aa67d4f471e5", "prec": 10478, "secs": 0.051, "lifted": { "logP": -139.14749127238355, "log_content": -19.795340274714476, "h": 28 }, "bitIdentical": true, "agree": true, "m": 4 }, { "h": 35, "deg": 35, "logP": -226.78756364918803, "logP_lo": -226.78756364918806, "logP_hi": -226.787563649188, "margin": -0.18513270501974533, "margin_lo": -0.18513270501974538, "margin_hi": -0.18513270501974527, "log_content": 270.8970436206273, "P_sha256": "e2079dd9d54a51a35a5527cfea545f3f42bd0687bdc6bec5125ee924d741f82a", "content_sha256": "d560736d7e8ae244cf8c0ade2a11d36d2255338032e1b4a673bf2e9f4a6e4ef8", "prec": 16096, "secs": 0.16, "lifted": { "logP": -226.78756364918803, "log_content": 270.8970436206273, "h": 35 }, "bitIdentical": true, "agree": true, "m": 5 } ], "secs": 0.26 }, "zeta7": { "constant": "ζ(7)", "k": 7, "spec": [ "Z", 7, "int", 8, 1, 4 ], "name": "Z_k7_int_a8_b1_r4", "record": "certs/zeta-hankel/runs/scan3/Z_k7_int_a8_b1_r4.jsonl", "record_sha256": "bec0bc144a8319787e943f604cd8535107809baf8461bbbb908eb859513d8b64", "rows": [ { "h": 7, "deg": 7, "logP": 26.25489707274107, "logP_lo": 26.254897072741066, "logP_hi": 26.254897072741073, "margin": 0.5358142259743075, "margin_lo": 0.5358142259743074, "margin_hi": 0.5358142259743077, "log_content": -107.03806462314738, "P_sha256": "e3a1d2fcd64708c652a23a732300752d1122d64ff0a695303acc09fa068f6edf", "content_sha256": "62a0092078bdd4065c28a8c96f74e62f6824c6033c6ce8103152d31106118b73", "prec": 597, "secs": 0.001, "lifted": { "logP": 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Numerical, not interval: it checks the formulas the exact engine is built on." }, "crosscheck": { "what": "crosscheck.py: Python standard library only, written from the docstring definitions, no code shared with the engine; moments from its own Bernoulli recurrence, partial fractions by schoolbook division, Δ by Fraction determinants at h+1 points and Lagrange interpolation, ζ(3) by an exact rational enclosure from Apéry's series. ζ(5), ζ(7) and G: the exact polynomial only.", "rows": [ { "spec": [ "Z", 3, "int", 4, 1, 4 ], "m": 1, "h": 3, "P_sha256_engine": "0697357a28c307f494c89241f9b0a2e7e15c88f6969f0332e63cbc5f8f30cc0f", "P_sha256_stdlib": "0697357a28c307f494c89241f9b0a2e7e15c88f6969f0332e63cbc5f8f30cc0f", "samePolynomial": true, "sameContent": true, "secsStdlib": 0.004, "zeta3Enclosure": { "aperyTerms": 126, "logP_lo_stdlib": -12.529922611959137, "logP_hi_stdlib": -12.529922611959137, "engineBallIntersectsRationalEnclosure": true, "liftedLogP": -12.529922611959266, "liftedWithinStdlib": true }, "agree": true }, { "spec": [ "Z", 3, "int", 4, 1, 4 ], "m": 2, "h": 6, "P_sha256_engine": "6d6a27cbf8387f51ef5e6118528b92366e0c37c1a18a85d97aeffab54d584772", "P_sha256_stdlib": "6d6a27cbf8387f51ef5e6118528b92366e0c37c1a18a85d97aeffab54d584772", "samePolynomial": true, "sameContent": true, "secsStdlib": 0.018, "zeta3Enclosure": { "aperyTerms": 274, "logP_lo_stdlib": -55.2290744427728, "logP_hi_stdlib": -55.2290744427728, "engineBallIntersectsRationalEnclosure": true, "liftedLogP": -55.22907444277261, "liftedWithinStdlib": true }, "agree": true }, { "spec": [ "Z", 3, "int", 4, 1, 4 ], "m": 3, "h": 9, "P_sha256_engine": "981a8f41eeb9408b3a44f22327baddd11f946aef636b153e1c3ca202ec4d8e9f", "P_sha256_stdlib": "981a8f41eeb9408b3a44f22327baddd11f946aef636b153e1c3ca202ec4d8e9f", "samePolynomial": true, "sameContent": true, "secsStdlib": 0.089, "zeta3Enclosure": { "aperyTerms": 545, "logP_lo_stdlib": -112.20694566573366, "logP_hi_stdlib": -112.20694566573366, "engineBallIntersectsRationalEnclosure": true, "liftedLogP": -112.20694566573398, "liftedWithinStdlib": true }, "agree": true }, { "spec": [ "Z", 5, "int", 8, 1, 4 ], "m": 1, "h": 7, "P_sha256_engine": "0eed2f5e027454fcd21bf7260009f86c0513115ec2c663640f57c966557563b5", "P_sha256_stdlib": "0eed2f5e027454fcd21bf7260009f86c0513115ec2c663640f57c966557563b5", "samePolynomial": true, "sameContent": true, "secsStdlib": 0.012, "agree": true }, { "spec": [ "Z", 7, "int", 8, 1, 4 ], "m": 1, "h": 7, "P_sha256_engine": "e3a1d2fcd64708c652a23a732300752d1122d64ff0a695303acc09fa068f6edf", "P_sha256_stdlib": "e3a1d2fcd64708c652a23a732300752d1122d64ff0a695303acc09fa068f6edf", "samePolynomial": true, "sameContent": true, "secsStdlib": 0.013, "agree": true }, { "spec": [ "E", 2, "half", 8, 1, 1 ], "m": 1, "h": 7, "P_sha256_engine": "fc4c86a7d41e343d615b92597c247f94c82afcb752c6bb22927137711f0f702b", "P_sha256_stdlib": "fc4c86a7d41e343d615b92597c247f94c82afcb752c6bb22927137711f0f702b", "samePolynomial": true, "sameContent": true, "secsStdlib": 0.011, "agree": true } ], "secs": 0.16 }, "classReading": { "status": "extrapolation", "statement": "The class of Hankel families measured here stops between ζ(5) and ζ(7): the best margin found at h ≈ 35 is negative at k = 3 and k = 5 and positive at k = 7, and every structural variant is worse. This is a MEASUREMENT across a finite set of families at finite h, extrapolated in h and in k. It is NOT a theorem: no statement here excludes a family outside the ones scanned, and no limit in h is proved.", "counts": { "families": 323, "scan3": 300, "struct": 12, "scan1": 11, "records": 4902, "errors": 0 }, "bestZ": { "3": { "family": "Z_k3_int_a6_b1_r4", "h": 40, "margin": -1.3837533198867897, "families": 30 }, "5": { "family": "Z_k5_int_a8_b1_r6", "h": 35, "margin": -0.18513270501974533, "families": 60 }, "7": { "family": "Z_k7_int_a8_b1_r4", "h": 35, "margin": 1.0157239176780057, "families": 85 } }, "bestE": { "3": { "family": "E_k3_int_a8_b1_r2", "h": 35, "margin": 0.1541321832104467, "families": 30 }, "5": { "family": "E_k5_int_a8_b1_r1", "h": 35, "margin": 1.4116908420983172, "families": 30 }, "7": { "family": "E_k7_int_a8_b1_r1", "h": 35, "margin": 2.5886257993085704, "families": 30 } }, "bestCatalan": { "family": "E_k2_half_a8_b1_r1", "h": 35, "margin": 0.428375085443837, "families": 30 }, "linearInK": { "slopePerUnitK": 0.5998693093911989, "intercept": -3.1837339160321707, "zeroCrossingFit": 5.307379234425761, "zeroCrossingInterp57": 5.308334403159372, "note": "least squares through the three best Z margins (k = 3, 5, 7); and the linear interpolation between k = 5 and k = 7. The claimant notes round the threshold to \"k ≈ 6\"." }, "struct": [ { "family": "above_k5", "k": 5, "h": 56, "margin": 0.22041362302663842 }, { "family": "above_k7", "k": 7, "h": 56, "margin": 1.4647773084135378 }, { "family": "grid_intzeros_k5", "k": 5, "h": 60, "margin": 1.1744141425816457 }, { "family": "grid_intzeros_k7", "k": 7, "h": 60, "margin": 2.1517769782185363 }, { "family": "interleave_k5", "k": 5, "h": 60, "margin": 2.972957015281721 }, { "family": "interleave_k7", "k": 7, "h": 60, "margin": 5.011367729207175 }, { "family": "oddpoles_k5", "k": 5, "h": 60, "margin": 1.4115715353405256 }, { "family": "oddpoles_k7", "k": 7, "h": 60, "margin": 3.556702482858265 }, { "family": "stair_k5", "k": 5, "h": 60, "margin": 0.32843997968859623 }, { "family": "stair_k7", "k": 7, "h": 60, "margin": 1.9416842358968365 }, { "family": "window_k5", "k": 5, "h": 56, "margin": 0.5117018777245672 }, { "family": "window_k7", "k": 7, "h": 56, "margin": 1.8235846933442121 } ], "structAllWorseThanBestZ5": true, "structRange": [ 0.22041362302663842, 5.011367729207175 ] }, "published": { "fauzan": { "source": "corpus/sources/zeta-hankel/zenodo-22826419.json", "sha256": "d2c0daa37dd5df07c51773bb813dfe64e23bfdedf42c76723df12739bd84f0d0", "stated": "integer polynomials Q_n of degree 37n with 0 < Q_n(ζ(5)) < exp(−139n²/5); |ζ(5) − a/b| > b^−260", "perN2": -27.8, "degreePerN": 37, "perH2": -0.020306793279766252 }, "calegari": { "source": "corpus/sources/zeta-hankel/calegari-2026-09-24-zeta5-is-irrational.html", "sha256": "48fa9c65c4c6eafaf7115213f9b13fa2818aafbad8229663c87ea45921a59646", "stated": "K = 12n, N = n, r = 6, h = 11n; deg P_{k,n} = 11n, P_{k,n}(ζ(k)) ≤ e^{−γ_k n²}, γ_5 = 3/2", "perN2": -1.5, "degreePerN": 11, "perH2": -0.012396694214876033 } }, "raceContext": { "status": "unverified", "note": "Reported by others; nothing in this list was checked by cert-machine. The sources are pinned (corpus/sources/zeta-hankel, sha256 in PROVENANCE.json).", "items": [ { "claim": "ζ(7) is irrational (Anand, Zenodo 22920911, v1 2026-09-23)", "status": "open issue: gmDevi/zeta-7-21-lean #1 (opened 2026-10-03 by a third party, GitHub user huntrontrakkr — not this lab) reports that the outer integral I_out does not follow from the paper's own formulas, moving the decay constant from −11.99 to +0.95", "sources": [ "zenodo-22920911.json", "github-gmDevi-zeta-7-21-lean-issue-1.json" ] }, { "claim": "Catalan's constant is irrational (Sun, arXiv 2609.04176, 2026-09-03)", "status": "Wachs, arXiv 2609.22339 (2026-09-16), reports exact computations locating a discrepancy at the prime 2", "sources": [ "arxiv-2609.04176.html", "arxiv-2609.22339.html" ] }, { "claim": "ζ(5) is irrational (Fauzan, Zenodo 22826419, 2026-09-17; Calegari's reconstruction 2026-09-24)", "status": "the method measured on this page; the proof itself is not re-checked here", "sources": [ "zenodo-22826419.json", "calegari-2026-09-24-zeta5-is-irrational.html" ] } ] }, "counts": { "rowsRerun": 51, "agree": 51, "bitIdentical": 51, "crosscheck": 6, "crosscheckAgree": 6, "maxHRerun": 99 }, "timings": { "totalSecs": 164.5, "families": { "zeta3": 0.66, "zeta5": 0.26, "zeta7": 0.24, "catalan": 0.26, "zeta5r4": 0.2 }, "calegari": { "calegari5": 52.77, "calegari7": 103.95 }, "padic": 5.77, "crosscheck": 0.16 }, "files": [ { "file": "instruments/zetahankel/hankel.py", "sha256": "8ad5358d5db2c92fee6d58465966146ac5da1fa548242575cc8aefcce15b65bf" }, { "file": "instruments/zetahankel/hankel2.py", "sha256": "e30bcdf35d7c700b6b1e8459775d145f40a3144549ff6fc4d7b38a0dff429c2a" }, { "file": "instruments/zetahankel/scan2.py", "sha256": "76fbace06c28fd57842f11b059f71930ee4bb0a2c69e0ed09185b9423effe0d2" }, { "file": "instruments/zetahankel/padic.py", "sha256": "480ef0d31ce6e1a60de0213c9e2a6eb084794b38ee49cd4237b9d130c2a1ed66" }, { "file": "instruments/zetahankel/test2.py", "sha256": "e2ef04f5c12c3199702ea33d5333f334a2fd114aafb0f5457ce6fdafbb7b3b8e" }, { "file": "instruments/zetahankel/crosscheck.py", "sha256": "98604c0903f316e6165fb9ab545fd2b0f1a02c568d04bea1b5e368d05e5fc919" }, { "file": "instruments/zetahankel/rerun.py", "sha256": "0eadcee43ffd22094d6ba740a5a840cc771436357213803e1f1b4fc211fec843" }, { "file": "certs/zeta-hankel/test2-certmachine.log", "sha256": "e995e9b92d164c26037cb46d1ddb5935a9bba04b4752a6e39b1699df71fc440e" } ], "verdict": "AGREE" }