{ "what": "x^x = y, every bracket decided here (tools/run-xx-ledger.py): the study claimbox stated from an AI model's proposals (claude-opus-5-5), read from the copies LIFT-claimbox.json made into corpus/claimbox-xx, each side one exact integer comparison by code that shares nothing with claimbox or the receiver; claimbox's word beside ours, which must agree", "claimboxCommit": "850213d77020d2e4228455b642366cbe797fff22", "pins": { "records/xxy-study.json": "bf49436db85d7e994e878ab328d48f6e891dca776e93ad785470a5226ee6468a", "records/xxy-check.json": "248620a59378685867f368bf9ad9fde3fec00cc8e26a8a11e7d39ed55e3650de", "records/xx64-check.json": "8bb2ec8074417da13b63e876c818db8b8e5ef191fc0d22eac868696cd26b8924", "claimbox/library/selfpower.py": "e414ab05c2937fc8ec266004bb25a1c467a27365a5e028e69f17d6754bb97ed8", "corpus/xx64/problem.json": "03733521516d8b3d69296d41472766fb69efa2a76ae228ffbc654b1601029324" }, "reduction": { "statement": "for N >= 2, x^x = N has exactly one positive real root x, and for whole numbers 1 <= q <= p: p/q < x iff p^p < N^q·q^p, p/q <= x iff p^p <= N^q·q^p, x < p/q iff N^q·q^p < p^p, x <= p/q iff N^q·q^p <= p^p; at q = 1, k <= x iff k^k <= N and x <= k iff N <= k^k", "rests on": "x^x <= 1 on (0, 1], x^x strictly increasing on [1, oo)", "read": "the negative-base convention: every theorem is about positive reals (Mathlib's Real.rpow); that a negative x is not a root worth counting is a reading of the problem (claimbox/library/selfpower.py), not decided here", "standing": "proved in Lean, kernel-checked", "record": "certs/xx-reduction-lean.json", "recordSha256": "f0b52eae30ab4de56ec4cf364ca6c2abea1d2d81078560c9a9795f1cab3e5daa", "run": { "id": 41221355209, "url": "https://github.com/carlostoledo1891/cert-machine/actions/runs/41221355209", "commit": "6241f331013389006ab351d6344a5d1a061541d0" }, "lean": "Lean (version 4.34.1, x86_64-unknown-linux-gnu, commit 5045d0056413266e57c625dcd7c365b10e377c52, Release)", "mathlib": "d13f23b723b8a846827a245b89c10fc7d3f11612", "kernels": [ "lean-build", "lean-comparator", "nanoda" ], "theorems": { "unique": [ "XXReduction.existsUnique_root", "XXReduction.one_lt_of_selfpow_eq" ], "fraction": { "gt": "XXReduction.lt_root_iff", "ge": "XXReduction.le_root_iff", "lt": "XXReduction.root_lt_iff", "le": "XXReduction.root_le_iff" }, "whole": { "gt": "XXReduction.lt_root_iff", "ge": "XXReduction.natCast_le_root_iff", "lt": "XXReduction.root_lt_iff", "le": "XXReduction.root_le_natCast_iff" }, "note": "a fraction p/q > 1 in lowest terms has 1 <= q < p, a whole bound k >= 1 is q = 1: both inside the theorems' 1 <= q <= p" } }, "counts": { "roots": 105, "exactRoots": 4, "claims": 218, "CERTIFIED": 210, "REFUTED": 8, "planted": 8, "agreeWithClaimbox": 218, "xx64Claims": 8, "xx64Certified": 6, "xx64Refuted": 2, "xx64AgreeWithClaimbox": 8, "mutants": 216, "mutantsFlipped": 216, "redControls": 228, "redControlsFired": 228, "own": 1, "ownRefused": 1 }, "own": { "standing": "cert-machine's own claims, through the same decider; claimbox stated none of them", "rows": [ { "id": "cm_xx64_transcendental", "y": 64, "statement": "the root of xˣ = 64 is transcendental", "form": "x is transcendental", "origin": "cert-machine's own claim (added 2026-10-31): not claimbox's, not the AI model's", "expect": "REFUSED", "reason": "This decider answers one question: does the root lie above or below a given fraction, by one comparison of two whole numbers. \"Transcendental\" says the root is a root of no polynomial with integer coefficients: infinitely many polynomials, not one comparison, and no number of decided brackets reaches it.", "trueBy": "Cited, not decided: the root is not a fraction (p/q in lowest terms with q > 1 would give p^p = 64^q·q^p, which q cannot divide, and no whole k has k^k = 64), and an irrational algebraic x would make x^x transcendental by the Gelfond–Schneider theorem, while 64 is not.", "decidableBy": "A kernel-checked proof: the Gelfond–Schneider theorem formalized (Mathlib at the pin of lean/xx-reduction, d13f23b7, holds no Gelfond–Schneider theorem), then the two-line argument above in Lean on top of XXReduction.existsUnique_root. With that, it is a theorem to check, not a comparison to compute.", "N": 64, "nFile": "corpus/xx64/problem.json", "word": "REFUSED", "why": "not a comparison of the root with one fraction, the one statement this decider reads" } ] }, "exactRoots": [ 4, 27, 256, 3125 ], "bracket64": { "lo": "458912/135009", "hi": "400097/117706", "sharedDecimals": 9, "loDec": "3.399121540045478449584842491982", "hiDec": "3.399121540108405688749936281923", "loShared": "3.399121540", "hiShared": "3.399121541" }, "claims": [ { "id": "y2_gt", "y": 2, "N": 2, "nFile": "corpus/xxy/n/2.json", "statement": "x > 471/302", "rel": "gt", "a": "471/302", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "471^471 vs 2^302·302^471", "sign": -1, "bits": [ 4183, 4183 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n2) > 471/302" } }, { "id": "y2_lt", "y": 2, "N": 2, "nFile": "corpus/xxy/n/2.json", "statement": "x < 641/411", "rel": "lt", "a": "641/411", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "641^641 vs 2^411·411^641", "sign": 1, "bits": [ 5977, 5977 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n2) < 641/411" } }, { "id": "y3_gt", "y": 3, "N": 3, "nFile": "corpus/xxy/n/3.json", "statement": "x > 502/275", "rel": "gt", "a": "502/275", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "502^502 vs 3^275·275^502", "sign": -1, "bits": [ 4504, 4504 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n3) > 502/275" } }, { "id": "y3_lt", "y": 3, "N": 3, "nFile": "corpus/xxy/n/3.json", "statement": "x < 387/212", "rel": "lt", "a": "387/212", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "387^387 vs 3^212·212^387", "sign": 1, "bits": [ 3327, 3327 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n3) < 387/212" } }, { "id": "y4_ge", "y": 4, "N": 4, "nFile": "corpus/xxy/n/4.json", "statement": "x ≥ 2", "rel": "ge", "a": "2", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2^2 vs 4", "sign": 0, "bits": [ 3, 3 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n4) ≥ 2" } }, { "id": "y4_le", "y": 4, "N": 4, "nFile": "corpus/xxy/n/4.json", "statement": "x ≤ 2", "rel": "le", "a": "2", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2^2 vs 4", "sign": 0, "bits": [ 3, 3 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n4) ≤ 2" } }, { "id": "y5_gt", "y": 5, "N": 5, "nFile": "corpus/xxy/n/5.json", "statement": "x > 609/286", "rel": "gt", "a": "609/286", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "609^609 vs 5^286·286^609", "sign": -1, "bits": [ 5634, 5634 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n5) > 609/286" } }, { "id": "y5_lt", "y": 5, "N": 5, "nFile": "corpus/xxy/n/5.json", "statement": "x < 181/85", "rel": "lt", "a": "181/85", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "181^181 vs 5^85·85^181", "sign": 1, "bits": [ 1358, 1358 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n5) < 181/85" } }, { "id": "y6_gt", "y": 6, "N": 6, "nFile": "corpus/xxy/n/6.json", "statement": "x > 1136/509", "rel": "gt", "a": "1136/509", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1136^1136 vs 6^509·509^1136", "sign": -1, "bits": [ 11531, 11531 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n6) > 1136/509" } }, { "id": "y6_lt", "y": 6, "N": 6, "nFile": "corpus/xxy/n/6.json", "statement": "x < 1781/798", "rel": "lt", "a": "1781/798", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1781^1781 vs 6^798·798^1781", "sign": 1, "bits": [ 19233, 19233 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n6) < 1781/798" } }, { "id": "y7_gt", "y": 7, "N": 7, "nFile": "corpus/xxy/n/7.json", "statement": "x > 44/19", "rel": "gt", "a": "44/19", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "44^44 vs 7^19·19^44", "sign": -1, "bits": [ 241, 241 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n7) > 44/19" } }, { "id": "y7_lt", "y": 7, "N": 7, "nFile": "corpus/xxy/n/7.json", "statement": "x < 183/79", "rel": "lt", "a": "183/79", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "183^183 vs 7^79·79^183", "sign": 1, "bits": [ 1376, 1376 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n7) < 183/79" } }, { "id": "y8_gt", "y": 8, "N": 8, "nFile": "corpus/xxy/n/8.json", "statement": "x > 246/103", "rel": "gt", "a": "246/103", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "246^246 vs 8^103·103^246", "sign": -1, "bits": [ 1954, 1954 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n8) > 246/103" } }, { "id": "y8_lt", "y": 8, "N": 8, "nFile": "corpus/xxy/n/8.json", "statement": "x < 289/121", "rel": "lt", "a": "289/121", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "289^289 vs 8^121·121^289", "sign": 1, "bits": [ 2363, 2363 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n8) < 289/121" } }, { "id": "y9_gt", "y": 9, "N": 9, "nFile": "corpus/xxy/n/9.json", "statement": "x > 1799/734", "rel": "gt", "a": "1799/734", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1799^1799 vs 9^734·734^1799", "sign": -1, "bits": [ 19453, 19453 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n9) > 1799/734" } }, { "id": "y9_lt", "y": 9, "N": 9, "nFile": "corpus/xxy/n/9.json", "statement": "x < 125/51", "rel": "lt", "a": "125/51", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "125^125 vs 9^51·51^125", "sign": 1, "bits": [ 871, 871 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n9) < 125/51" } }, { "id": "y10_gt", "y": 10, "N": 10, "nFile": "corpus/xxy/n/10.json", "statement": "x > 203/81", "rel": "gt", "a": "203/81", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "203^203 vs 10^81·81^203", "sign": -1, "bits": [ 1557, 1557 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n10) > 203/81" } }, { "id": "y10_lt", "y": 10, "N": 10, "nFile": "corpus/xxy/n/10.json", "statement": "x < 198/79", "rel": "lt", "a": "198/79", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "198^198 vs 10^79·79^198", "sign": 1, "bits": [ 1511, 1511 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n10) < 198/79" } }, { "id": "y11_gt", "y": 11, "N": 11, "nFile": "corpus/xxy/n/11.json", "statement": "x > 23/9", "rel": "gt", "a": "23/9", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "23^23 vs 11^9·9^23", "sign": -1, "bits": [ 105, 105 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n11) > 23/9" } }, { "id": "y11_lt", "y": 11, "N": 11, "nFile": "corpus/xxy/n/11.json", "statement": "x < 18/7", "rel": "lt", "a": "18/7", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "18^18 vs 11^7·7^18", "sign": 1, "bits": [ 76, 75 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n11) < 18/7" } }, { "id": "y12_gt", "y": 12, "N": 12, "nFile": "corpus/xxy/n/12.json", "statement": "x > 1763/678", "rel": "gt", "a": "1763/678", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1763^1763 vs 12^678·678^1763", "sign": -1, "bits": [ 19012, 19012 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n12) > 1763/678" } }, { "id": "y12_lt", "y": 12, "N": 12, "nFile": "corpus/xxy/n/12.json", "statement": "x < 1750/673", "rel": "lt", "a": "1750/673", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1750^1750 vs 12^673·673^1750", "sign": 1, "bits": [ 18853, 18853 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n12) < 1750/673" } }, { "id": "y13_gt", "y": 13, "N": 13, "nFile": "corpus/xxy/n/13.json", "statement": "x > 1891/716", "rel": "gt", "a": "1891/716", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1891^1891 vs 13^716·716^1891", "sign": -1, "bits": [ 20584, 20584 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n13) > 1891/716" } }, { "id": "y13_lt", "y": 13, "N": 13, "nFile": "corpus/xxy/n/13.json", "statement": "x < 1788/677", "rel": "lt", "a": "1788/677", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1788^1788 vs 13^677·677^1788", "sign": 1, "bits": [ 19318, 19318 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n13) < 1788/677" } }, { "id": "y14_gt", "y": 14, "N": 14, "nFile": "corpus/xxy/n/14.json", "statement": "x > 1958/731", "rel": "gt", "a": "1958/731", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1958^1958 vs 14^731·731^1958", "sign": -1, "bits": [ 21412, 21412 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n14) > 1958/731" } }, { "id": "y14_lt", "y": 14, "N": 14, "nFile": "corpus/xxy/n/14.json", "statement": "x < 75/28", "rel": "lt", "a": "75/28", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "75^75 vs 14^28·28^75", "sign": 1, "bits": [ 468, 468 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n14) < 75/28" } }, { "id": "y15_gt", "y": 15, "N": 15, "nFile": "corpus/xxy/n/15.json", "statement": "x > 1381/509", "rel": "gt", "a": "1381/509", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1381^1381 vs 15^509·509^1381", "sign": -1, "bits": [ 14406, 14406 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n15) > 1381/509" } }, { "id": "y15_lt", "y": 15, "N": 15, "nFile": "corpus/xxy/n/15.json", "statement": "x < 350/129", "rel": "lt", "a": "350/129", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "350^350 vs 15^129·129^350", "sign": 1, "bits": [ 2958, 2958 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n15) < 350/129" } }, { "id": "y16_gt", "y": 16, "N": 16, "nFile": "corpus/xxy/n/16.json", "statement": "x > 442/161", "rel": "gt", "a": "442/161", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "442^442 vs 16^161·161^442", "sign": -1, "bits": [ 3885, 3885 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n16) > 442/161" } }, { "id": "y16_lt", "y": 16, "N": 16, "nFile": "corpus/xxy/n/16.json", "statement": "x < 593/216", "rel": "lt", "a": "593/216", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "593^593 vs 16^216·216^593", "sign": 1, "bits": [ 5463, 5463 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n16) < 593/216" } }, { "id": "y17_gt", "y": 17, "N": 17, "nFile": "corpus/xxy/n/17.json", "statement": "x > 927/334", "rel": "gt", "a": "927/334", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "927^927 vs 17^334·334^927", "sign": -1, "bits": [ 9137, 9137 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n17) > 927/334" } }, { "id": "y17_lt", "y": 17, "N": 17, "nFile": "corpus/xxy/n/17.json", "statement": "x < 136/49", "rel": "lt", "a": "136/49", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "136^136 vs 17^49·49^136", "sign": 1, "bits": [ 964, 964 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n17) < 136/49" } }, { "id": "y18_gt", "y": 18, "N": 18, "nFile": "corpus/xxy/n/18.json", "statement": "x > 614/219", "rel": "gt", "a": "614/219", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "614^614 vs 18^219·219^614", "sign": -1, "bits": [ 5687, 5687 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n18) > 614/219" } }, { "id": "y18_lt", "y": 18, "N": 18, "nFile": "corpus/xxy/n/18.json", "statement": "x < 1071/382", "rel": "lt", "a": "1071/382", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1071^1071 vs 18^382·382^1071", "sign": 1, "bits": [ 10780, 10780 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n18) < 1071/382" } }, { "id": "y19_gt", "y": 19, "N": 19, "nFile": "corpus/xxy/n/19.json", "statement": "x > 150/53", "rel": "gt", "a": "150/53", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "150^150 vs 19^53·53^150", "sign": -1, "bits": [ 1085, 1085 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n19) > 150/53" } }, { "id": "y19_lt", "y": 19, "N": 19, "nFile": "corpus/xxy/n/19.json", "statement": "x < 1517/536", "rel": "lt", "a": "1517/536", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1517^1517 vs 19^536·536^1517", "sign": 1, "bits": [ 16031, 16031 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n19) < 1517/536" } }, { "id": "y20_gt", "y": 20, "N": 20, "nFile": "corpus/xxy/n/20.json", "statement": "x > 888/311", "rel": "gt", "a": "888/311", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "888^888 vs 20^311·311^888", "sign": -1, "bits": [ 8698, 8698 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n20) > 888/311" } }, { "id": "y20_lt", "y": 20, "N": 20, "nFile": "corpus/xxy/n/20.json", "statement": "x < 2447/857", "rel": "lt", "a": "2447/857", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2447^2447 vs 20^857·857^2447", "sign": 1, "bits": [ 27546, 27546 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n20) < 2447/857" } }, { "id": "y21_gt", "y": 21, "N": 21, "nFile": "corpus/xxy/n/21.json", "statement": "x > 619/215", "rel": "gt", "a": "619/215", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "619^619 vs 21^215·215^619", "sign": -1, "bits": [ 5741, 5741 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n21) > 619/215" } }, { "id": "y21_lt", "y": 21, "N": 21, "nFile": "corpus/xxy/n/21.json", "statement": "x < 262/91", "rel": "lt", "a": "262/91", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "262^262 vs 21^91·91^262", "sign": 1, "bits": [ 2105, 2105 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n21) < 262/91" } }, { "id": "y22_gt", "y": 22, "N": 22, "nFile": "corpus/xxy/n/22.json", "statement": "x > 29/10", "rel": "gt", "a": "29/10", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "29^29 vs 22^10·10^29", "sign": -1, "bits": [ 141, 141 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n22) > 29/10" } }, { "id": "y22_lt", "y": 22, "N": 22, "nFile": "corpus/xxy/n/22.json", "statement": "x < 177/61", "rel": "lt", "a": "177/61", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "177^177 vs 22^61·61^177", "sign": 1, "bits": [ 1322, 1322 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n22) < 177/61" } }, { "id": "y23_gt", "y": 23, "N": 23, "nFile": "corpus/xxy/n/23.json", "statement": "x > 38/13", "rel": "gt", "a": "38/13", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "38^38 vs 23^13·13^38", "sign": -1, "bits": [ 200, 200 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n23) > 38/13" } }, { "id": "y23_lt", "y": 23, "N": 23, "nFile": "corpus/xxy/n/23.json", "statement": "x < 3", "rel": "lt", "a": "3", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "3^3 vs 23", "sign": 1, "bits": [ 5, 5 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n23) < 3" } }, { "id": "y24_gt", "y": 24, "N": 24, "nFile": "corpus/xxy/n/24.json", "statement": "x > 992/337", "rel": "gt", "a": "992/337", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "992^992 vs 24^337·337^992", "sign": -1, "bits": [ 9875, 9875 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n24) > 992/337" } }, { "id": "y24_lt", "y": 24, "N": 24, "nFile": "corpus/xxy/n/24.json", "statement": "x < 209/71", "rel": "lt", "a": "209/71", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "209^209 vs 24^71·71^209", "sign": 1, "bits": [ 1611, 1611 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n24) < 209/71" } }, { "id": "y25_gt", "y": 25, "N": 25, "nFile": "corpus/xxy/n/25.json", "statement": "x > 1289/435", "rel": "gt", "a": "1289/435", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1289^1289 vs 25^435·435^1289", "sign": -1, "bits": [ 13318, 13318 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n25) > 1289/435" } }, { "id": "y25_lt", "y": 25, "N": 25, "nFile": "corpus/xxy/n/25.json", "statement": "x < 403/136", "rel": "lt", "a": "403/136", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "403^403 vs 25^136·136^403", "sign": 1, "bits": [ 3488, 3488 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n25) < 403/136" } }, { "id": "y26_gt", "y": 26, "N": 26, "nFile": "corpus/xxy/n/26.json", "statement": "x > 331/111", "rel": "gt", "a": "331/111", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "331^331 vs 26^111·111^331", "sign": -1, "bits": [ 2771, 2771 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n26) > 331/111" } }, { "id": "y26_lt", "y": 26, "N": 26, "nFile": "corpus/xxy/n/26.json", "statement": "x < 2815/944", "rel": "lt", "a": "2815/944", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2815^2815 vs 26^944·944^2815", "sign": 1, "bits": [ 32257, 32257 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n26) < 2815/944" } }, { "id": "y27_ge", "y": 27, "N": 27, "nFile": "corpus/xxy/n/27.json", "statement": "x ≥ 3", "rel": "ge", "a": "3", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "3^3 vs 27", "sign": 0, "bits": [ 5, 5 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n27) ≥ 3" } }, { "id": "y27_le", "y": 27, "N": 27, "nFile": "corpus/xxy/n/27.json", "statement": "x ≤ 3", "rel": "le", "a": "3", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "3^3 vs 27", "sign": 0, "bits": [ 5, 5 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n27) ≤ 3" } }, { "id": "y28_gt", "y": 28, "N": 28, "nFile": "corpus/xxy/n/28.json", "statement": "x > 2441/809", "rel": "gt", "a": "2441/809", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2441^2441 vs 28^809·809^2441", "sign": -1, "bits": [ 27470, 27470 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n28) > 2441/809" } }, { "id": "y28_lt", "y": 28, "N": 28, "nFile": "corpus/xxy/n/28.json", "statement": "x < 1569/520", "rel": "lt", "a": "1569/520", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1569^1569 vs 28^520·520^1569", "sign": 1, "bits": [ 16656, 16656 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n28) < 1569/520" } }, { "id": "y29_gt", "y": 29, "N": 29, "nFile": "corpus/xxy/n/29.json", "statement": "x > 179/59", "rel": "gt", "a": "179/59", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "179^179 vs 29^59·59^179", "sign": -1, "bits": [ 1340, 1340 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n29) > 179/59" } }, { "id": "y29_lt", "y": 29, "N": 29, "nFile": "corpus/xxy/n/29.json", "statement": "x < 804/265", "rel": "lt", "a": "804/265", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "804^804 vs 29^265·265^804", "sign": 1, "bits": [ 7760, 7760 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n29) < 804/265" } }, { "id": "y30_gt", "y": 30, "N": 30, "nFile": "corpus/xxy/n/30.json", "statement": "x > 61/20", "rel": "gt", "a": "61/20", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "61^61 vs 30^20·20^61", "sign": -1, "bits": [ 362, 362 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n30) > 61/20" } }, { "id": "y30_lt", "y": 30, "N": 30, "nFile": "corpus/xxy/n/30.json", "statement": "x < 58/19", "rel": "lt", "a": "58/19", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "58^58 vs 30^19·19^58", "sign": 1, "bits": [ 340, 340 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n30) < 58/19" } }, { "id": "y31_gt", "y": 31, "N": 31, "nFile": "corpus/xxy/n/31.json", "statement": "x > 1217/397", "rel": "gt", "a": "1217/397", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1217^1217 vs 31^397·397^1217", "sign": -1, "bits": [ 12474, 12474 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n31) > 1217/397" } }, { "id": "y31_lt", "y": 31, "N": 31, "nFile": "corpus/xxy/n/31.json", "statement": "x < 702/229", "rel": "lt", "a": "702/229", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "702^702 vs 31^229·229^702", "sign": 1, "bits": [ 6638, 6638 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n31) < 702/229" } }, { "id": "y32_gt", "y": 32, "N": 32, "nFile": "corpus/xxy/n/32.json", "statement": "x > 3025/982", "rel": "gt", "a": "3025/982", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "3025^3025 vs 32^982·982^3025", "sign": -1, "bits": [ 34978, 34978 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n32) > 3025/982" } }, { "id": "y32_lt", "y": 32, "N": 32, "nFile": "corpus/xxy/n/32.json", "statement": "x < 268/87", "rel": "lt", "a": "268/87", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "268^268 vs 32^87·87^268", "sign": 1, "bits": [ 2162, 2162 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n32) < 268/87" } }, { "id": "y33_gt", "y": 33, "N": 33, "nFile": "corpus/xxy/n/33.json", "statement": "x > 424/137", "rel": "gt", "a": "424/137", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "424^424 vs 33^137·137^424", "sign": -1, "bits": [ 3701, 3701 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n33) > 424/137" } }, { "id": "y33_lt", "y": 33, "N": 33, "nFile": "corpus/xxy/n/33.json", "statement": "x < 913/295", "rel": "lt", "a": "913/295", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "913^913 vs 33^295·295^913", "sign": 1, "bits": [ 8979, 8979 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n33) < 913/295" } }, { "id": "y34_gt", "y": 34, "N": 34, "nFile": "corpus/xxy/n/34.json", "statement": "x > 314/101", "rel": "gt", "a": "314/101", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "314^314 vs 34^101·101^314", "sign": -1, "bits": [ 2605, 2605 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n34) > 314/101" } }, { "id": "y34_lt", "y": 34, "N": 34, "nFile": "corpus/xxy/n/34.json", "statement": "x < 171/55", "rel": "lt", "a": "171/55", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "171^171 vs 34^55·55^171", "sign": 1, "bits": [ 1269, 1269 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n34) < 171/55" } }, { "id": "y35_gt", "y": 35, "N": 35, "nFile": "corpus/xxy/n/35.json", "statement": "x > 153/49", "rel": "gt", "a": "153/49", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "153^153 vs 35^49·49^153", "sign": -1, "bits": [ 1111, 1111 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n35) > 153/49" } }, { "id": "y35_lt", "y": 35, "N": 35, "nFile": "corpus/xxy/n/35.json", "statement": "x < 1861/596", "rel": "lt", "a": "1861/596", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1861^1861 vs 35^596·596^1861", "sign": 1, "bits": [ 20214, 20214 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n35) < 1861/596" } }, { "id": "y36_gt", "y": 36, "N": 36, "nFile": "corpus/xxy/n/36.json", "statement": "x > 2173/693", "rel": "gt", "a": "2173/693", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2173^2173 vs 36^693·693^2173", "sign": -1, "bits": [ 24089, 24089 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n36) > 2173/693" } }, { "id": "y36_lt", "y": 36, "N": 36, "nFile": "corpus/xxy/n/36.json", "statement": "x < 994/317", "rel": "lt", "a": "994/317", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "994^994 vs 36^317·317^994", "sign": 1, "bits": [ 9898, 9898 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n36) < 994/317" } }, { "id": "y37_gt", "y": 37, "N": 37, "nFile": "corpus/xxy/n/37.json", "statement": "x > 891/283", "rel": "gt", "a": "891/283", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "891^891 vs 37^283·283^891", "sign": -1, "bits": [ 8732, 8732 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n37) > 891/283" } }, { "id": "y37_lt", "y": 37, "N": 37, "nFile": "corpus/xxy/n/37.json", "statement": "x < 1294/411", "rel": "lt", "a": "1294/411", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1294^1294 vs 37^411·411^1294", "sign": 1, "bits": [ 13377, 13377 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n37) < 1294/411" } }, { "id": "y38_gt", "y": 38, "N": 38, "nFile": "corpus/xxy/n/38.json", "statement": "x > 1533/485", "rel": "gt", "a": "1533/485", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1533^1533 vs 38^485·485^1533", "sign": -1, "bits": [ 16223, 16223 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n38) > 1533/485" } }, { "id": "y38_lt", "y": 38, "N": 38, "nFile": "corpus/xxy/n/38.json", "statement": "x < 1985/628", "rel": "lt", "a": "1985/628", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1985^1985 vs 38^628·628^1985", "sign": 1, "bits": [ 21746, 21746 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n38) < 1985/628" } }, { "id": "y39_gt", "y": 39, "N": 39, "nFile": "corpus/xxy/n/39.json", "statement": "x > 257/81", "rel": "gt", "a": "257/81", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "257^257 vs 39^81·81^257", "sign": -1, "bits": [ 2058, 2058 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n39) > 257/81" } }, { "id": "y39_lt", "y": 39, "N": 39, "nFile": "corpus/xxy/n/39.json", "statement": "x < 679/214", "rel": "lt", "a": "679/214", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "679^679 vs 39^214·214^679", "sign": 1, "bits": [ 6388, 6388 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n39) < 679/214" } }, { "id": "y40_gt", "y": 40, "N": 40, "nFile": "corpus/xxy/n/40.json", "statement": "x > 2777/872", "rel": "gt", "a": "2777/872", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2777^2777 vs 40^872·872^2777", "sign": -1, "bits": [ 31767, 31767 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n40) > 2777/872" } }, { "id": "y40_lt", "y": 40, "N": 40, "nFile": "corpus/xxy/n/40.json", "statement": "x < 2570/807", "rel": "lt", "a": "2570/807", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2570^2570 vs 40^807·807^2570", "sign": 1, "bits": [ 29112, 29112 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n40) < 2570/807" } }, { "id": "y41_gt", "y": 41, "N": 41, "nFile": "corpus/xxy/n/41.json", "statement": "x > 147/46", "rel": "gt", "a": "147/46", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "147^147 vs 41^46·46^147", "sign": -1, "bits": [ 1059, 1059 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n41) > 147/46" } }, { "id": "y41_lt", "y": 41, "N": 41, "nFile": "corpus/xxy/n/41.json", "statement": "x < 163/51", "rel": "lt", "a": "163/51", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "163^163 vs 41^51·51^163", "sign": 1, "bits": [ 1198, 1198 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n41) < 163/51" } }, { "id": "y42_gt", "y": 42, "N": 42, "nFile": "corpus/xxy/n/42.json", "statement": "x > 93/29", "rel": "gt", "a": "93/29", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "93^93 vs 42^29·29^93", "sign": -1, "bits": [ 609, 609 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n42) > 93/29" } }, { "id": "y42_lt", "y": 42, "N": 42, "nFile": "corpus/xxy/n/42.json", "statement": "x < 356/111", "rel": "lt", "a": "356/111", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "356^356 vs 42^111·111^356", "sign": 1, "bits": [ 3018, 3018 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n42) < 356/111" } }, { "id": "y43_gt", "y": 43, "N": 43, "nFile": "corpus/xxy/n/43.json", "statement": "x > 428/133", "rel": "gt", "a": "428/133", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "428^428 vs 43^133·133^428", "sign": -1, "bits": [ 3742, 3742 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n43) > 428/133" } }, { "id": "y43_lt", "y": 43, "N": 43, "nFile": "corpus/xxy/n/43.json", "statement": "x < 1461/454", "rel": "lt", "a": "1461/454", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1461^1461 vs 43^454·454^1461", "sign": 1, "bits": [ 15360, 15360 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n43) < 1461/454" } }, { "id": "y44_gt", "y": 44, "N": 44, "nFile": "corpus/xxy/n/44.json", "statement": "x > 1172/363", "rel": "gt", "a": "1172/363", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1172^1172 vs 44^363·363^1172", "sign": -1, "bits": [ 11949, 11949 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n44) > 1172/363" } }, { "id": "y44_lt", "y": 44, "N": 44, "nFile": "corpus/xxy/n/44.json", "statement": "x < 1059/328", "rel": "lt", "a": "1059/328", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1059^1059 vs 44^328·328^1059", "sign": 1, "bits": [ 10642, 10642 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n44) < 1059/328" } }, { "id": "y45_gt", "y": 45, "N": 45, "nFile": "corpus/xxy/n/45.json", "statement": "x > 366/113", "rel": "gt", "a": "366/113", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "366^366 vs 45^113·113^366", "sign": -1, "bits": [ 3117, 3117 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n45) > 366/113" } }, { "id": "y45_lt", "y": 45, "N": 45, "nFile": "corpus/xxy/n/45.json", "statement": "x < 515/159", "rel": "lt", "a": "515/159", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "515^515 vs 45^159·159^515", "sign": 1, "bits": [ 4640, 4640 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n45) < 515/159" } }, { "id": "y46_gt", "y": 46, "N": 46, "nFile": "corpus/xxy/n/46.json", "statement": "x > 887/273", "rel": "gt", "a": "887/273", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "887^887 vs 46^273·273^887", "sign": -1, "bits": [ 8687, 8687 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n46) > 887/273" } }, { "id": "y46_lt", "y": 46, "N": 46, "nFile": "corpus/xxy/n/46.json", "statement": "x < 2674/823", "rel": "lt", "a": "2674/823", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2674^2674 vs 46^823·823^2674", "sign": 1, "bits": [ 30443, 30443 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n46) < 2674/823" } }, { "id": "y47_gt", "y": 47, "N": 47, "nFile": "corpus/xxy/n/47.json", "statement": "x > 1183/363", "rel": "gt", "a": "1183/363", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1183^1183 vs 47^363·363^1183", "sign": -1, "bits": [ 12077, 12077 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n47) > 1183/363" } }, { "id": "y47_lt", "y": 47, "N": 47, "nFile": "corpus/xxy/n/47.json", "statement": "x < 818/251", "rel": "lt", "a": "818/251", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "818^818 vs 47^251·251^818", "sign": 1, "bits": [ 7915, 7915 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n47) < 818/251" } }, { "id": "y48_gt", "y": 48, "N": 48, "nFile": "corpus/xxy/n/48.json", "statement": "x > 791/242", "rel": "gt", "a": "791/242", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "791^791 vs 48^242·242^791", "sign": -1, "bits": [ 7616, 7616 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n48) > 791/242" } }, { "id": "y48_lt", "y": 48, "N": 48, "nFile": "corpus/xxy/n/48.json", "statement": "x < 219/67", "rel": "lt", "a": "219/67", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "219^219 vs 48^67·67^219", "sign": 1, "bits": [ 1703, 1703 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n48) < 219/67" } }, { "id": "y49_gt", "y": 49, "N": 49, "nFile": "corpus/xxy/n/49.json", "statement": "x > 731/223", "rel": "gt", "a": "731/223", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "731^731 vs 49^223·223^731", "sign": -1, "bits": [ 6955, 6955 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n49) > 731/223" } }, { "id": "y49_lt", "y": 49, "N": 49, "nFile": "corpus/xxy/n/49.json", "statement": "x < 2865/874", "rel": "lt", "a": "2865/874", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2865^2865 vs 49^874·874^2865", "sign": 1, "bits": [ 32903, 32903 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n49) < 2865/874" } }, { "id": "y50_gt", "y": 50, "N": 50, "nFile": "corpus/xxy/n/50.json", "statement": "x > 309/94", "rel": "gt", "a": "309/94", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "309^309 vs 50^94·94^309", "sign": -1, "bits": [ 2556, 2556 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n50) > 309/94" } }, { "id": "y50_lt", "y": 50, "N": 50, "nFile": "corpus/xxy/n/50.json", "statement": "x < 1213/369", "rel": "lt", "a": "1213/369", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1213^1213 vs 50^369·369^1213", "sign": 1, "bits": [ 12427, 12427 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n50) < 1213/369" } }, { "id": "y51_gt", "y": 51, "N": 51, "nFile": "corpus/xxy/n/51.json", "statement": "x > 89/27", "rel": "gt", "a": "89/27", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "89^89 vs 51^27·27^89", "sign": -1, "bits": [ 577, 577 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n51) > 89/27" } }, { "id": "y51_lt", "y": 51, "N": 51, "nFile": "corpus/xxy/n/51.json", "statement": "x < 33/10", "rel": "lt", "a": "33/10", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "33^33 vs 51^10·10^33", "sign": 1, "bits": [ 167, 167 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n51) < 33/10" } }, { "id": "y52_gt", "y": 52, "N": 52, "nFile": "corpus/xxy/n/52.json", "statement": "x > 899/272", "rel": "gt", "a": "899/272", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "899^899 vs 52^272·272^899", "sign": -1, "bits": [ 8822, 8822 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n52) > 899/272" } }, { "id": "y52_lt", "y": 52, "N": 52, "nFile": "corpus/xxy/n/52.json", "statement": "x < 704/213", "rel": "lt", "a": "704/213", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "704^704 vs 52^213·213^704", "sign": 1, "bits": [ 6660, 6660 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n52) < 704/213" } }, { "id": "y53_gt", "y": 53, "N": 53, "nFile": "corpus/xxy/n/53.json", "statement": "x > 1415/427", "rel": "gt", "a": "1415/427", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1415^1415 vs 53^427·427^1415", "sign": -1, "bits": [ 14811, 14811 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n53) > 1415/427" } }, { "id": "y53_lt", "y": 53, "N": 53, "nFile": "corpus/xxy/n/53.json", "statement": "x < 623/188", "rel": "lt", "a": "623/188", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "623^623 vs 53^188·188^623", "sign": 1, "bits": [ 5784, 5784 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n53) < 623/188" } }, { "id": "y54_gt", "y": 54, "N": 54, "nFile": "corpus/xxy/n/54.json", "statement": "x > 402/121", "rel": "gt", "a": "402/121", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "402^402 vs 54^121·121^402", "sign": -1, "bits": [ 3478, 3478 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n54) > 402/121" } }, { "id": "y54_lt", "y": 54, "N": 54, "nFile": "corpus/xxy/n/54.json", "statement": "x < 103/31", "rel": "lt", "a": "103/31", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "103^103 vs 54^31·31^103", "sign": 1, "bits": [ 689, 689 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n54) < 103/31" } }, { "id": "y55_gt", "y": 55, "N": 55, "nFile": "corpus/xxy/n/55.json", "statement": "x > 413/124", "rel": "gt", "a": "413/124", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "413^413 vs 55^124·124^413", "sign": -1, "bits": [ 3589, 3589 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n55) > 413/124" } }, { "id": "y55_lt", "y": 55, "N": 55, "nFile": "corpus/xxy/n/55.json", "statement": "x < 10/3", "rel": "lt", "a": "10/3", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "10^10 vs 55^3·3^10", "sign": 1, "bits": [ 34, 34 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n55) < 10/3" } }, { "id": "y56_gt", "y": 56, "N": 56, "nFile": "corpus/xxy/n/56.json", "statement": "x > 1419/425", "rel": "gt", "a": "1419/425", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1419^1419 vs 56^425·425^1419", "sign": -1, "bits": [ 14858, 14858 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n56) > 1419/425" } }, { "id": "y56_lt", "y": 56, "N": 56, "nFile": "corpus/xxy/n/56.json", "statement": "x < 3242/971", "rel": "lt", "a": "3242/971", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "3242^3242 vs 56^971·971^3242", "sign": 1, "bits": [ 37811, 37811 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n56) < 3242/971" } }, { "id": "y57_gt", "y": 57, "N": 57, "nFile": "corpus/xxy/n/57.json", "statement": "x > 579/173", "rel": "gt", "a": "579/173", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "579^579 vs 57^173·173^579", "sign": -1, "bits": [ 5314, 5314 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n57) > 579/173" } }, { "id": "y57_lt", "y": 57, "N": 57, "nFile": "corpus/xxy/n/57.json", "statement": "x < 743/222", "rel": "lt", "a": "743/222", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "743^743 vs 57^222·222^743", "sign": 1, "bits": [ 7087, 7087 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n57) < 743/222" } }, { "id": "y58_gt", "y": 58, "N": 58, "nFile": "corpus/xxy/n/58.json", "statement": "x > 889/265", "rel": "gt", "a": "889/265", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "889^889 vs 58^265·265^889", "sign": -1, "bits": [ 8709, 8709 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n58) > 889/265" } }, { "id": "y58_lt", "y": 58, "N": 58, "nFile": "corpus/xxy/n/58.json", "statement": "x < 104/31", "rel": "lt", "a": "104/31", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "104^104 vs 58^31·31^104", "sign": 1, "bits": [ 697, 697 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n58) < 104/31" } }, { "id": "y59_gt", "y": 59, "N": 59, "nFile": "corpus/xxy/n/59.json", "statement": "x > 770/229", "rel": "gt", "a": "770/229", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "770^770 vs 59^229·229^770", "sign": -1, "bits": [ 7384, 7384 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n59) > 770/229" } }, { "id": "y59_lt", "y": 59, "N": 59, "nFile": "corpus/xxy/n/59.json", "statement": "x < 269/80", "rel": "lt", "a": "269/80", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "269^269 vs 59^80·80^269", "sign": 1, "bits": [ 2172, 2172 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n59) < 269/80" } }, { "id": "y60_gt", "y": 60, "N": 60, "nFile": "corpus/xxy/n/60.json", "statement": "x > 337/100", "rel": "gt", "a": "337/100", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "337^337 vs 60^100·100^337", "sign": -1, "bits": [ 2830, 2830 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n60) > 337/100" } }, { "id": "y60_lt", "y": 60, "N": 60, "nFile": "corpus/xxy/n/60.json", "statement": "x < 765/227", "rel": "lt", "a": "765/227", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "765^765 vs 60^227·227^765", "sign": 1, "bits": [ 7329, 7329 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n60) < 765/227" } }, { "id": "y61_gt", "y": 61, "N": 61, "nFile": "corpus/xxy/n/61.json", "statement": "x > 510/151", "rel": "gt", "a": "510/151", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "510^510 vs 61^151·151^510", "sign": -1, "bits": [ 4588, 4588 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n61) > 510/151" } }, { "id": "y61_lt", "y": 61, "N": 61, "nFile": "corpus/xxy/n/61.json", "statement": "x < 1351/400", "rel": "lt", "a": "1351/400", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1351^1351 vs 61^400·400^1351", "sign": 1, "bits": [ 14051, 14051 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n61) < 1351/400" } }, { "id": "y62_gt", "y": 62, "N": 62, "nFile": "corpus/xxy/n/62.json", "statement": "x > 44/13", "rel": "gt", "a": "44/13", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "44^44 vs 62^13·13^44", "sign": -1, "bits": [ 241, 241 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n62) > 44/13" } }, { "id": "y62_lt", "y": 62, "N": 62, "nFile": "corpus/xxy/n/62.json", "statement": "x < 1205/356", "rel": "lt", "a": "1205/356", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1205^1205 vs 62^356·356^1205", "sign": 1, "bits": [ 12333, 12333 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n62) < 1205/356" } }, { "id": "y63_gt", "y": 63, "N": 63, "nFile": "corpus/xxy/n/63.json", "statement": "x > 1618/477", "rel": "gt", "a": "1618/477", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1618^1618 vs 63^477·477^1618", "sign": -1, "bits": [ 17248, 17248 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n63) > 1618/477" } }, { "id": "y63_lt", "y": 63, "N": 63, "nFile": "corpus/xxy/n/63.json", "statement": "x < 2215/653", "rel": "lt", "a": "2215/653", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2215^2215 vs 63^653·653^2215", "sign": 1, "bits": [ 24616, 24616 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n63) < 2215/653" } }, { "id": "y64_gt", "y": 64, "N": 64, "nFile": "corpus/xxy/n/64.json", "statement": "x > 758/223", "rel": "gt", "a": "758/223", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "758^758 vs 64^223·223^758", "sign": -1, "bits": [ 7252, 7252 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n64) > 758/223" } }, { "id": "y64_lt", "y": 64, "N": 64, "nFile": "corpus/xxy/n/64.json", "statement": "x < 775/228", "rel": "lt", "a": "775/228", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "775^775 vs 64^228·228^775", "sign": 1, "bits": [ 7439, 7439 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n64) < 775/228" } }, { "id": "y65_gt", "y": 65, "N": 65, "nFile": "corpus/xxy/n/65.json", "statement": "x > 562/165", "rel": "gt", "a": "562/165", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "562^562 vs 65^165·165^562", "sign": -1, "bits": [ 5134, 5134 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n65) > 562/165" } }, { "id": "y65_lt", "y": 65, "N": 65, "nFile": "corpus/xxy/n/65.json", "statement": "x < 671/197", "rel": "lt", "a": "671/197", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "671^671 vs 65^197·197^671", "sign": 1, "bits": [ 6301, 6301 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n65) < 671/197" } }, { "id": "y66_gt", "y": 66, "N": 66, "nFile": "corpus/xxy/n/66.json", "statement": "x > 1529/448", "rel": "gt", "a": "1529/448", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1529^1529 vs 66^448·448^1529", "sign": -1, "bits": [ 16175, 16175 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n66) > 1529/448" } }, { "id": "y66_lt", "y": 66, "N": 66, "nFile": "corpus/xxy/n/66.json", "statement": "x < 843/247", "rel": "lt", "a": "843/247", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "843^843 vs 66^247·247^843", "sign": 1, "bits": [ 8194, 8194 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n66) < 843/247" } }, { "id": "y67_gt", "y": 67, "N": 67, "nFile": "corpus/xxy/n/67.json", "statement": "x > 2917/853", "rel": "gt", "a": "2917/853", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2917^2917 vs 67^853·853^2917", "sign": -1, "bits": [ 33576, 33576 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n67) > 2917/853" } }, { "id": "y67_lt", "y": 67, "N": 67, "nFile": "corpus/xxy/n/67.json", "statement": "x < 2257/660", "rel": "lt", "a": "2257/660", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2257^2257 vs 67^660·660^2257", "sign": 1, "bits": [ 25144, 25144 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n67) < 2257/660" } }, { "id": "y68_gt", "y": 68, "N": 68, "nFile": "corpus/xxy/n/68.json", "statement": "x > 1093/319", "rel": "gt", "a": "1093/319", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1093^1093 vs 68^319·319^1093", "sign": -1, "bits": [ 11033, 11033 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n68) > 1093/319" } }, { "id": "y68_lt", "y": 68, "N": 68, "nFile": "corpus/xxy/n/68.json", "statement": "x < 1535/448", "rel": "lt", "a": "1535/448", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1535^1535 vs 68^448·448^1535", "sign": 1, "bits": [ 16247, 16247 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n68) < 1535/448" } }, { "id": "y69_gt", "y": 69, "N": 69, "nFile": "corpus/xxy/n/69.json", "statement": "x > 1253/365", "rel": "gt", "a": "1253/365", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1253^1253 vs 69^365·365^1253", "sign": -1, "bits": [ 12895, 12895 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n69) > 1253/365" } }, { "id": "y69_lt", "y": 69, "N": 69, "nFile": "corpus/xxy/n/69.json", "statement": "x < 1023/298", "rel": "lt", "a": "1023/298", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1023^1023 vs 69^298·298^1023", "sign": 1, "bits": [ 10229, 10229 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n69) < 1023/298" } }, { "id": "y70_gt", "y": 70, "N": 70, "nFile": "corpus/xxy/n/70.json", "statement": "x > 2012/585", "rel": "gt", "a": "2012/585", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2012^2012 vs 70^585·585^2012", "sign": -1, "bits": [ 22081, 22081 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n70) > 2012/585" } }, { "id": "y70_lt", "y": 70, "N": 70, "nFile": "corpus/xxy/n/70.json", "statement": "x < 1417/412", "rel": "lt", "a": "1417/412", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1417^1417 vs 70^412·412^1417", "sign": 1, "bits": [ 14835, 14835 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n70) < 1417/412" } }, { "id": "y71_gt", "y": 71, "N": 71, "nFile": "corpus/xxy/n/71.json", "statement": "x > 317/92", "rel": "gt", "a": "317/92", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "317^317 vs 71^92·92^317", "sign": -1, "bits": [ 2634, 2634 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n71) > 317/92" } }, { "id": "y71_lt", "y": 71, "N": 71, "nFile": "corpus/xxy/n/71.json", "statement": "x < 286/83", "rel": "lt", "a": "286/83", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "286^286 vs 71^83·83^286", "sign": 1, "bits": [ 2334, 2334 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n71) < 286/83" } }, { "id": "y72_gt", "y": 72, "N": 72, "nFile": "corpus/xxy/n/72.json", "statement": "x > 2261/655", "rel": "gt", "a": "2261/655", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2261^2261 vs 72^655·655^2261", "sign": -1, "bits": [ 25194, 25194 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n72) > 2261/655" } }, { "id": "y72_lt", "y": 72, "N": 72, "nFile": "corpus/xxy/n/72.json", "statement": "x < 2620/759", "rel": "lt", "a": "2620/759", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2620^2620 vs 72^759·759^2620", "sign": 1, "bits": [ 29752, 29752 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n72) < 2620/759" } }, { "id": "y73_gt", "y": 73, "N": 73, "nFile": "corpus/xxy/n/73.json", "statement": "x > 536/155", "rel": "gt", "a": "536/155", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "536^536 vs 73^155·155^536", "sign": -1, "bits": [ 4860, 4860 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n73) > 536/155" } }, { "id": "y73_lt", "y": 73, "N": 73, "nFile": "corpus/xxy/n/73.json", "statement": "x < 83/24", "rel": "lt", "a": "83/24", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "83^83 vs 73^24·24^83", "sign": 1, "bits": [ 530, 530 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n73) < 83/24" } }, { "id": "y74_gt", "y": 74, "N": 74, "nFile": "corpus/xxy/n/74.json", "statement": "x > 821/237", "rel": "gt", "a": "821/237", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "821^821 vs 74^237·237^821", "sign": -1, "bits": [ 7949, 7949 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n74) > 821/237" } }, { "id": "y74_lt", "y": 74, "N": 74, "nFile": "corpus/xxy/n/74.json", "statement": "x < 97/28", "rel": "lt", "a": "97/28", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "97^97 vs 74^28·28^97", "sign": 1, "bits": [ 641, 641 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n74) < 97/28" } }, { "id": "y75_gt", "y": 75, "N": 75, "nFile": "corpus/xxy/n/75.json", "statement": "x > 871/251", "rel": "gt", "a": "871/251", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "871^871 vs 75^251·251^871", "sign": -1, "bits": [ 8507, 8507 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n75) > 871/251" } }, { "id": "y75_lt", "y": 75, "N": 75, "nFile": "corpus/xxy/n/75.json", "statement": "x < 465/134", "rel": "lt", "a": "465/134", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "465^465 vs 75^134·134^465", "sign": 1, "bits": [ 4121, 4121 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n75) < 465/134" } }, { "id": "y76_gt", "y": 76, "N": 76, "nFile": "corpus/xxy/n/76.json", "statement": "x > 942/271", "rel": "gt", "a": "942/271", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "942^942 vs 76^271·271^942", "sign": -1, "bits": [ 9307, 9307 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n76) > 942/271" } }, { "id": "y76_lt", "y": 76, "N": 76, "nFile": "corpus/xxy/n/76.json", "statement": "x < 1957/563", "rel": "lt", "a": "1957/563", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1957^1957 vs 76^563·563^1957", "sign": 1, "bits": [ 21399, 21399 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n76) < 1957/563" } }, { "id": "y77_gt", "y": 77, "N": 77, "nFile": "corpus/xxy/n/77.json", "statement": "x > 383/110", "rel": "gt", "a": "383/110", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "383^383 vs 77^110·110^383", "sign": -1, "bits": [ 3287, 3287 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n77) > 383/110" } }, { "id": "y77_lt", "y": 77, "N": 77, "nFile": "corpus/xxy/n/77.json", "statement": "x < 1438/413", "rel": "lt", "a": "1438/413", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1438^1438 vs 77^413·413^1438", "sign": 1, "bits": [ 15085, 15085 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n77) < 1438/413" } }, { "id": "y78_gt", "y": 78, "N": 78, "nFile": "corpus/xxy/n/78.json", "statement": "x > 1123/322", "rel": "gt", "a": "1123/322", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1123^1123 vs 78^322·322^1123", "sign": -1, "bits": [ 11380, 11380 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n78) > 1123/322" } }, { "id": "y78_lt", "y": 78, "N": 78, "nFile": "corpus/xxy/n/78.json", "statement": "x < 422/121", "rel": "lt", "a": "422/121", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "422^422 vs 78^121·121^422", "sign": 1, "bits": [ 3681, 3681 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n78) < 422/121" } }, { "id": "y79_gt", "y": 79, "N": 79, "nFile": "corpus/xxy/n/79.json", "statement": "x > 255/73", "rel": "gt", "a": "255/73", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "255^255 vs 79^73·73^255", "sign": -1, "bits": [ 2039, 2039 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n79) > 255/73" } }, { "id": "y79_lt", "y": 79, "N": 79, "nFile": "corpus/xxy/n/79.json", "statement": "x < 517/148", "rel": "lt", "a": "517/148", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "517^517 vs 79^148·148^517", "sign": 1, "bits": [ 4661, 4661 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n79) < 517/148" } }, { "id": "y80_gt", "y": 80, "N": 80, "nFile": "corpus/xxy/n/80.json", "statement": "x > 2981/852", "rel": "gt", "a": "2981/852", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2981^2981 vs 80^852·852^2981", "sign": -1, "bits": [ 34406, 34406 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n80) > 2981/852" } }, { "id": "y80_lt", "y": 80, "N": 80, "nFile": "corpus/xxy/n/80.json", "statement": "x < 1494/427", "rel": "lt", "a": "1494/427", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1494^1494 vs 80^427·427^1494", "sign": 1, "bits": [ 15755, 15755 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n80) < 1494/427" } }, { "id": "y81_gt", "y": 81, "N": 81, "nFile": "corpus/xxy/n/81.json", "statement": "x > 7/2", "rel": "gt", "a": "7/2", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "7^7 vs 81^2·2^7", "sign": -1, "bits": [ 20, 20 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n81) > 7/2" } }, { "id": "y81_lt", "y": 81, "N": 81, "nFile": "corpus/xxy/n/81.json", "statement": "x < 403/115", "rel": "lt", "a": "403/115", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "403^403 vs 81^115·115^403", "sign": 1, "bits": [ 3488, 3488 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n81) < 403/115" } }, { "id": "y82_gt", "y": 82, "N": 82, "nFile": "corpus/xxy/n/82.json", "statement": "x > 3050/869", "rel": "gt", "a": "3050/869", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "3050^3050 vs 82^869·869^3050", "sign": -1, "bits": [ 35303, 35303 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n82) > 3050/869" } }, { "id": "y82_lt", "y": 82, "N": 82, "nFile": "corpus/xxy/n/82.json", "statement": "x < 179/51", "rel": "lt", "a": "179/51", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "179^179 vs 82^51·51^179", "sign": 1, "bits": [ 1340, 1340 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n82) < 179/51" } }, { "id": "y83_gt", "y": 83, "N": 83, "nFile": "corpus/xxy/n/83.json", "statement": "x > 116/33", "rel": "gt", "a": "116/33", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "116^116 vs 83^33·33^116", "sign": -1, "bits": [ 796, 796 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n83) > 116/33" } }, { "id": "y83_lt", "y": 83, "N": 83, "nFile": "corpus/xxy/n/83.json", "statement": "x < 109/31", "rel": "lt", "a": "109/31", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "109^109 vs 83^31·31^109", "sign": 1, "bits": [ 738, 738 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n83) < 109/31" } }, { "id": "y84_gt", "y": 84, "N": 84, "nFile": "corpus/xxy/n/84.json", "statement": "x > 1549/440", "rel": "gt", "a": "1549/440", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1549^1549 vs 84^440·440^1549", "sign": -1, "bits": [ 16415, 16415 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n84) > 1549/440" } }, { "id": "y84_lt", "y": 84, "N": 84, "nFile": "corpus/xxy/n/84.json", "statement": "x < 2151/611", "rel": "lt", "a": "2151/611", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2151^2151 vs 84^611·611^2151", "sign": 1, "bits": [ 23814, 23814 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n84) < 2151/611" } }, { "id": "y85_gt", "y": 85, "N": 85, "nFile": "corpus/xxy/n/85.json", "statement": "x > 892/253", "rel": "gt", "a": "892/253", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "892^892 vs 85^253·253^892", "sign": -1, "bits": [ 8743, 8743 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n85) > 892/253" } }, { "id": "y85_lt", "y": 85, "N": 85, "nFile": "corpus/xxy/n/85.json", "statement": "x < 3293/934", "rel": "lt", "a": "3293/934", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "3293^3293 vs 85^934·934^3293", "sign": 1, "bits": [ 38480, 38480 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n85) < 3293/934" } }, { "id": "y86_gt", "y": 86, "N": 86, "nFile": "corpus/xxy/n/86.json", "statement": "x > 286/81", "rel": "gt", "a": "286/81", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "286^286 vs 86^81·81^286", "sign": -1, "bits": [ 2334, 2334 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n86) > 286/81" } }, { "id": "y86_lt", "y": 86, "N": 86, "nFile": "corpus/xxy/n/86.json", "statement": "x < 113/32", "rel": "lt", "a": "113/32", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "113^113 vs 86^32·32^113", "sign": 1, "bits": [ 771, 771 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n86) < 113/32" } }, { "id": "y87_gt", "y": 87, "N": 87, "nFile": "corpus/xxy/n/87.json", "statement": "x > 983/278", "rel": "gt", "a": "983/278", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "983^983 vs 87^278·278^983", "sign": -1, "bits": [ 9773, 9773 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n87) > 983/278" } }, { "id": "y87_lt", "y": 87, "N": 87, "nFile": "corpus/xxy/n/87.json", "statement": "x < 1425/403", "rel": "lt", "a": "1425/403", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1425^1425 vs 87^403·403^1425", "sign": 1, "bits": [ 14930, 14930 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n87) < 1425/403" } }, { "id": "y88_gt", "y": 88, "N": 88, "nFile": "corpus/xxy/n/88.json", "statement": "x > 1381/390", "rel": "gt", "a": "1381/390", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1381^1381 vs 88^390·390^1381", "sign": -1, "bits": [ 14406, 14406 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n88) > 1381/390" } }, { "id": "y88_lt", "y": 88, "N": 88, "nFile": "corpus/xxy/n/88.json", "statement": "x < 2546/719", "rel": "lt", "a": "2546/719", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2546^2546 vs 88^719·719^2546", "sign": 1, "bits": [ 28806, 28806 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n88) < 2546/719" } }, { "id": "y89_gt", "y": 89, "N": 89, "nFile": "corpus/xxy/n/89.json", "statement": "x > 578/163", "rel": "gt", "a": "578/163", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "578^578 vs 89^163·163^578", "sign": -1, "bits": [ 5304, 5304 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n89) > 578/163" } }, { "id": "y89_lt", "y": 89, "N": 89, "nFile": "corpus/xxy/n/89.json", "statement": "x < 539/152", "rel": "lt", "a": "539/152", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "539^539 vs 89^152·152^539", "sign": 1, "bits": [ 4891, 4891 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n89) < 539/152" } }, { "id": "y90_gt", "y": 90, "N": 90, "nFile": "corpus/xxy/n/90.json", "statement": "x > 941/265", "rel": "gt", "a": "941/265", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "941^941 vs 90^265·265^941", "sign": -1, "bits": [ 9296, 9296 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n90) > 941/265" } }, { "id": "y90_lt", "y": 90, "N": 90, "nFile": "corpus/xxy/n/90.json", "statement": "x < 174/49", "rel": "lt", "a": "174/49", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "174^174 vs 90^49·49^174", "sign": 1, "bits": [ 1296, 1296 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n90) < 174/49" } }, { "id": "y91_gt", "y": 91, "N": 91, "nFile": "corpus/xxy/n/91.json", "statement": "x > 32/9", "rel": "gt", "a": "32/9", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "32^32 vs 91^9·9^32", "sign": -1, "bits": [ 161, 161 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n91) > 32/9" } }, { "id": "y91_lt", "y": 91, "N": 91, "nFile": "corpus/xxy/n/91.json", "statement": "x < 1497/421", "rel": "lt", "a": "1497/421", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1497^1497 vs 91^421·421^1497", "sign": 1, "bits": [ 15791, 15791 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n91) < 1497/421" } }, { "id": "y92_gt", "y": 92, "N": 92, "nFile": "corpus/xxy/n/92.json", "statement": "x > 235/66", "rel": "gt", "a": "235/66", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "235^235 vs 92^66·66^235", "sign": -1, "bits": [ 1851, 1851 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n92) > 235/66" } }, { "id": "y92_lt", "y": 92, "N": 92, "nFile": "corpus/xxy/n/92.json", "statement": "x < 1791/503", "rel": "lt", "a": "1791/503", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1791^1791 vs 92^503·503^1791", "sign": 1, "bits": [ 19355, 19355 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n92) < 1791/503" } }, { "id": "y93_gt", "y": 93, "N": 93, "nFile": "corpus/xxy/n/93.json", "statement": "x > 2617/734", "rel": "gt", "a": "2617/734", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2617^2617 vs 93^734·734^2617", "sign": -1, "bits": [ 29713, 29713 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n93) > 2617/734" } }, { "id": "y93_lt", "y": 93, "N": 93, "nFile": "corpus/xxy/n/93.json", "statement": "x < 3462/971", "rel": "lt", "a": "3462/971", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "3462^3462 vs 93^971·971^3462", "sign": 1, "bits": [ 40705, 40705 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n93) < 3462/971" } }, { "id": "y94_gt", "y": 94, "N": 94, "nFile": "corpus/xxy/n/94.json", "statement": "x > 382/107", "rel": "gt", "a": "382/107", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "382^382 vs 94^107·107^382", "sign": -1, "bits": [ 3277, 3277 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n94) > 382/107" } }, { "id": "y94_lt", "y": 94, "N": 94, "nFile": "corpus/xxy/n/94.json", "statement": "x < 3081/863", "rel": "lt", "a": "3081/863", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "3081^3081 vs 94^863·863^3081", "sign": 1, "bits": [ 35707, 35707 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n94) < 3081/863" } }, { "id": "y95_gt", "y": 95, "N": 95, "nFile": "corpus/xxy/n/95.json", "statement": "x > 1841/515", "rel": "gt", "a": "1841/515", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1841^1841 vs 95^515·515^1841", "sign": -1, "bits": [ 19968, 19968 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n95) > 1841/515" } }, { "id": "y95_lt", "y": 95, "N": 95, "nFile": "corpus/xxy/n/95.json", "statement": "x < 765/214", "rel": "lt", "a": "765/214", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "765^765 vs 95^214·214^765", "sign": 1, "bits": [ 7329, 7329 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n95) < 765/214" } }, { "id": "y96_gt", "y": 96, "N": 96, "nFile": "corpus/xxy/n/96.json", "statement": "x > 68/19", "rel": "gt", "a": "68/19", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "68^68 vs 96^19·19^68", "sign": -1, "bits": [ 414, 414 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n96) > 68/19" } }, { "id": "y96_lt", "y": 96, "N": 96, "nFile": "corpus/xxy/n/96.json", "statement": "x < 451/126", "rel": "lt", "a": "451/126", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "451^451 vs 96^126·126^451", "sign": 1, "bits": [ 3977, 3977 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n96) < 451/126" } }, { "id": "y97_gt", "y": 97, "N": 97, "nFile": "corpus/xxy/n/97.json", "statement": "x > 534/149", "rel": "gt", "a": "534/149", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "534^534 vs 97^149·149^534", "sign": -1, "bits": [ 4839, 4839 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n97) > 534/149" } }, { "id": "y97_lt", "y": 97, "N": 97, "nFile": "corpus/xxy/n/97.json", "statement": "x < 1025/286", "rel": "lt", "a": "1025/286", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1025^1025 vs 97^286·286^1025", "sign": 1, "bits": [ 10252, 10252 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n97) < 1025/286" } }, { "id": "y98_gt", "y": 98, "N": 98, "nFile": "corpus/xxy/n/98.json", "statement": "x > 2293/639", "rel": "gt", "a": "2293/639", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2293^2293 vs 98^639·639^2293", "sign": -1, "bits": [ 25597, 25597 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n98) > 2293/639" } }, { "id": "y98_lt", "y": 98, "N": 98, "nFile": "corpus/xxy/n/98.json", "statement": "x < 1116/311", "rel": "lt", "a": "1116/311", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1116^1116 vs 98^311·311^1116", "sign": 1, "bits": [ 11299, 11299 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n98) < 1116/311" } }, { "id": "y99_gt", "y": 99, "N": 99, "nFile": "corpus/xxy/n/99.json", "statement": "x > 1412/393", "rel": "gt", "a": "1412/393", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "1412^1412 vs 99^393·393^1412", "sign": -1, "bits": [ 14775, 14775 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n99) > 1412/393" } }, { "id": "y99_lt", "y": 99, "N": 99, "nFile": "corpus/xxy/n/99.json", "statement": "x < 909/253", "rel": "lt", "a": "909/253", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "909^909 vs 99^253·253^909", "sign": 1, "bits": [ 8934, 8934 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n99) < 909/253" } }, { "id": "y100_gt", "y": 100, "N": 100, "nFile": "corpus/xxy/n/100.json", "statement": "x > 259/72", "rel": "gt", "a": "259/72", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "259^259 vs 100^72·72^259", "sign": -1, "bits": [ 2077, 2077 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n100) > 259/72" } }, { "id": "y100_lt", "y": 100, "N": 100, "nFile": "corpus/xxy/n/100.json", "statement": "x < 795/221", "rel": "lt", "a": "795/221", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "795^795 vs 100^221·221^795", "sign": 1, "bits": [ 7660, 7660 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n100) < 795/221" } }, { "id": "y255_gt", "y": 255, "N": 255, "nFile": "corpus/xxy/n/255.json", "statement": "x > 2435/609", "rel": "gt", "a": "2435/609", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2435^2435 vs 255^609·609^2435", "sign": -1, "bits": [ 27394, 27394 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n255) > 2435/609" } }, { "id": "y255_lt", "y": 255, "N": 255, "nFile": "corpus/xxy/n/255.json", "statement": "x < 2439/610", "rel": "lt", "a": "2439/610", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2439^2439 vs 255^610·610^2439", "sign": 1, "bits": [ 27444, 27444 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n255) < 2439/610" } }, { "id": "y256_ge", "y": 256, "N": 256, "nFile": "corpus/xxy/n/256.json", "statement": "x ≥ 4", "rel": "ge", "a": "4", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "4^4 vs 256", "sign": 0, "bits": [ 9, 9 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n256) ≥ 4" } }, { "id": "y256_le", "y": 256, "N": 256, "nFile": "corpus/xxy/n/256.json", "statement": "x ≤ 4", "rel": "le", "a": "4", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "4^4 vs 256", "sign": 0, "bits": [ 9, 9 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n256) ≤ 4" } }, { "id": "y257_gt", "y": 257, "N": 257, "nFile": "corpus/xxy/n/257.json", "statement": "x > 4", "rel": "gt", "a": "4", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "4^4 vs 257", "sign": -1, "bits": [ 9, 9 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n257) > 4" } }, { "id": "y257_lt", "y": 257, "N": 257, "nFile": "corpus/xxy/n/257.json", "statement": "x < 2449/612", "rel": "lt", "a": "2449/612", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "2449^2449 vs 257^612·612^2449", "sign": 1, "bits": [ 27571, 27571 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n257) < 2449/612" } }, { "id": "y3124_gt", "y": 3124, "N": 3124, "nFile": "corpus/xxy/n/3124.json", "statement": "x > 4", "rel": "gt", "a": "4", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "4^4 vs 3124", "sign": -1, "bits": [ 9, 12 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n3124) > 4" } }, { "id": "y3124_lt", "y": 3124, "N": 3124, "nFile": "corpus/xxy/n/3124.json", "statement": "x < 5", "rel": "lt", "a": "5", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "5^5 vs 3124", "sign": 1, "bits": [ 12, 12 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n3124) < 5" } }, { "id": "y3125_ge", "y": 3125, "N": 3125, "nFile": "corpus/xxy/n/3125.json", "statement": "x ≥ 5", "rel": "ge", "a": "5", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "5^5 vs 3125", "sign": 0, "bits": [ 12, 12 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n3125) ≥ 5" } }, { "id": "y3125_le", "y": 3125, "N": 3125, "nFile": "corpus/xxy/n/3125.json", "statement": "x ≤ 5", "rel": "le", "a": "5", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "5^5 vs 3125", "sign": 0, "bits": [ 12, 12 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n3125) ≤ 5" } }, { "id": "y3126_gt", "y": 3126, "N": 3126, "nFile": "corpus/xxy/n/3126.json", "statement": "x > 5", "rel": "gt", "a": "5", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "5^5 vs 3126", "sign": -1, "bits": [ 12, 12 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n3126) > 5" } }, { "id": "y3126_lt", "y": 3126, "N": 3126, "nFile": "corpus/xxy/n/3126.json", "statement": "x < 6", "rel": "lt", "a": "6", "origin": "the study's bracket (proposed)", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "6^6 vs 3126", "sign": 1, "bits": [ 16, 12 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n3126) < 6" } }, { "id": "y10_planted_lt", "y": 10, "N": 10, "nFile": "corpus/xxy/n/10.json", "statement": "x < 203/81", "rel": "lt", "a": "203/81", "origin": "planted wrong bracket", "word": "REFUTED", "expect": "REFUTED", "compared": "203^203 vs 10^81·81^203", "sign": -1, "bits": [ 1557, 1557 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n10) < 203/81" } }, { "id": "y10_planted_gt", "y": 10, "N": 10, "nFile": "corpus/xxy/n/10.json", "statement": "x > 198/79", "rel": "gt", "a": "198/79", "origin": "planted wrong bracket", "word": "REFUTED", "expect": "REFUTED", "compared": "198^198 vs 10^79·79^198", "sign": 1, "bits": [ 1511, 1511 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n10) > 198/79" } }, { "id": "y64_planted_lt", "y": 64, "N": 64, "nFile": "corpus/xxy/n/64.json", "statement": "x < 758/223", "rel": "lt", "a": "758/223", "origin": "planted wrong bracket", "word": "REFUTED", "expect": "REFUTED", "compared": "758^758 vs 64^223·223^758", "sign": -1, "bits": [ 7252, 7252 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n64) < 758/223" } }, { "id": "y64_planted_gt", "y": 64, "N": 64, "nFile": "corpus/xxy/n/64.json", "statement": "x > 775/228", "rel": "gt", "a": "775/228", "origin": "planted wrong bracket", "word": "REFUTED", "expect": "REFUTED", "compared": "775^775 vs 64^228·228^775", "sign": 1, "bits": [ 7439, 7439 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n64) > 775/228" } }, { "id": "y100_planted_lt", "y": 100, "N": 100, "nFile": "corpus/xxy/n/100.json", "statement": "x < 259/72", "rel": "lt", "a": "259/72", "origin": "planted wrong bracket", "word": "REFUTED", "expect": "REFUTED", "compared": "259^259 vs 100^72·72^259", "sign": -1, "bits": [ 2077, 2077 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n100) < 259/72" } }, { "id": "y100_planted_gt", "y": 100, "N": 100, "nFile": "corpus/xxy/n/100.json", "statement": "x > 795/221", "rel": "gt", "a": "795/221", "origin": "planted wrong bracket", "word": "REFUTED", "expect": "REFUTED", "compared": "795^795 vs 100^221·221^795", "sign": 1, "bits": [ 7660, 7660 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n100) > 795/221" } }, { "id": "y255_planted_lt", "y": 255, "N": 255, "nFile": "corpus/xxy/n/255.json", "statement": "x < 2435/609", "rel": "lt", "a": "2435/609", "origin": "planted wrong bracket", "word": "REFUTED", "expect": "REFUTED", "compared": "2435^2435 vs 255^609·609^2435", "sign": -1, "bits": [ 27394, 27394 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n255) < 2435/609" } }, { "id": "y255_planted_gt", "y": 255, "N": 255, "nFile": "corpus/xxy/n/255.json", "statement": "x > 2439/610", "rel": "gt", "a": "2439/610", "origin": "planted wrong bracket", "word": "REFUTED", "expect": "REFUTED", "compared": "2439^2439 vs 255^610·610^2439", "sign": 1, "bits": [ 27444, 27444 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n255) > 2439/610" } } ], "xx64": [ { "id": "above", "y": 64, "N": 64, "nFile": "corpus/xx64/problem.json", "statement": "x > 33991/10000", "rel": "gt", "a": "33991/10000", "origin": "proposed", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "33991^33991 vs 64^10000·10000^33991", "sign": -1, "bits": [ 511662, 511663 ], "digits": [ 154026, 154026 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n) > 3.3991" } }, { "id": "below", "y": 64, "N": 64, "nFile": "corpus/xx64/problem.json", "statement": "x < 4249/1250", "rel": "lt", "a": "4249/1250", "origin": "proposed", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "4249^4249 vs 64^1250·1250^4249", "sign": 1, "bits": [ 51213, 51213 ], "digits": [ 15417, 15417 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n) < 3.3992" } }, { "id": "planted_above", "y": 64, "N": 64, "nFile": "corpus/xx64/problem.json", "statement": "x > 4249/1250", "rel": "gt", "a": "4249/1250", "origin": "planted wrong bound", "word": "REFUTED", "expect": "REFUTED", "compared": "4249^4249 vs 64^1250·1250^4249", "sign": 1, "bits": [ 51213, 51213 ], "digits": [ 15417, 15417 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n) > 3.3992" } }, { "id": "planted_below", "y": 64, "N": 64, "nFile": "corpus/xx64/problem.json", "statement": "x < 33991/10000", "rel": "lt", "a": "33991/10000", "origin": "planted wrong bound", "word": "REFUTED", "expect": "REFUTED", "compared": "33991^33991 vs 64^10000·10000^33991", "sign": -1, "bits": [ 511662, 511663 ], "digits": [ 154026, 154026 ], "claimbox": { "word": "REFUTED", "expect": "REFUTED", "statement": "xroot(n) < 3.3991" } }, { "id": "cf_above_8", "y": 64, "N": 64, "nFile": "corpus/xx64/problem.json", "statement": "x > 58815/17303", "rel": "gt", "a": "58815/17303", "origin": "proposed", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "58815^58815 vs 64^17303·17303^58815", "sign": -1, "bits": [ 931859, 931859 ], "digits": [ 280518, 280518 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n) > 58815/17303" } }, { "id": "cf_below_7", "y": 64, "N": 64, "nFile": "corpus/xx64/problem.json", "statement": "x < 47207/13888", "rel": "lt", "a": "47207/13888", "origin": "proposed", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "47207^47207 vs 64^13888·13888^47207", "sign": 1, "bits": [ 732970, 732970 ], "digits": [ 220646, 220646 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n) < 47207/13888" } }, { "id": "cf_above_10", "y": 64, "N": 64, "nFile": "corpus/xx64/problem.json", "statement": "x > 458912/135009", "rel": "gt", "a": "458912/135009", "origin": "proposed", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "458912^458912 vs 64^135009·135009^458912", "sign": -1, "bits": [ 8631152, 8631152 ], "digits": [ 2598236, 2598236 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n) > 458912/135009" } }, { "id": "cf_below_9", "y": 64, "N": 64, "nFile": "corpus/xx64/problem.json", "statement": "x < 400097/117706", "rel": "lt", "a": "400097/117706", "origin": "proposed", "word": "CERTIFIED", "expect": "CERTIFIED", "compared": "400097^400097 vs 64^117706·117706^400097", "sign": 1, "bits": [ 7445802, 7445802 ], "digits": [ 2241410, 2241410 ], "claimbox": { "word": "CERTIFIED", "expect": "CERTIFIED", "statement": "xroot(n) < 400097/117706" } } ], "mutants": [ { "of": "y2_gt", "y": 2, "statement": "x > 236/151", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y2_lt", "y": 2, "statement": "x < 640/411", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y3_gt", "y": 3, "statement": "x > 503/275", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y3_lt", "y": 3, "statement": "x < 193/106", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y4_ge", "y": 4, "statement": "x > 2", "how": "the bound made strict", "word": "REFUTED", "sign": 0 }, { "of": "y4_le", "y": 4, "statement": "x < 2", "how": "the bound made strict", "word": "REFUTED", "sign": 0 }, { "of": "y5_gt", "y": 5, "statement": "x > 305/143", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y5_lt", "y": 5, "statement": "x < 36/17", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y6_gt", "y": 6, "statement": "x > 1137/509", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y6_lt", "y": 6, "statement": "x < 890/399", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y7_gt", "y": 7, "statement": "x > 45/19", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y7_lt", "y": 7, "statement": "x < 182/79", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y8_gt", "y": 8, "statement": "x > 247/103", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y8_lt", "y": 8, "statement": "x < 288/121", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y9_gt", "y": 9, "statement": "x > 900/367", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y9_lt", "y": 9, "statement": "x < 124/51", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y10_gt", "y": 10, "statement": "x > 68/27", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y10_lt", "y": 10, "statement": "x < 197/79", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y11_gt", "y": 11, "statement": "x > 8/3", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y11_lt", "y": 11, "statement": "x < 17/7", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y12_gt", "y": 12, "statement": "x > 294/113", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y12_lt", "y": 12, "statement": "x < 1749/673", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y13_gt", "y": 13, "statement": "x > 473/179", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y13_lt", "y": 13, "statement": "x < 1787/677", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y14_gt", "y": 14, "statement": "x > 1959/731", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y14_lt", "y": 14, "statement": "x < 37/14", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y15_gt", "y": 15, "statement": "x > 1382/509", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y15_lt", "y": 15, "statement": "x < 349/129", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y16_gt", "y": 16, "statement": "x > 443/161", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y16_lt", "y": 16, "statement": "x < 74/27", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y17_gt", "y": 17, "statement": "x > 464/167", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y17_lt", "y": 17, "statement": "x < 135/49", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y18_gt", "y": 18, "statement": "x > 205/73", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y18_lt", "y": 18, "statement": "x < 535/191", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y19_gt", "y": 19, "statement": "x > 151/53", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y19_lt", "y": 19, "statement": "x < 379/134", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y20_gt", "y": 20, "statement": "x > 889/311", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y20_lt", "y": 20, "statement": "x < 2446/857", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y21_gt", "y": 21, "statement": "x > 124/43", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y21_lt", "y": 21, "statement": "x < 261/91", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y22_gt", "y": 22, "statement": "x > 3", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y22_lt", "y": 22, "statement": "x < 176/61", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y23_gt", "y": 23, "statement": "x > 3", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y23_lt", "y": 23, "statement": "x < 2", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y24_gt", "y": 24, "statement": "x > 993/337", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y24_lt", "y": 24, "statement": "x < 208/71", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y25_gt", "y": 25, "statement": "x > 86/29", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y25_lt", "y": 25, "statement": "x < 201/68", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y26_gt", "y": 26, "statement": "x > 332/111", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y26_lt", "y": 26, "statement": "x < 1407/472", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y27_ge", "y": 27, "statement": "x > 3", "how": "the bound made strict", "word": "REFUTED", "sign": 0 }, { "of": "y27_le", "y": 27, "statement": "x < 3", "how": "the bound made strict", "word": "REFUTED", "sign": 0 }, { "of": "y28_gt", "y": 28, "statement": "x > 2442/809", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y28_lt", "y": 28, "statement": "x < 196/65", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y29_gt", "y": 29, "statement": "x > 180/59", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y29_lt", "y": 29, "statement": "x < 803/265", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y30_gt", "y": 30, "statement": "x > 31/10", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y30_lt", "y": 30, "statement": "x < 3", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y31_gt", "y": 31, "statement": "x > 1218/397", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y31_lt", "y": 31, "statement": "x < 701/229", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y32_gt", "y": 32, "statement": "x > 1513/491", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y32_lt", "y": 32, "statement": "x < 89/29", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y33_gt", "y": 33, "statement": "x > 425/137", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y33_lt", "y": 33, "statement": "x < 912/295", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y34_gt", "y": 34, "statement": "x > 315/101", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y34_lt", "y": 34, "statement": "x < 34/11", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y35_gt", "y": 35, "statement": "x > 22/7", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y35_lt", "y": 35, "statement": "x < 465/149", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y36_gt", "y": 36, "statement": "x > 2174/693", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y36_lt", "y": 36, "statement": "x < 993/317", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y37_gt", "y": 37, "statement": "x > 892/283", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y37_lt", "y": 37, "statement": "x < 431/137", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y38_gt", "y": 38, "statement": "x > 1534/485", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y38_lt", "y": 38, "statement": "x < 496/157", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y39_gt", "y": 39, "statement": "x > 86/27", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y39_lt", "y": 39, "statement": "x < 339/107", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y40_gt", "y": 40, "statement": "x > 1389/436", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y40_lt", "y": 40, "statement": "x < 2569/807", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y41_gt", "y": 41, "statement": "x > 74/23", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y41_lt", "y": 41, "statement": "x < 54/17", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y42_gt", "y": 42, "statement": "x > 94/29", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y42_lt", "y": 42, "statement": "x < 355/111", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y43_gt", "y": 43, "statement": "x > 429/133", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y43_lt", "y": 43, "statement": "x < 730/227", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y44_gt", "y": 44, "statement": "x > 391/121", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y44_lt", "y": 44, "statement": "x < 529/164", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y45_gt", "y": 45, "statement": "x > 367/113", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y45_lt", "y": 45, "statement": "x < 514/159", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y46_gt", "y": 46, "statement": "x > 296/91", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y46_lt", "y": 46, "statement": "x < 2673/823", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y47_gt", "y": 47, "statement": "x > 1184/363", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y47_lt", "y": 47, "statement": "x < 817/251", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y48_gt", "y": 48, "statement": "x > 36/11", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y48_lt", "y": 48, "statement": "x < 218/67", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y49_gt", "y": 49, "statement": "x > 732/223", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y49_lt", "y": 49, "statement": "x < 1432/437", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y50_gt", "y": 50, "statement": "x > 155/47", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y50_lt", "y": 50, "statement": "x < 404/123", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y51_gt", "y": 51, "statement": "x > 10/3", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y51_lt", "y": 51, "statement": "x < 16/5", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y52_gt", "y": 52, "statement": "x > 225/68", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y52_lt", "y": 52, "statement": "x < 703/213", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y53_gt", "y": 53, "statement": "x > 1416/427", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y53_lt", "y": 53, "statement": "x < 311/94", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y54_gt", "y": 54, "statement": "x > 403/121", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y54_lt", "y": 54, "statement": "x < 102/31", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y55_gt", "y": 55, "statement": "x > 207/62", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y55_lt", "y": 55, "statement": "x < 3", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y56_gt", "y": 56, "statement": "x > 284/85", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y56_lt", "y": 56, "statement": "x < 3241/971", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y57_gt", "y": 57, "statement": "x > 580/173", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y57_lt", "y": 57, "statement": "x < 371/111", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y58_gt", "y": 58, "statement": "x > 178/53", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y58_lt", "y": 58, "statement": "x < 103/31", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y59_gt", "y": 59, "statement": "x > 771/229", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y59_lt", "y": 59, "statement": "x < 67/20", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y60_gt", "y": 60, "statement": "x > 169/50", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y60_lt", "y": 60, "statement": "x < 764/227", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y61_gt", "y": 61, "statement": "x > 511/151", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y61_lt", "y": 61, "statement": "x < 27/8", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y62_gt", "y": 62, "statement": "x > 45/13", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y62_lt", "y": 62, "statement": "x < 301/89", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y63_gt", "y": 63, "statement": "x > 1619/477", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y63_lt", "y": 63, "statement": "x < 2214/653", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y64_gt", "y": 64, "statement": "x > 759/223", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y64_lt", "y": 64, "statement": "x < 129/38", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y65_gt", "y": 65, "statement": "x > 563/165", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y65_lt", "y": 65, "statement": "x < 670/197", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y66_gt", "y": 66, "statement": "x > 765/224", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y66_lt", "y": 66, "statement": "x < 842/247", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y67_gt", "y": 67, "statement": "x > 2918/853", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y67_lt", "y": 67, "statement": "x < 188/55", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y68_gt", "y": 68, "statement": "x > 1094/319", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y68_lt", "y": 68, "statement": "x < 767/224", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y69_gt", "y": 69, "statement": "x > 1254/365", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y69_lt", "y": 69, "statement": "x < 511/149", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y70_gt", "y": 70, "statement": "x > 671/195", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y70_lt", "y": 70, "statement": "x < 354/103", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y71_gt", "y": 71, "statement": "x > 159/46", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y71_lt", "y": 71, "statement": "x < 285/83", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y72_gt", "y": 72, "statement": "x > 2262/655", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y72_lt", "y": 72, "statement": "x < 873/253", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y73_gt", "y": 73, "statement": "x > 537/155", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y73_lt", "y": 73, "statement": "x < 41/12", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y74_gt", "y": 74, "statement": "x > 274/79", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y74_lt", "y": 74, "statement": "x < 24/7", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y75_gt", "y": 75, "statement": "x > 872/251", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y75_lt", "y": 75, "statement": "x < 232/67", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y76_gt", "y": 76, "statement": "x > 943/271", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y76_lt", "y": 76, "statement": "x < 1956/563", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y77_gt", "y": 77, "statement": "x > 192/55", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y77_lt", "y": 77, "statement": "x < 1437/413", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y78_gt", "y": 78, "statement": "x > 562/161", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y78_lt", "y": 78, "statement": "x < 421/121", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y79_gt", "y": 79, "statement": "x > 256/73", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y79_lt", "y": 79, "statement": "x < 129/37", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y80_gt", "y": 80, "statement": "x > 7/2", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y80_lt", "y": 80, "statement": "x < 1493/427", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y81_gt", "y": 81, "statement": "x > 4", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y81_lt", "y": 81, "statement": "x < 402/115", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y82_gt", "y": 82, "statement": "x > 3051/869", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y82_lt", "y": 82, "statement": "x < 178/51", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y83_gt", "y": 83, "statement": "x > 39/11", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y83_lt", "y": 83, "statement": "x < 108/31", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y84_gt", "y": 84, "statement": "x > 155/44", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y84_lt", "y": 84, "statement": "x < 2150/611", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y85_gt", "y": 85, "statement": "x > 893/253", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y85_lt", "y": 85, "statement": "x < 1646/467", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y86_gt", "y": 86, "statement": "x > 287/81", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y86_lt", "y": 86, "statement": "x < 7/2", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y87_gt", "y": 87, "statement": "x > 492/139", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y87_lt", "y": 87, "statement": "x < 1424/403", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y88_gt", "y": 88, "statement": "x > 691/195", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y88_lt", "y": 88, "statement": "x < 2545/719", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y89_gt", "y": 89, "statement": "x > 579/163", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y89_lt", "y": 89, "statement": "x < 269/76", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y90_gt", "y": 90, "statement": "x > 942/265", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y90_lt", "y": 90, "statement": "x < 173/49", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y91_gt", "y": 91, "statement": "x > 11/3", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y91_lt", "y": 91, "statement": "x < 1496/421", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y92_gt", "y": 92, "statement": "x > 118/33", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y92_lt", "y": 92, "statement": "x < 1790/503", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y93_gt", "y": 93, "statement": "x > 1309/367", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y93_lt", "y": 93, "statement": "x < 3461/971", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y94_gt", "y": 94, "statement": "x > 383/107", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y94_lt", "y": 94, "statement": "x < 3080/863", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y95_gt", "y": 95, "statement": "x > 1842/515", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y95_lt", "y": 95, "statement": "x < 382/107", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y96_gt", "y": 96, "statement": "x > 69/19", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y96_lt", "y": 96, "statement": "x < 25/7", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y97_gt", "y": 97, "statement": "x > 535/149", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y97_lt", "y": 97, "statement": "x < 512/143", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y98_gt", "y": 98, "statement": "x > 2294/639", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y98_lt", "y": 98, "statement": "x < 1115/311", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y99_gt", "y": 99, "statement": "x > 471/131", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y99_lt", "y": 99, "statement": "x < 908/253", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y100_gt", "y": 100, "statement": "x > 65/18", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y100_lt", "y": 100, "statement": "x < 794/221", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y255_gt", "y": 255, "statement": "x > 4", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y255_lt", "y": 255, "statement": "x < 1219/305", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y256_ge", "y": 256, "statement": "x > 4", "how": "the bound made strict", "word": "REFUTED", "sign": 0 }, { "of": "y256_le", "y": 256, "statement": "x < 4", "how": "the bound made strict", "word": "REFUTED", "sign": 0 }, { "of": "y257_gt", "y": 257, "statement": "x > 5", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y257_lt", "y": 257, "statement": "x < 4", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y3124_gt", "y": 3124, "statement": "x > 5", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y3124_lt", "y": 3124, "statement": "x < 4", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "y3125_ge", "y": 3125, "statement": "x > 5", "how": "the bound made strict", "word": "REFUTED", "sign": 0 }, { "of": "y3125_le", "y": 3125, "statement": "x < 5", "how": "the bound made strict", "word": "REFUTED", "sign": 0 }, { "of": "y3126_gt", "y": 3126, "statement": "x > 6", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "y3126_lt", "y": 3126, "statement": "x < 5", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "64/above", "y": 64, "statement": "x > 4249/1250", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "64/below", "y": 64, "statement": "x < 2124/625", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "64/cf_above_8", "y": 64, "statement": "x > 58816/17303", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "64/cf_below_7", "y": 64, "statement": "x < 23603/6944", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 }, { "of": "64/cf_above_10", "y": 64, "statement": "x > 21853/6429", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": 1 }, { "of": "64/cf_below_9", "y": 64, "statement": "x < 200048/58853", "how": "the numerator moved one unit the wrong way", "word": "REFUTED", "sign": -1 } ], "brackets": [ { "y": 2, "exact": false, "lo": "471/302", "hi": "641/411", "width": "1/124122", "widthLog10": -5.093849, "sharedDecimals": 4, "loDec": "1.559602649006622516556291390728", "hiDec": "1.559610705596107055961070559611" }, { "y": 3, "exact": false, "lo": "502/275", "hi": "387/212", "width": "1/58300", "widthLog10": -4.765669, "sharedDecimals": 4, "loDec": "1.825454545454545454545454545454", "hiDec": "1.825471698113207547169811320755" }, { "y": 4, "exact": true, "k": 2, "lo": "2", "hi": "2", "width": "0", "sharedDecimals": null, "loDec": "2", "hiDec": "2" }, { "y": 5, "exact": false, "lo": "609/286", "hi": "181/85", "width": "1/24310", "widthLog10": -4.385785, "sharedDecimals": 3, "loDec": "2.129370629370629370629370629370", "hiDec": "2.129411764705882352941176470589" }, { "y": 6, "exact": false, "lo": "1136/509", "hi": "1781/798", "width": "1/406182", "widthLog10": -5.608721, "sharedDecimals": 5, "loDec": "2.231827111984282907662082514734", "hiDec": "2.231829573934837092731829573935" }, { "y": 7, "exact": false, "lo": "44/19", "hi": "183/79", "width": "1/1501", "widthLog10": -3.176381, "sharedDecimals": 2, "loDec": "2.315789473684210526315789473684", "hiDec": "2.316455696202531645569620253165" }, { "y": 8, "exact": false, "lo": "246/103", "hi": "289/121", "width": "1/12463", "widthLog10": -4.095623, "sharedDecimals": 3, "loDec": "2.388349514563106796116504854368", "hiDec": "2.388429752066115702479338842976" }, { "y": 9, "exact": false, "lo": "1799/734", "hi": "125/51", "width": "1/37434", "widthLog10": -4.573266, "sharedDecimals": 4, "loDec": "2.450953678474114441416893732970", "hiDec": "2.450980392156862745098039215687" }, { "y": 10, "exact": false, "lo": "203/81", "hi": "198/79", "width": "1/6399", "widthLog10": -3.806112, "sharedDecimals": 3, "loDec": "2.506172839506172839506172839506", "hiDec": "2.506329113924050632911392405064" }, { "y": 11, "exact": false, "lo": "23/9", "hi": "18/7", "width": "1/63", "widthLog10": -1.799341, "sharedDecimals": 1, "loDec": "2.555555555555555555555555555555", "hiDec": "2.571428571428571428571428571429" }, { "y": 12, "exact": false, "lo": "1763/678", "hi": "1750/673", "width": "1/456294", "widthLog10": -5.659245, "sharedDecimals": 5, "loDec": "2.600294985250737463126843657817", "hiDec": "2.600297176820208023774145616642" }, { "y": 13, "exact": false, "lo": "1891/716", "hi": "1788/677", "width": "1/484732", "widthLog10": -5.685502, "sharedDecimals": 5, "loDec": "2.641061452513966480446927374301", "hiDec": "2.641063515509601181683899556869" }, { "y": 14, "exact": false, "lo": "1958/731", "hi": "75/28", "width": "1/20468", "widthLog10": -4.311075, "sharedDecimals": 4, "loDec": "2.678522571819425444596443228454", "hiDec": "2.678571428571428571428571428572" }, { "y": 15, "exact": false, "lo": "1381/509", "hi": "350/129", "width": "1/65661", "widthLog10": -4.817307, "sharedDecimals": 4, "loDec": "2.713163064833005893909626719056", "hiDec": "2.713178294573643410852713178295" }, { "y": 16, "exact": false, "lo": "442/161", "hi": "593/216", "width": "1/34776", "widthLog10": -4.54128, "sharedDecimals": 4, "loDec": "2.745341614906832298136645962732", "hiDec": "2.745370370370370370370370370371" }, { "y": 17, "exact": false, "lo": "927/334", "hi": "136/49", "width": "1/16366", "widthLog10": -4.213943, "sharedDecimals": 3, "loDec": "2.775449101796407185628742514970", "hiDec": "2.775510204081632653061224489796" }, { "y": 18, "exact": false, "lo": "614/219", "hi": "1071/382", "width": "1/83658", "widthLog10": -4.922507, "sharedDecimals": 4, "loDec": "2.803652968036529680365296803652", "hiDec": "2.803664921465968586387434554974" }, { "y": 19, "exact": false, "lo": "150/53", "hi": "1517/536", "width": "1/28408", "widthLog10": -4.453441, "sharedDecimals": 3, "loDec": "2.830188679245283018867924528301", "hiDec": "2.830223880597014925373134328359" }, { "y": 20, "exact": false, "lo": "888/311", "hi": "2447/857", "width": "1/266527", "widthLog10": -5.425741, "sharedDecimals": 5, "loDec": "2.855305466237942122186495176848", "hiDec": "2.855309218203033838973162193699" }, { "y": 21, "exact": false, "lo": "619/215", "hi": "262/91", "width": "1/19565", "widthLog10": -4.29148, "sharedDecimals": 3, "loDec": "2.879069767441860465116279069767", "hiDec": "2.879120879120879120879120879121" }, { "y": 22, "exact": false, "lo": "29/10", "hi": "177/61", "width": "1/610", "widthLog10": -2.78533, "sharedDecimals": 2, "loDec": "2.900000000000000000000000000000", "hiDec": "2.901639344262295081967213114755" }, { "y": 23, "exact": false, "lo": "38/13", "hi": "3", "width": "1/13", "widthLog10": -1.113943, "sharedDecimals": 0, "loDec": "2.923076923076923076923076923076", "hiDec": "3.000000000000000000000000000000" }, { "y": 24, "exact": false, "lo": "992/337", "hi": "209/71", "width": "1/23927", "widthLog10": -4.378888, "sharedDecimals": 4, "loDec": "2.943620178041543026706231454005", "hiDec": "2.943661971830985915492957746479" }, { "y": 25, "exact": false, "lo": "1289/435", "hi": "403/136", "width": "1/59160", "widthLog10": -4.772028, "sharedDecimals": 4, "loDec": "2.963218390804597701149425287356", "hiDec": "2.963235294117647058823529411765" }, { "y": 26, "exact": false, "lo": "331/111", "hi": "2815/944", "width": "1/104784", "widthLog10": -5.020295, "sharedDecimals": 4, "loDec": "2.981981981981981981981981981981", "hiDec": "2.981991525423728813559322033899" }, { "y": 27, "exact": true, "k": 3, "lo": "3", "hi": "3", "width": "0", "sharedDecimals": null, "loDec": "3", "hiDec": "3" }, { "y": 28, "exact": false, "lo": "2441/809", "hi": "1569/520", "width": "1/420680", "widthLog10": -5.623952, "sharedDecimals": 5, "loDec": "3.017305315203955500618046971569", "hiDec": "3.017307692307692307692307692308" }, { "y": 29, "exact": false, "lo": "179/59", "hi": "804/265", "width": "1/15635", "widthLog10": -4.194098, "sharedDecimals": 3, "loDec": "3.033898305084745762711864406779", "hiDec": "3.033962264150943396226415094340" }, { "y": 30, "exact": false, "lo": "61/20", "hi": "58/19", "width": "1/380", "widthLog10": -2.579784, "sharedDecimals": 2, "loDec": "3.050000000000000000000000000000", "hiDec": "3.052631578947368421052631578948" }, { "y": 31, "exact": false, "lo": "1217/397", "hi": "702/229", "width": "1/90913", "widthLog10": -4.958626, "sharedDecimals": 3, "loDec": "3.065491183879093198992443324937", "hiDec": "3.065502183406113537117903930132" }, { "y": 32, "exact": false, "lo": "3025/982", "hi": "268/87", "width": "1/85434", "widthLog10": -4.931631, "sharedDecimals": 4, "loDec": "3.080448065173116089613034623217", "hiDec": "3.080459770114942528735632183909" }, { "y": 33, "exact": false, "lo": "424/137", "hi": "913/295", "width": "1/40415", "widthLog10": -4.606543, "sharedDecimals": 3, "loDec": "3.094890510948905109489051094890", "hiDec": "3.094915254237288135593220338984" }, { "y": 34, "exact": false, "lo": "314/101", "hi": "171/55", "width": "1/5555", "widthLog10": -3.744684, "sharedDecimals": 2, "loDec": "3.108910891089108910891089108910", "hiDec": "3.109090909090909090909090909091" }, { "y": 35, "exact": false, "lo": "153/49", "hi": "1861/596", "width": "1/29204", "widthLog10": -4.465442, "sharedDecimals": 4, "loDec": "3.122448979591836734693877551020", "hiDec": "3.122483221476510067114093959732" }, { "y": 36, "exact": false, "lo": "2173/693", "hi": "994/317", "width": "1/219681", "widthLog10": -5.341792, "sharedDecimals": 5, "loDec": "3.135642135642135642135642135642", "hiDec": "3.135646687697160883280757097792" }, { "y": 37, "exact": false, "lo": "891/283", "hi": "1294/411", "width": "1/116313", "widthLog10": -5.065628, "sharedDecimals": 4, "loDec": "3.148409893992932862190812720848", "hiDec": "3.148418491484184914841849148419" }, { "y": 38, "exact": false, "lo": "1533/485", "hi": "1985/628", "width": "1/304580", "widthLog10": -5.483701, "sharedDecimals": 5, "loDec": "3.160824742268041237113402061855", "hiDec": "3.160828025477707006369426751593" }, { "y": 39, "exact": false, "lo": "257/81", "hi": "679/214", "width": "1/17334", "widthLog10": -4.238899, "sharedDecimals": 4, "loDec": "3.172839506172839506172839506172", "hiDec": "3.172897196261682242990654205608" }, { "y": 40, "exact": false, "lo": "2777/872", "hi": "2570/807", "width": "1/703704", "widthLog10": -5.84739, "sharedDecimals": 5, "loDec": "3.184633027522935779816513761467", "hiDec": "3.184634448574969021065675340769" }, { "y": 41, "exact": false, "lo": "147/46", "hi": "163/51", "width": "1/2346", "widthLog10": -3.370328, "sharedDecimals": 2, "loDec": "3.195652173913043478260869565217", "hiDec": "3.196078431372549019607843137255" }, { "y": 42, "exact": false, "lo": "93/29", "hi": "356/111", "width": "1/3219", "widthLog10": -3.507721, "sharedDecimals": 2, "loDec": "3.206896551724137931034482758620", "hiDec": "3.207207207207207207207207207208" }, { "y": 43, "exact": false, "lo": "428/133", "hi": "1461/454", "width": "1/60382", "widthLog10": -4.780907, "sharedDecimals": 4, "loDec": "3.218045112781954887218045112781", "hiDec": "3.218061674008810572687224669604" }, { "y": 44, "exact": false, "lo": "1172/363", "hi": "1059/328", "width": "1/119064", "widthLog10": -5.07578, "sharedDecimals": 5, "loDec": "3.228650137741046831955922865013", "hiDec": "3.228658536585365853658536585366" }, { "y": 45, "exact": false, "lo": "366/113", "hi": "515/159", "width": "1/17967", "widthLog10": -4.254476, "sharedDecimals": 4, "loDec": "3.238938053097345132743362831858", "hiDec": "3.238993710691823899371069182390" }, { "y": 46, "exact": false, "lo": "887/273", "hi": "2674/823", "width": "1/224679", "widthLog10": -5.351562, "sharedDecimals": 5, "loDec": "3.249084249084249084249084249084", "hiDec": "3.249088699878493317132442284326" }, { "y": 47, "exact": false, "lo": "1183/363", "hi": "818/251", "width": "1/91113", "widthLog10": -4.95958, "sharedDecimals": 4, "loDec": "3.258953168044077134986225895316", "hiDec": "3.258964143426294820717131474104" }, { "y": 48, "exact": false, "lo": "791/242", "hi": "219/67", "width": "1/16214", "widthLog10": -4.20989, "sharedDecimals": 3, "loDec": "3.268595041322314049586776859504", "hiDec": "3.268656716417910447761194029851" }, { "y": 49, "exact": false, "lo": "731/223", "hi": "2865/874", "width": "1/194902", "widthLog10": -5.289816, "sharedDecimals": 4, "loDec": "3.278026905829596412556053811659", "hiDec": "3.278032036613272311212814645309" }, { "y": 50, "exact": false, "lo": "309/94", "hi": "1213/369", "width": "1/34686", "widthLog10": -4.540154, "sharedDecimals": 4, "loDec": "3.287234042553191489361702127659", "hiDec": "3.287262872628726287262872628727" }, { "y": 51, "exact": false, "lo": "89/27", "hi": "33/10", "width": "1/270", "widthLog10": -2.431364, "sharedDecimals": 0, "loDec": "3.296296296296296296296296296296", "hiDec": "3.300000000000000000000000000000" }, { "y": 52, "exact": false, "lo": "899/272", "hi": "704/213", "width": "1/57936", "widthLog10": -4.762949, "sharedDecimals": 4, "loDec": "3.305147058823529411764705882352", "hiDec": "3.305164319248826291079812206573" }, { "y": 53, "exact": false, "lo": "1415/427", "hi": "623/188", "width": "1/80276", "widthLog10": -4.904586, "sharedDecimals": 4, "loDec": "3.313817330210772833723653395784", "hiDec": "3.313829787234042553191489361703" }, { "y": 54, "exact": false, "lo": "402/121", "hi": "103/31", "width": "1/3751", "widthLog10": -3.574147, "sharedDecimals": 3, "loDec": "3.322314049586776859504132231404", "hiDec": "3.322580645161290322580645161291" }, { "y": 55, "exact": false, "lo": "413/124", "hi": "10/3", "width": "1/372", "widthLog10": -2.570543, "sharedDecimals": 2, "loDec": "3.330645161290322580645161290322", "hiDec": "3.333333333333333333333333333334" }, { "y": 56, "exact": false, "lo": "1419/425", "hi": "3242/971", "width": "1/412675", "widthLog10": -5.615608, "sharedDecimals": 5, "loDec": "3.338823529411764705882352941176", "hiDec": "3.338825952626158599382080329558" }, { "y": 57, "exact": false, "lo": "579/173", "hi": "743/222", "width": "1/38406", "widthLog10": -4.584399, "sharedDecimals": 4, "loDec": "3.346820809248554913294797687861", "hiDec": "3.346846846846846846846846846847" }, { "y": 58, "exact": false, "lo": "889/265", "hi": "104/31", "width": "1/8215", "widthLog10": -3.914608, "sharedDecimals": 3, "loDec": "3.354716981132075471698113207547", "hiDec": "3.354838709677419354838709677420" }, { "y": 59, "exact": false, "lo": "770/229", "hi": "269/80", "width": "1/18320", "widthLog10": -4.262925, "sharedDecimals": 3, "loDec": "3.362445414847161572052401746724", "hiDec": "3.362500000000000000000000000000" }, { "y": 60, "exact": false, "lo": "337/100", "hi": "765/227", "width": "1/22700", "widthLog10": -4.356026, "sharedDecimals": 4, "loDec": "3.370000000000000000000000000000", "hiDec": "3.370044052863436123348017621146" }, { "y": 61, "exact": false, "lo": "510/151", "hi": "1351/400", "width": "1/60400", "widthLog10": -4.781037, "sharedDecimals": 3, "loDec": "3.377483443708609271523178807947", "hiDec": "3.377500000000000000000000000000" }, { "y": 62, "exact": false, "lo": "44/13", "hi": "1205/356", "width": "1/4628", "widthLog10": -3.665393, "sharedDecimals": 3, "loDec": "3.384615384615384615384615384615", "hiDec": "3.384831460674157303370786516854" }, { "y": 63, "exact": false, "lo": "1618/477", "hi": "2215/653", "width": "1/311481", "widthLog10": -5.493432, "sharedDecimals": 5, "loDec": "3.392033542976939203354297693920", "hiDec": "3.392036753445635528330781010720" }, { "y": 64, "exact": false, "lo": "758/223", "hi": "775/228", "width": "1/50844", "widthLog10": -4.70624, "sharedDecimals": 4, "loDec": "3.399103139013452914798206278026", "hiDec": "3.399122807017543859649122807018" }, { "y": 65, "exact": false, "lo": "562/165", "hi": "671/197", "width": "1/32505", "widthLog10": -4.51195, "sharedDecimals": 4, "loDec": "3.406060606060606060606060606060", "hiDec": "3.406091370558375634517766497462" }, { "y": 66, "exact": false, "lo": "1529/448", "hi": "843/247", "width": "1/110656", "widthLog10": -5.043975, "sharedDecimals": 4, "loDec": "3.412946428571428571428571428571", "hiDec": "3.412955465587044534412955465588" }, { "y": 67, "exact": false, "lo": "2917/853", "hi": "2257/660", "width": "1/562980", "widthLog10": -5.750493, "sharedDecimals": 5, "loDec": "3.419695193434935521688159437280", "hiDec": "3.419696969696969696969696969697" }, { "y": 68, "exact": false, "lo": "1093/319", "hi": "1535/448", "width": "1/142912", "widthLog10": -5.155069, "sharedDecimals": 5, "loDec": "3.426332288401253918495297805642", "hiDec": "3.426339285714285714285714285715" }, { "y": 69, "exact": false, "lo": "1253/365", "hi": "1023/298", "width": "1/108770", "widthLog10": -5.036509, "sharedDecimals": 4, "loDec": "3.432876712328767123287671232876", "hiDec": "3.432885906040268456375838926175" }, { "y": 70, "exact": false, "lo": "2012/585", "hi": "1417/412", "width": "1/241020", "widthLog10": -5.382053, "sharedDecimals": 4, "loDec": "3.439316239316239316239316239316", "hiDec": "3.439320388349514563106796116505" }, { "y": 71, "exact": false, "lo": "317/92", "hi": "286/83", "width": "1/7636", "widthLog10": -3.882866, "sharedDecimals": 3, "loDec": "3.445652173913043478260869565217", "hiDec": "3.445783132530120481927710843374" }, { "y": 72, "exact": false, "lo": "2261/655", "hi": "2620/759", "width": "1/497145", "widthLog10": -5.696483, "sharedDecimals": 4, "loDec": "3.451908396946564885496183206106", "hiDec": "3.451910408432147562582345191041" }, { "y": 73, "exact": false, "lo": "536/155", "hi": "83/24", "width": "1/3720", "widthLog10": -3.570543, "sharedDecimals": 3, "loDec": "3.458064516129032258064516129032", "hiDec": "3.458333333333333333333333333334" }, { "y": 74, "exact": false, "lo": "821/237", "hi": "97/28", "width": "1/6636", "widthLog10": -3.821906, "sharedDecimals": 3, "loDec": "3.464135021097046413502109704641", "hiDec": "3.464285714285714285714285714286" }, { "y": 75, "exact": false, "lo": "871/251", "hi": "465/134", "width": "1/33634", "widthLog10": -4.526779, "sharedDecimals": 4, "loDec": "3.470119521912350597609561752988", "hiDec": "3.470149253731343283582089552239" }, { "y": 76, "exact": false, "lo": "942/271", "hi": "1957/563", "width": "1/152573", "widthLog10": -5.183478, "sharedDecimals": 4, "loDec": "3.476014760147601476014760147601", "hiDec": "3.476021314387211367673179396093" }, { "y": 77, "exact": false, "lo": "383/110", "hi": "1438/413", "width": "1/45430", "widthLog10": -4.657343, "sharedDecimals": 4, "loDec": "3.481818181818181818181818181818", "hiDec": "3.481840193704600484261501210654" }, { "y": 78, "exact": false, "lo": "1123/322", "hi": "422/121", "width": "1/38962", "widthLog10": -4.590641, "sharedDecimals": 3, "loDec": "3.487577639751552795031055900621", "hiDec": "3.487603305785123966942148760331" }, { "y": 79, "exact": false, "lo": "255/73", "hi": "517/148", "width": "1/10804", "widthLog10": -4.033585, "sharedDecimals": 3, "loDec": "3.493150684931506849315068493150", "hiDec": "3.493243243243243243243243243244" }, { "y": 80, "exact": false, "lo": "2981/852", "hi": "1494/427", "width": "1/363804", "widthLog10": -5.560867, "sharedDecimals": 5, "loDec": "3.498826291079812206572769953051", "hiDec": "3.498829039812646370023419203748" }, { "y": 81, "exact": false, "lo": "7/2", "hi": "403/115", "width": "1/230", "widthLog10": -2.361728, "sharedDecimals": 2, "loDec": "3.500000000000000000000000000000", "hiDec": "3.504347826086956521739130434783" }, { "y": 82, "exact": false, "lo": "3050/869", "hi": "179/51", "width": "1/44319", "widthLog10": -4.64659, "sharedDecimals": 3, "loDec": "3.509781357882623705408515535097", "hiDec": "3.509803921568627450980392156863" }, { "y": 83, "exact": false, "lo": "116/33", "hi": "109/31", "width": "1/1023", "widthLog10": -3.009876, "sharedDecimals": 2, "loDec": "3.515151515151515151515151515151", "hiDec": "3.516129032258064516129032258065" }, { "y": 84, "exact": false, "lo": "1549/440", "hi": "2151/611", "width": "1/268840", "widthLog10": -5.429494, "sharedDecimals": 5, "loDec": "3.520454545454545454545454545454", "hiDec": "3.520458265139116202945990180033" }, { "y": 85, "exact": false, "lo": "892/253", "hi": "3293/934", "width": "1/236302", "widthLog10": -5.373467, "sharedDecimals": 5, "loDec": "3.525691699604743083003952569169", "hiDec": "3.525695931477516059957173447538" }, { "y": 86, "exact": false, "lo": "286/81", "hi": "113/32", "width": "1/2592", "widthLog10": -3.413635, "sharedDecimals": 2, "loDec": "3.530864197530864197530864197530", "hiDec": "3.531250000000000000000000000000" }, { "y": 87, "exact": false, "lo": "983/278", "hi": "1425/403", "width": "1/112034", "widthLog10": -5.04935, "sharedDecimals": 4, "loDec": "3.535971223021582733812949640287", "hiDec": "3.535980148883374689826302729529" }, { "y": 88, "exact": false, "lo": "1381/390", "hi": "2546/719", "width": "1/280410", "widthLog10": -5.447793, "sharedDecimals": 5, "loDec": "3.541025641025641025641025641025", "hiDec": "3.541029207232267037552155771906" }, { "y": 89, "exact": false, "lo": "578/163", "hi": "539/152", "width": "1/24776", "widthLog10": -4.394031, "sharedDecimals": 4, "loDec": "3.546012269938650306748466257668", "hiDec": "3.546052631578947368421052631579" }, { "y": 90, "exact": false, "lo": "941/265", "hi": "174/49", "width": "1/12985", "widthLog10": -4.113442, "sharedDecimals": 2, "loDec": "3.550943396226415094339622641509", "hiDec": "3.551020408163265306122448979592" }, { "y": 91, "exact": false, "lo": "32/9", "hi": "1497/421", "width": "1/3789", "widthLog10": -3.578525, "sharedDecimals": 3, "loDec": "3.555555555555555555555555555555", "hiDec": "3.555819477434679334916864608077" }, { "y": 92, "exact": false, "lo": "235/66", "hi": "1791/503", "width": "1/33198", "widthLog10": -4.521112, "sharedDecimals": 4, "loDec": "3.560606060606060606060606060606", "hiDec": "3.560636182902584493041749502983" }, { "y": 93, "exact": false, "lo": "2617/734", "hi": "3462/971", "width": "1/712714", "widthLog10": -5.852915, "sharedDecimals": 5, "loDec": "3.565395095367847411444141689373", "hiDec": "3.565396498455200823892893923790" }, { "y": 94, "exact": false, "lo": "382/107", "hi": "3081/863", "width": "1/92341", "widthLog10": -4.965395, "sharedDecimals": 3, "loDec": "3.570093457943925233644859813084", "hiDec": "3.570104287369640787949015063732" }, { "y": 95, "exact": false, "lo": "1841/515", "hi": "765/214", "width": "1/110210", "widthLog10": -5.042221, "sharedDecimals": 4, "loDec": "3.574757281553398058252427184466", "hiDec": "3.574766355140186915887850467290" }, { "y": 96, "exact": false, "lo": "68/19", "hi": "451/126", "width": "1/2394", "widthLog10": -3.379124, "sharedDecimals": 2, "loDec": "3.578947368421052631578947368421", "hiDec": "3.579365079365079365079365079366" }, { "y": 97, "exact": false, "lo": "534/149", "hi": "1025/286", "width": "1/42614", "widthLog10": -4.629552, "sharedDecimals": 3, "loDec": "3.583892617449664429530201342281", "hiDec": "3.583916083916083916083916083917" }, { "y": 98, "exact": false, "lo": "2293/639", "hi": "1116/311", "width": "1/198729", "widthLog10": -5.298261, "sharedDecimals": 4, "loDec": "3.588419405320813771517996870109", "hiDec": "3.588424437299035369774919614148" }, { "y": 99, "exact": false, "lo": "1412/393", "hi": "909/253", "width": "1/99429", "widthLog10": -4.997513, "sharedDecimals": 4, "loDec": "3.592875318066157760814249363867", "hiDec": "3.592885375494071146245059288538" }, { "y": 100, "exact": false, "lo": "259/72", "hi": "795/221", "width": "1/15912", "widthLog10": -4.201725, "sharedDecimals": 4, "loDec": "3.597222222222222222222222222222", "hiDec": "3.597285067873303167420814479639" }, { "y": 255, "exact": false, "lo": "2435/609", "hi": "2439/610", "width": "1/371490", "widthLog10": -5.569947, "sharedDecimals": 4, "loDec": "3.998357963875205254515599343185", "hiDec": "3.998360655737704918032786885246" }, { "y": 256, "exact": true, "k": 4, "lo": "4", "hi": "4", "width": "0", "sharedDecimals": null, "loDec": "4", "hiDec": "4" }, { "y": 257, "exact": false, "lo": "4", "hi": "2449/612", "width": "1/612", "widthLog10": -2.786751, "sharedDecimals": 2, "loDec": "4.000000000000000000000000000000", "hiDec": "4.001633986928104575163398692811" }, { "y": 3124, "exact": false, "lo": "4", "hi": "5", "width": "1", "widthLog10": 0.0, "sharedDecimals": 0, "loDec": "4.000000000000000000000000000000", "hiDec": "5.000000000000000000000000000000" }, { "y": 3125, "exact": true, "k": 5, "lo": "5", "hi": "5", "width": "0", "sharedDecimals": null, "loDec": "5", "hiDec": "5" }, { "y": 3126, "exact": false, "lo": "5", "hi": "6", "width": "1", "widthLog10": 0.0, "sharedDecimals": 0, "loDec": "5.000000000000000000000000000000", "hiDec": "6.000000000000000000000000000000" } ], "champions": { "standing": "computed: the study's numbers, transcribed as strings and checked against its own continued fractions; nothing decided", "rows": [ { "y": 709, "n": 22, "a": 4651670, "p": "20921543179", "q": "4735484816" }, { "y": 419, "n": 32, "a": 35362, "p": "13411503747543", "q": "3189935931869" }, { "y": 621, "n": 26, "a": 24682, "p": "433820684589981", "q": "99395501124953" }, { "y": 101, "n": 29, "a": 16855, "p": "927575580554664451", "q": "257542007895192516" }, { "y": 441, "n": 28, "a": 8503, "p": "216551952620850577", "q": "51251230167401757" }, { "y": 3126, "n": 1, "a": 8155, "p": "5", "q": "1" }, { "y": 3124, "n": 2, "a": 8152, "p": "5", "q": "1" }, { "y": 559, "n": 18, "a": 7265, "p": "92456025", "q": "21392036" }, { "y": 551, "n": 19, "a": 6687, "p": "430879037", "q": "99829925" }, { "y": 184, "n": 33, "a": 5222, "p": "60797132994905165", "q": "15748191489283486" }, { "y": 907, "n": 30, "a": 5221, "p": "34845572519084601", "q": "7714867346196346" }, { "y": 616, "n": 20, "a": 5099, "p": "272886334", "q": "62569637" } ] }, "generated": "2026-10-31T17:07:14Z", "seconds": 8.5 }