{
 "what": "The environments record. Three environments over one idea: a certified enclosure is a canary factory. If a quantity is certified to width w and a grader accepts anything within tol > w of a stored decimal, every value in the surrounding band is simultaneously provably NOT the quantity and guaranteed to pass — so adversarial submissions are minted, without limit, from certificates already on disk. canary.js grades OTHER PEOPLE'S graders with them; the uniformity gym rewards evidence over verdicts; the attacker environment rewards breaking a grader, and scores \"I could not break it\" separately from a false break.",
 "honestyRule": "Canaries are minted ONLY from facts marked certified, and mintCanaries throws on anything else rather than quietly degrading: the claim \"provably wrong\" is the product, and it may not rest on a decimal somebody re-typed. Every fact here is read out of a record in certs/ and that record is sha256-pinned beside it; the battery refuses on drift.",
 "network": "Offline. No model was called to produce this record; the harness refuses the network unless ENVS_ALLOW_NETWORK=1, which is the operator's decision, not the harness's.",
 "corpus": [
  {
   "id": "erdos1038.upper",
   "what": "L(mu*) for the conjectured minimiser of Erdos #1038 (an upper bound for the infimum)",
   "lo": 1.8344304971956489,
   "hi": 1.8344304971959908,
   "width": 3.419486915845482e-13,
   "record": "erdos1038-inf.json",
   "sha256": "782671075726514595b8d889b1fc4f8a378cfc5709fd103d455125e9a9485f74",
   "source": "certs/erdos1038-inf.json (T1_upper) · sha256:7826710757265145",
   "publishedWrong": null
  },
  {
   "id": "erdos1038.xL",
   "what": "left endpoint x_L of {U_mu* > 0}",
   "lo": -1.8081074413361427,
   "hi": -1.8081074413360059,
   "width": 1.3677947663381929e-13,
   "record": "erdos1038-inf.json",
   "sha256": "782671075726514595b8d889b1fc4f8a378cfc5709fd103d455125e9a9485f74",
   "source": "certs/erdos1038-inf.json (T1_upper) · sha256:7826710757265145",
   "publishedWrong": null
  },
  {
   "id": "erdos1038.xR",
   "what": "right endpoint x_R of {U_mu* > 0}",
   "lo": 0.026323055859643337,
   "hi": 0.02632305585984798,
   "width": 2.0464185901403198e-13,
   "record": "erdos1038-inf.json",
   "sha256": "782671075726514595b8d889b1fc4f8a378cfc5709fd103d455125e9a9485f74",
   "source": "certs/erdos1038-inf.json (T1_upper) · sha256:7826710757265145",
   "publishedWrong": null
  },
  {
   "id": "erdos1038.inf",
   "what": "the Erdos-Herzog-Piranian infimum itself — bracketed unconditionally, not pinned",
   "lo": 1.8279999999999998,
   "hi": 1.8344304971959908,
   "width": 0.006430497195990981,
   "record": "erdos1038-inf.json",
   "sha256": "782671075726514595b8d889b1fc4f8a378cfc5709fd103d455125e9a9485f74",
   "source": "certs/erdos1038-inf.json (bracket) · sha256:7826710757265145",
   "publishedWrong": null
  },
  {
   "id": "erdos852.cstar",
   "what": "C* = (1/2)(prod_{p>=3}(1 + 1/(p-1)^3) - 1), the Erdos #852 constant",
   "lo": 0.07524038617830923,
   "hi": 0.07524038617830958,
   "width": 3.469446951953614e-16,
   "record": "erdos852-certificate.json",
   "sha256": "4379194d0bd4e63bb906e2f45f6a8443e9934c292a5feab2e9e0195005f445de",
   "source": "certs/erdos852-certificate.json (cstar.enclosure) · sha256:4379194d0bd4e63b",
   "publishedWrong": 0.0752403861777
  },
  {
   "id": "erdos852.c0",
   "what": "c0, the unique positive root of I0(c) = 1 (Erdos #852) — bracketed to 40 decimals",
   "lo": 1.3232282768639492,
   "hi": 1.3232282768639496,
   "width": 4.440892098500626e-16,
   "record": "erdos852-certificate.json",
   "sha256": "4379194d0bd4e63bb906e2f45f6a8443e9934c292a5feab2e9e0195005f445de",
   "source": "certs/erdos852-certificate.json (c0.bracket40) · sha256:4379194d0bd4e63b",
   "publishedWrong": null
  },
  {
   "id": "chowla.lambda4",
   "what": "lambda(4) = -L(1,2,3,4), the third exact value of Chowla's cosine dip",
   "lo": 1.5195578816428479,
   "hi": 1.5195578816428486,
   "width": 6.661338147750939e-16,
   "record": "lambda4-campaign.json",
   "sha256": "a3cae1ee336d7c4e7fb9f56b4f125333728347ffeb9f6b2518a1a2aee7461a6e",
   "source": "certs/lambda4-campaign.json (targets.L4, negated) · sha256:a3cae1ee336d7c4e",
   "publishedWrong": null
  },
  {
   "id": "chowla.lambda5",
   "what": "lambda(5) = -L(1,2,4,5,6), the fourth exact value — algebraic of degree exactly 5",
   "lo": 1.6274606644665792,
   "hi": 1.6274606644665799,
   "width": 6.661338147750939e-16,
   "record": "lambda56-campaign.json",
   "sha256": "8c12b5fcf291d584abde4a1ccee7d7651cb59f3a807d7edb0bedf6d8277b253d",
   "source": "certs/lambda56-campaign.json (targets.L5, negated) · sha256:8c12b5fcf291d584",
   "publishedWrong": null
  },
  {
   "id": "terra.sigmaStar",
   "what": "sigma* = 1/(8 pi^2), the viscosity at which the second harmonic stops being attenuated",
   "lo": 0.012665147955292213,
   "hi": 0.012665147955292229,
   "width": 1.5612511283791264e-17,
   "record": null,
   "sha256": null,
   "source": "closed form, enclosed here from an enclosure of pi — never a typed decimal (certs/terra-sigmastar.json decides the same constant in exact rationals)",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,2,4,6,7,8]",
   "what": "certified Chowla merit c <= 0.6498628271515711 for the 6-element set [1,2,4,6,7,8]",
   "lo": 0.6498628271515705,
   "hi": 0.6498628271515711,
   "width": 5.551115123125783e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,2,3,5,6,7,8]",
   "what": "certified Chowla merit c <= 0.7156588796059644 for the 7-element set [1,2,3,5,6,7,8]",
   "lo": 0.7156588796059639,
   "hi": 0.7156588796059644,
   "width": 5.551115123125783e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,2,3,5,7,8,9,10]",
   "what": "certified Chowla merit c <= 0.7159675818506821 for the 8-element set [1,2,3,5,7,8,9,10]",
   "lo": 0.7159675818506815,
   "hi": 0.7159675818506821,
   "width": 5.551115123125783e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,2,4,6,8,9,10]",
   "what": "certified Chowla merit c <= 0.7251273020447072 for the 7-element set [1,2,4,6,8,9,10]",
   "lo": 0.7251273020447067,
   "hi": 0.7251273020447072,
   "width": 5.551115123125783e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,2,3,5,6,8,9,10,11]",
   "what": "certified Chowla merit c <= 0.7259873111972207 for the 9-element set [1,2,3,5,6,8,9,10,11]",
   "lo": 0.7259873111972202,
   "hi": 0.7259873111972207,
   "width": 5.551115123125783e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,3,4,5,6,9,10]",
   "what": "certified Chowla merit c <= 0.742177616900114 for the 7-element set [1,3,4,5,6,9,10]",
   "lo": 0.7421776169001134,
   "hi": 0.742177616900114,
   "width": 5.551115123125783e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,4,5,6,9,10]",
   "what": "certified Chowla merit c <= 0.7422227192150118 for the 6-element set [1,4,5,6,9,10]",
   "lo": 0.7422227192150113,
   "hi": 0.7422227192150118,
   "width": 5.551115123125783e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,2,4,5,6,9,10,11]",
   "what": "certified Chowla merit c <= 0.7508101717481561 for the 8-element set [1,2,4,5,6,9,10,11]",
   "lo": 0.7508101717481555,
   "hi": 0.7508101717481561,
   "width": 6.661338147750939e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,2,3,4,6,8,9,10,11,12]",
   "what": "certified Chowla merit c <= 0.7594443738919295 for the 10-element set [1,2,3,4,6,8,9,10,11,12]",
   "lo": 0.759444373891929,
   "hi": 0.7594443738919295,
   "width": 5.551115123125783e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,2,3,5,8,10,11,12,13]",
   "what": "certified Chowla merit c <= 0.7599428051340827 for the 9-element set [1,2,3,5,8,10,11,12,13]",
   "lo": 0.7599428051340821,
   "hi": 0.7599428051340827,
   "width": 6.661338147750939e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,2,3,4,8,10,11,12,13,14]",
   "what": "certified Chowla merit c <= 0.7636174164521902 for the 10-element set [1,2,3,4,8,10,11,12,13,14]",
   "lo": 0.7636174164521896,
   "hi": 0.7636174164521902,
   "width": 5.551115123125783e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "chowla-cosine [1,3,4,7,8,10,11]",
   "what": "certified Chowla merit c <= 0.7636986073348424 for the 7-element set [1,3,4,7,8,10,11]",
   "lo": 0.7636986073348415,
   "hi": 0.7636986073348424,
   "width": 8.881784197001252e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "erdos852-constants erdos852-c0-enclosure",
   "what": "THEOREM: c0 = 1.3232282768639494690289693932974634613586535126004759968489856... — the unique positive root of I0(c) = 1, enclosed to width 7.78e-62 (200 certified bisections at 320-bit directed rounding). The first certified enclosure of this constant; the thread holds only an unverified decimal.",
   "lo": 1.3232282768639494,
   "hi": 1.3232282768639496,
   "width": 2.220446049250313e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "erdos852-constants erdos852-c0-digits",
   "what": "AUDIT: the published c0 = 1.32322827686395... is VERIFIED AS A ROUNDING to 14 places — but its trailing ellipsis is wrong: the certified expansion continues 1.3232282768639494..., i.e. ...9469, not ...95. A half-ulp presentation slip on an otherwise correct constant, invisible to any float check.",
   "lo": 1.3232282768639494,
   "hi": 1.3232282768639496,
   "width": 2.220446049250313e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "erdos852-constants erdos852-cstar-enclosure",
   "what": "THEOREM: C* = 0.075240386178309... — enclosed to width 3.20e-16 (1857858 odd primes to 30000000, tail proved). The first certified enclosure of this constant.",
   "lo": 0.07524038617830923,
   "hi": 0.07524038617830957,
   "width": 3.3306690738754696e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.4|0.3|8",
   "what": "the Hénon map with a=1.4, b=0.3 has EXACTLY 64 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 7 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.428571, 86045 boxes)",
   "lo": 64,
   "hi": 64,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.34|0.3|8",
   "what": "the Hénon map with a=1.34, b=0.3 has EXACTLY 48 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 5 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.475815, 69027 boxes)",
   "lo": 48,
   "hi": 48,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.36|0.3|8",
   "what": "the Hénon map with a=1.36, b=0.3 has EXACTLY 48 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 5 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.459635, 70935 boxes)",
   "lo": 48,
   "hi": 48,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.38|0.3|8",
   "what": "the Hénon map with a=1.38, b=0.3 has EXACTLY 48 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 5 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.443893, 81223 boxes)",
   "lo": 48,
   "hi": 48,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.14|0.3|8",
   "what": "the Hénon map with a=1.14, b=0.3 has EXACTLY 32 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 3 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.666667, 36713 boxes)",
   "lo": 32,
   "hi": 32,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.16|0.3|8",
   "what": "the Hénon map with a=1.16, b=0.3 has EXACTLY 32 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 3 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.644806, 39385 boxes)",
   "lo": 32,
   "hi": 32,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.18|0.3|8",
   "what": "the Hénon map with a=1.18, b=0.3 has EXACTLY 32 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 3 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.623643, 38547 boxes)",
   "lo": 32,
   "hi": 32,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.2|0.3|8",
   "what": "the Hénon map with a=1.2, b=0.3 has EXACTLY 32 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 3 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.603145, 40027 boxes)",
   "lo": 32,
   "hi": 32,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.22|0.3|8",
   "what": "the Hénon map with a=1.22, b=0.3 has EXACTLY 32 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 3 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.583279, 42507 boxes)",
   "lo": 32,
   "hi": 32,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.24|0.3|8",
   "what": "the Hénon map with a=1.24, b=0.3 has EXACTLY 32 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 3 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.564016, 43951 boxes)",
   "lo": 32,
   "hi": 32,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.26|0.3|8",
   "what": "the Hénon map with a=1.26, b=0.3 has EXACTLY 32 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 3 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.545327, 49623 boxes)",
   "lo": 32,
   "hi": 32,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-census 1.28|0.3|8",
   "what": "the Hénon map with a=1.28, b=0.3 has EXACTLY 32 points of period 8 (2 fixed, 1 of period 2, 1 of period 4, 3 of period 8) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.527187, 50859 boxes)",
   "lo": 32,
   "hi": 32,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.6|0.3|1|0.833333333",
   "what": "the Hénon map with a=0.6, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.8333333333332327,
   "hi": 0.8333333333334338,
   "width": 2.0117241206207837e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.62|0.3|1|0.825297414",
   "what": "the Hénon map with a=0.62, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.8252974144849063,
   "hi": 0.8252974144851075,
   "width": 2.0117241206207837e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.64|0.3|1|0.817519468",
   "what": "the Hénon map with a=0.64, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.8175194684821635,
   "hi": 0.8175194684823647,
   "width": 2.0117241206207837e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.66|0.3|1|0.809985304",
   "what": "the Hénon map with a=0.66, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.8099853040115761,
   "hi": 0.8099853040117775,
   "width": 2.013944566670034e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.68|0.3|1|0.802681828",
   "what": "the Hénon map with a=0.68, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.8026818284682021,
   "hi": 0.8026818284684033,
   "width": 2.0117241206207837e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.7|0.3|1|0.795596939",
   "what": "the Hénon map with a=0.7, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.7955969390868318,
   "hi": 0.795596939087033,
   "width": 2.0117241206207837e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.72|0.3|1|0.788719427",
   "what": "the Hénon map with a=0.72, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.7887194271308591,
   "hi": 0.7887194271310602,
   "width": 2.0117241206207837e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.74|0.3|1|0.782038893",
   "what": "the Hénon map with a=0.74, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.7820388933111634,
   "hi": 0.7820388933113648,
   "width": 2.013944566670034e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.76|0.3|1|0.775545673",
   "what": "the Hénon map with a=0.76, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.7755456728983161,
   "hi": 0.7755456728985177,
   "width": 2.0161650127192843e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.78|0.3|1|0.769230769",
   "what": "the Hénon map with a=0.78, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.7692307692306687,
   "hi": 0.7692307692308699,
   "width": 2.0117241206207837e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.8|0.3|1|0.763085795",
   "what": "the Hénon map with a=0.8, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.7630857945185582,
   "hi": 0.7630857945187598,
   "width": 2.0161650127192843e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "henon-orbits 0.82|0.3|1|0.757102917",
   "what": "the Hénon map with a=0.82, b=0.3 has a period-1 orbit in an explicit box of radius 4.441e-16, and exactly one there (Krawczyk, strict interior containment)",
   "lo": 0.7571029170088993,
   "hi": 0.7571029170091007,
   "width": 2.013944566670034e-13,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.7|0.2|4",
   "what": "the Holmes cubic map with d=2.7, b=0.2 has EXACTLY 49 points of period 4 (3 fixed, 3 of period 2, 10 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.974842, 491611 boxes)",
   "lo": 49,
   "hi": 49,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.775|0.2|4",
   "what": "the Holmes cubic map with d=2.775, b=0.2 has EXACTLY 49 points of period 4 (3 fixed, 3 of period 2, 10 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.993740, 516113 boxes)",
   "lo": 49,
   "hi": 49,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.85|0.2|4",
   "what": "the Holmes cubic map with d=2.85, b=0.2 has EXACTLY 49 points of period 4 (3 fixed, 3 of period 2, 10 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 2.012461, 622239 boxes)",
   "lo": 49,
   "hi": 49,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.55|0.2|4",
   "what": "the Holmes cubic map with d=2.55, b=0.2 has EXACTLY 33 points of period 4 (3 fixed, 3 of period 2, 6 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.936492, 380375 boxes)",
   "lo": 33,
   "hi": 33,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.625|0.2|4",
   "what": "the Holmes cubic map with d=2.625, b=0.2 has EXACTLY 33 points of period 4 (3 fixed, 3 of period 2, 6 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.955761, 430925 boxes)",
   "lo": 33,
   "hi": 33,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 1.95|0.2|4",
   "what": "the Holmes cubic map with d=1.95, b=0.2 has EXACTLY 17 points of period 4 (3 fixed, 3 of period 2, 2 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.774824, 117107 boxes)",
   "lo": 17,
   "hi": 17,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.025|0.2|4",
   "what": "the Holmes cubic map with d=2.025, b=0.2 has EXACTLY 17 points of period 4 (3 fixed, 3 of period 2, 2 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.795829, 117511 boxes)",
   "lo": 17,
   "hi": 17,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.1|0.2|4",
   "what": "the Holmes cubic map with d=2.1, b=0.2 has EXACTLY 17 points of period 4 (3 fixed, 3 of period 2, 2 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.816590, 148785 boxes)",
   "lo": 17,
   "hi": 17,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.175|0.2|4",
   "what": "the Holmes cubic map with d=2.175, b=0.2 has EXACTLY 17 points of period 4 (3 fixed, 3 of period 2, 2 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.837117, 163717 boxes)",
   "lo": 17,
   "hi": 17,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.25|0.2|4",
   "what": "the Holmes cubic map with d=2.25, b=0.2 has EXACTLY 17 points of period 4 (3 fixed, 3 of period 2, 2 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.857418, 181317 boxes)",
   "lo": 17,
   "hi": 17,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.325|0.2|4",
   "what": "the Holmes cubic map with d=2.325, b=0.2 has EXACTLY 17 points of period 4 (3 fixed, 3 of period 2, 2 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.877498, 216523 boxes)",
   "lo": 17,
   "hi": 17,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "holmes-census 2.4|0.2|4",
   "what": "the Holmes cubic map with d=2.4, b=0.2 has EXACTLY 17 points of period 4 (3 fixed, 3 of period 2, 2 of period 4) — every one in a certified uniqueness box, the rest of the plane excluded (bound |x| < 1.897367, 261565 boxes)",
   "lo": 17,
   "hi": 17,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit Meng–Yang arXiv:2607.22198|5",
   "what": "the HESSIAN conjecture is FALSE in 5 variables: an explicit degree-14 integer polynomial whose Hessian determinant is 128 as a polynomial identity while its gradient identifies 2 distinct rational points, all decided in exact arithmetic (Meng–Yang arXiv:2607.22198, audited here)",
   "lo": 128,
   "hi": 128,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit Gallagher zenodo.21479195 d=2|3",
   "what": "the Jacobian conjecture is FALSE in dimension 3: Gallagher zenodo.21479195 d=2 reconstructed from its seed — det J = 1 proved as a polynomial identity, generic fiber degree 3, 2 distinct rational points sharing one image, every claim decided in exact arithmetic",
   "lo": 1,
   "hi": 1,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit Gallagher zenodo.21479195 d=3|3",
   "what": "the Jacobian conjecture is FALSE in dimension 3: Gallagher zenodo.21479195 d=3 reconstructed from its seed — det J = 1 proved as a polynomial identity, generic fiber degree 4, 2 distinct rational points sharing one image, every claim decided in exact arithmetic",
   "lo": 1,
   "hi": 1,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit Gallagher zenodo.21479195 d=4|3",
   "what": "the Jacobian conjecture is FALSE in dimension 3: Gallagher zenodo.21479195 d=4 reconstructed from its seed — det J = 1 proved as a polynomial identity, generic fiber degree 5, 2 distinct rational points sharing one image, every claim decided in exact arithmetic",
   "lo": 1,
   "hi": 1,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit Gallagher zenodo.21479195 d=5|3",
   "what": "the Jacobian conjecture is FALSE in dimension 3: Gallagher zenodo.21479195 d=5 reconstructed from its seed — det J = 1 proved as a polynomial identity, generic fiber degree 6, 2 distinct rational points sharing one image, every claim decided in exact arithmetic",
   "lo": 1,
   "hi": 1,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit Gallagher zenodo.21479195 distinct member (w-2w^3)|3",
   "what": "the Jacobian conjecture is FALSE in dimension 3: Gallagher zenodo.21479195 distinct member (w-2w^3) reconstructed from its seed — det J = -1 proved as a polynomial identity, generic fiber degree 4, 2 distinct rational points sharing one image, every claim decided in exact arithmetic",
   "lo": -1,
   "hi": -1,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit Alpöge 2026-07-19|3",
   "what": "the Jacobian conjecture is FALSE in dimension 3: an explicit polynomial map with det J = -2 proved as a polynomial identity, and 3 distinct rational points sharing one image, all decided in exact arithmetic (Alpöge 2026-07-19, audited here)",
   "lo": -2,
   "hi": -2,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit Alpöge 2026-07-19|8",
   "what": "the STABILIZATION, stated once: adjoining identity coordinates carries the n=3 counterexample to every dimension n >= 3 with det J and the witnesses unchanged — audited here at n=8 as the one padded representative (det J = -2 through the 8x8 symbolic determinant, 3 collisions re-evaluated); identity padding, not new mathematics",
   "lo": -2,
   "hi": -2,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit tangent-sweep d=3 (new curve through the published mechanism)|3",
   "what": "a NEW instance through the PUBLISHED tangent-sweep mechanism: our own degree-3 curve (coefficients [6, -6, 1]) gives geometric degree 4, det J = -2 proved as a polynomial identity, 2 distinct rational points sharing one image — a new curve, not a new mechanism, and not coordinate-equivalence-checked against Gallagher's members; generated AND decided in exact arithmetic",
   "lo": -2,
   "hi": -2,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit tangent-sweep d=4 (new curve through the published mechanism)|3",
   "what": "a NEW instance through the PUBLISHED tangent-sweep mechanism: our own degree-4 curve (coefficients [52/5, -51/5, 0, 1]) gives geometric degree 5, det J = -2 proved as a polynomial identity, 2 distinct rational points sharing one image — a new curve, not a new mechanism, and not coordinate-equivalence-checked against Gallagher's members; generated AND decided in exact arithmetic",
   "lo": -2,
   "hi": -2,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-audit tangent-sweep d=5 (new curve through the published mechanism)|3",
   "what": "a NEW instance through the PUBLISHED tangent-sweep mechanism: our own degree-5 curve (coefficients [20, -19, 0, 0, 1]) gives geometric degree 6, det J = -2 proved as a polynomial identity, 2 distinct rational points sharing one image — a new curve, not a new mechanism, and not coordinate-equivalence-checked against Gallagher's members; generated AND decided in exact arithmetic",
   "lo": -2,
   "hi": -2,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-fibers fiber|alpoge",
   "what": "alpoge: AT LEAST 3 preimages of one rational point, each in a certified Krawczyk box, boxes pairwise disjoint — non-injectivity re-proved BLIND, no witnesses consumed",
   "lo": 3,
   "hi": 3,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-fibers fiber|alpoge-own-target",
   "what": "alpoge-own-target: AT LEAST 3 preimages of one rational point, each in a certified Krawczyk box, boxes pairwise disjoint — non-injectivity re-proved BLIND, no witnesses consumed — and the TARGET is self-chosen too, not a published image",
   "lo": 3,
   "hi": 3,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-fibers fiber|sweep-d3",
   "what": "sweep-d3: AT LEAST 3 preimages of one rational point, each in a certified Krawczyk box, boxes pairwise disjoint — non-injectivity re-proved BLIND, no witnesses consumed (MORE than the 2 constructed witnesses)",
   "lo": 3,
   "hi": 3,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-fibers fiber|gallagher-d2",
   "what": "gallagher-d2: AT LEAST 3 preimages of one rational point, each in a certified Krawczyk box, boxes pairwise disjoint — non-injectivity re-proved BLIND, no witnesses consumed (MORE than the 2 constructed witnesses)",
   "lo": 3,
   "hi": 3,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-fibers fiber|gallagher-d3",
   "what": "gallagher-d3: AT LEAST 3 preimages of one rational point, each in a certified Krawczyk box, boxes pairwise disjoint — non-injectivity re-proved BLIND, no witnesses consumed (MORE than the 2 constructed witnesses)",
   "lo": 3,
   "hi": 3,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-fibers fiber|sweep-d4",
   "what": "sweep-d4: AT LEAST 2 preimages of one rational point, each in a certified Krawczyk box, boxes pairwise disjoint — non-injectivity re-proved BLIND, no witnesses consumed",
   "lo": 2,
   "hi": 2,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "keller-fibers fiber|gallagher-distinct",
   "what": "gallagher-distinct: AT LEAST 2 preimages of one rational point, each in a certified Krawczyk box, boxes pairwise disjoint — non-injectivity re-proved BLIND, no witnesses consumed",
   "lo": 2,
   "hi": 2,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "newman-minmod [0,1,2,3,4,7,8,10,12]",
   "what": "min|f| >= 1.3623731781333241 for the 9-term set [0,2,4,5,8,9,10,11,12], exceeding 1.3111013028723257",
   "lo": 1.3623731781333241,
   "hi": 1.3623731781333246,
   "width": 4.440892098500626e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "newman-minmod [0,1,2,4,5,9,11,17]",
   "what": "min|f| >= 1.2549331390311127 for the 8-term set [0,6,8,12,13,15,16,17], exceeding 1.1018829384861857",
   "lo": 1.2549331390311127,
   "hi": 1.2549331390311134,
   "width": 6.661338147750939e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "newman-minmod [0,1,2,6,11,14]",
   "what": "min|f| >= 1.0130074540165868 for the 6-term set [0,3,8,12,13,14], exceeding 1",
   "lo": 1.0130074540165868,
   "hi": 1.0130074540165874,
   "width": 6.661338147750939e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "newman-minmod [0,1,4,5,10,12]",
   "what": "min|f| >= 1.0092308306986966 for the 6-term set [0,2,7,8,11,12], exceeding 1",
   "lo": 1.0092308306986966,
   "hi": 1.009230830698697,
   "width": 4.440892098500626e-16,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-cat-22",
   "what": "rm-cat-22 — a row the Machine marks NEW AND UNPROVEN — 12/(-90G + 83) lies inside a rigorous enclosure of width 7.11e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (minus-CF backward interval evaluation from a PROVED tail band (U(n) = b(n): terminal containment and (I+) are identities); constant bracket width 1.2e-18; final comparison in exact rationals); equality remains open, as it must",
   "lo": 21.310733573145463,
   "hi": 21.31073357314547,
   "width": 7.105427357601002e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-z2-new8",
   "what": "rm-z2-new8 — a row the Machine marks NEW AND UNPROVEN — (3pi^2 + 16)/(-pi^2 + 16) lies inside a rigorous enclosure of width 1.07e-14 — the conjecture SURVIVES an UNCONDITIONAL audit (head-shifted minus-CF: shifted spec satisfies a(n) > 0, tail band proved, claimed form transformed exactly; constant bracket width 5.1e-57; final comparison in exact rationals); equality remains open, as it must",
   "lo": 18.19078790743853,
   "hi": 18.19078790743854,
   "width": 1.0658141036401503e-14,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-cat-21",
   "what": "rm-cat-21 — a row the Machine marks NEW AND UNPROVEN — 8/(54G -49) lies inside a rigorous enclosure of width 7.11e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (minus-CF backward interval evaluation from a PROVED tail band (U(n) = b(n): terminal containment and (I+) are identities); constant bracket width 1.2e-18; final comparison in exact rationals); equality remains open, as it must",
   "lo": 17.31069350703237,
   "hi": 17.310693507032376,
   "width": 7.105427357601002e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-cat-18",
   "what": "rm-cat-18 — a row the Machine marks NEW AND UNPROVEN — 48/(90G -79) lies inside a rigorous enclosure of width 3.55e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (minus-CF backward interval evaluation from a PROVED tail band (U(n) = b(n): terminal containment and (I+) are identities); constant bracket width 1.2e-18; final comparison in exact rationals); equality remains open, as it must",
   "lo": 13.96605995364367,
   "hi": 13.966059953643674,
   "width": 3.552713678800501e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-z2-new7",
   "what": "rm-z2-new7 — a row the Machine marks NEW AND UNPROVEN — 32/(-3pi^2 + 32) lies inside a rigorous enclosure of width 3.55e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (minus-CF backward interval evaluation from a PROVED tail band (U(n) = b(n): terminal containment and (I+) are identities); constant bracket width 5.1e-57; final comparison in exact rationals); equality remains open, as it must",
   "lo": 13.38247603396562,
   "hi": 13.382476033965624,
   "width": 3.552713678800501e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-zo-z5z3c",
   "what": "rm-zo-z5z3c — a row the Machine marks NEW AND UNPROVEN — 64/(64 zeta(5) + 176 zeta(3) - 273) lies inside a rigorous minus-CF enclosure of width 3.55e-15 (form bracket width 4.48e-14) — the conjecture SURVIVES an UNCONDITIONAL audit: sharp tail band at the true (c-1)^2 branch proved by shift-and-check, convergence proved inside the certificate, zeta values bracketed exactly; final comparison in exact rationals; equality remains open, as it must",
   "lo": 12.993891508980104,
   "hi": 12.993891508980107,
   "width": 3.552713678800501e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-cat-19",
   "what": "rm-cat-19 — a row the Machine marks NEW AND UNPROVEN — 32/(-18G + 19) lies inside a rigorous enclosure of width 5.33e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (minus-CF backward interval evaluation from a PROVED tail band (U(n) = b(n): terminal containment and (I+) are identities); constant bracket width 1.2e-18; final comparison in exact rationals); equality remains open, as it must",
   "lo": 12.735713658945658,
   "hi": 12.735713658945663,
   "width": 5.329070518200751e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-z2-new4",
   "what": "rm-z2-new4 — a row the Machine marks NEW AND UNPROVEN — 32/(pi^2) lies inside a rigorous enclosure of width 7.11e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (head-shifted minus-CF: shifted spec satisfies a(n) > 0, tail band proved, claimed form transformed exactly; constant bracket width 5.1e-57; final comparison in exact rationals); equality remains open, as it must",
   "lo": 12.382476033965618,
   "hi": 12.382476033965625,
   "width": 7.105427357601002e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-cat-17",
   "what": "rm-cat-17 — a row the Machine marks NEW AND UNPROVEN — 6/(-18G + 17) lies inside a rigorous enclosure of width 5.33e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (minus-CF backward interval evaluation from a PROVED tail band (U(n) = b(n): terminal containment and (I+) are identities); constant bracket width 1.2e-18; final comparison in exact rationals); equality remains open, as it must",
   "lo": 11.704592362597806,
   "hi": 11.704592362597811,
   "width": 5.329070518200751e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-cat-20",
   "what": "rm-cat-20 — a row the Machine marks NEW AND UNPROVEN — 128/(-6G + 17) lies inside a rigorous enclosure of width 7.11e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (minus-CF backward interval evaluation from a PROVED tail band (U(n) = b(n): terminal containment and (I+) are identities); constant bracket width 1.2e-18; final comparison in exact rationals); equality remains open, as it must",
   "lo": 11.126365014737708,
   "hi": 11.126365014737715,
   "width": 7.105427357601002e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-z2-new9",
   "what": "rm-z2-new9 — a row the Machine marks NEW AND UNPROVEN — 18/(pi^2 -8) lies inside a rigorous enclosure of width 3.55e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (minus-CF backward interval evaluation from a PROVED tail band (U(n) = b(n): terminal containment and (I+) are identities); constant bracket width 5.1e-57; final comparison in exact rationals); equality remains open, as it must",
   "lo": 9.62770519234549,
   "hi": 9.627705192345493,
   "width": 3.552713678800501e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "ramanujan-audit rm-z2-new5",
   "what": "rm-z2-new5 — a row the Machine marks NEW AND UNPROVEN — 16/(pi^2 -8) lies inside a rigorous enclosure of width 7.11e-15 — the conjecture SURVIVES an UNCONDITIONAL audit (minus-CF backward interval evaluation from a PROVED tail band (U(n) = b(n): terminal containment and (I+) are identities); constant bracket width 5.1e-57; final comparison in exact rationals); equality remains open, as it must",
   "lo": 8.557960170973766,
   "hi": 8.557960170973773,
   "width": 7.105427357601002e-15,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|alphatensor-f2-5x5x5",
   "what": "alphatensor-f2-5x5x5: 5x5 times 5x5 in 96 multiplications VERIFIED over F2 — all 15625 tensor-identity equations hold exactly (layout CA); rank 96 < 125 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2",
   "lo": 96,
   "hi": 96,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|alphatensor-q-4x5x5",
   "what": "alphatensor-q-4x5x5: 4x5 times 5x5 in 76 multiplications VERIFIED over Q — all 10000 tensor-identity equations hold exactly (layout CA); rank 76 < 100 naive",
   "lo": 76,
   "hi": 76,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|strassen-squared-4x4x4",
   "what": "strassen-squared-4x4x4: 4x4 times 4x4 in 49 multiplications VERIFIED over Q — all 4096 tensor-identity equations hold exactly (layout AC); rank 49 < 64 naive — generated AND decided here",
   "lo": 49,
   "hi": 49,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|alphatensor-q-4x4x4",
   "what": "alphatensor-q-4x4x4: 4x4 times 4x4 in 49 multiplications VERIFIED over Q — all 4096 tensor-identity equations hold exactly (layout CA); rank 49 < 64 naive",
   "lo": 49,
   "hi": 49,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|alphaevolve-48-4x4x4",
   "what": "alphaevolve-48-4x4x4: 4x4 times 4x4 in 48 multiplications VERIFIED over Z[i] (doubled half-Gaussian factors; identity = 8*T, denominators cleared) — all 4096 tensor-identity equations hold exactly (layout CA); rank 48 < 64 naive",
   "lo": 48,
   "hi": 48,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|alphatensor-q-3x4x5",
   "what": "alphatensor-q-3x4x5: 3x4 times 4x5 in 47 multiplications VERIFIED over Q — all 3600 tensor-identity equations hold exactly (layout CA); rank 47 < 60 naive",
   "lo": 47,
   "hi": 47,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|alphatensor-f2-4x4x4",
   "what": "alphatensor-f2-4x4x4: 4x4 times 4x4 in 47 multiplications VERIFIED over F2 — all 4096 tensor-identity equations hold exactly (layout CA); rank 47 < 64 naive; REFUTED over Q — the algorithm genuinely requires characteristic 2",
   "lo": 47,
   "hi": 47,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|alphatensor-q-3x3x3",
   "what": "alphatensor-q-3x3x3: 3x3 times 3x3 in 23 multiplications VERIFIED over Q — all 729 tensor-identity equations hold exactly (layout CA); rank 23 < 27 naive",
   "lo": 23,
   "hi": 23,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|strassen-1969",
   "what": "strassen-1969: 2x2 times 2x2 in 7 multiplications VERIFIED over Q — all 64 tensor-identity equations hold exactly (layout AC); rank 7 < 8 naive",
   "lo": 7,
   "hi": 7,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  },
  {
   "id": "strassen-audit mm|alphatensor-q-2x2x2",
   "what": "alphatensor-q-2x2x2: 2x2 times 2x2 in 7 multiplications VERIFIED over Q — all 64 tensor-identity equations hold exactly (layout CA); rank 7 < 8 naive",
   "lo": 7,
   "hi": 7,
   "width": 0,
   "record": "ledger.json",
   "sha256": "2a34c34f14867fbfc02b51f18972e25c8d0cd41014660b91b801df616b1b32ae",
   "source": "ledger.json (certified conjecture) · sha256:2a34c34f14867fbf",
   "publishedWrong": null
  }
 ],
 "canaryFamilies": {
  "tolerance-interior": 1649,
  "ulp-outside": 1872,
  "over-truncated": 468,
  "control": 418,
  "published-wrong": 9,
  "float-cancellation": 2
 },
 "submissions": 4418,
 "provablyWrong": 4000,
 "provablyRight": 418,
 "tolerancesProbed": [
  0.001,
  0.0001,
  0.000001,
  1e-8,
  1e-9,
  1e-10,
  1e-12,
  1e-14,
  1e-15
 ],
 "graders": [
  {
   "name": "absolute-tolerance (|v - key| < tol)",
   "falseAccept": 0.8955,
   "falseReject": 0.004784688995215311,
   "soundness": 0.10400000000000004,
   "wrongSubmissions": 4000,
   "rightSubmissions": 418,
   "falseAcceptByTolerance": {
    "0.001": 0.9935760171306209,
    "0.0001": 0.9935760171306209,
    "0.000001": 0.9935760171306209,
    "1e-8": 0.9528907922912205,
    "1e-9": 0.9360341151385928,
    "1e-10": 0.9207708779443254,
    "1e-12": 0.8886509635974305,
    "1e-14": 0.7753623188405797,
    "1e-15": 0.4444444444444444
   },
   "fooledBy": {
    "tolerance-interior": 1649,
    "ulp-outside": 1696,
    "over-truncated": 229,
    "published-wrong": 7,
    "float-cancellation": 1
   }
  },
  {
   "name": "relative-tolerance (|v - key|/|key| < tol)",
   "falseAccept": 0.9035,
   "falseReject": 0.004784688995215311,
   "soundness": 0.09603827751196176,
   "wrongSubmissions": 4000,
   "rightSubmissions": 418,
   "falseAcceptByTolerance": {
    "0.001": 0.9764453961456103,
    "0.0001": 0.9764453961456103,
    "0.000001": 0.9764453961456103,
    "1e-8": 0.9507494646680942,
    "1e-9": 0.9232409381663113,
    "1e-10": 0.9057815845824411,
    "1e-12": 0.8629550321199143,
    "1e-14": 0.7801932367149759,
    "1e-15": 0.6984126984126984
   },
   "fooledBy": {
    "tolerance-interior": 1581,
    "ulp-outside": 1788,
    "over-truncated": 239,
    "published-wrong": 6
   }
  },
  {
   "name": "exact-match (v === key)",
   "falseAccept": 0,
   "falseReject": 0.24401913875598086,
   "soundness": 0.7559808612440191,
   "wrongSubmissions": 4000,
   "rightSubmissions": 418,
   "falseAcceptByTolerance": {
    "0.001": 0,
    "0.0001": 0,
    "0.000001": 0,
    "1e-8": 0,
    "1e-9": 0,
    "1e-10": 0,
    "1e-12": 0,
    "1e-14": 0,
    "1e-15": 0
   },
   "fooledBy": {}
  },
  {
   "name": "enclosure (v in certified [lo,hi])  <- the sound grader",
   "falseAccept": 0,
   "falseReject": 0,
   "soundness": 1,
   "wrongSubmissions": 4000,
   "rightSubmissions": 418,
   "falseAcceptByTolerance": {
    "0.001": 0,
    "0.0001": 0,
    "0.000001": 0,
    "1e-8": 0,
    "1e-9": 0,
    "1e-10": 0,
    "1e-12": 0,
    "1e-14": 0,
    "1e-15": 0
   },
   "fooledBy": {}
  }
 ],
 "uniformity": {
  "instances": 12,
  "twoDimensional": 5,
  "needled": 10,
  "razor": 2,
  "scoring": "+1 correct WITH evidence · 0 correct but unsupported · +0.25 honest UNDECIDED · -1 wrong",
  "solvers": [
   {
    "name": "sampling K=1e3",
    "score": 1,
    "correct": 1,
    "wrong": 0,
    "unsupported": 11,
    "abstained": 0,
    "needlesMissed": 9
   },
   {
    "name": "sampling K=1e5",
    "score": 3,
    "correct": 3,
    "wrong": 0,
    "unsupported": 9,
    "abstained": 0,
    "needlesMissed": 7
   },
   {
    "name": "sampling + bluffed tiling",
    "score": -6,
    "correct": 3,
    "wrong": 9,
    "unsupported": 0,
    "abstained": 0,
    "needlesMissed": 9
   },
   {
    "name": "interval bisection (sound)",
    "score": 11.25,
    "correct": 11,
    "wrong": 0,
    "unsupported": 0,
    "abstained": 1,
    "needlesMissed": 0
   },
   {
    "name": "interval, 2e3-cell budget",
    "score": 9,
    "correct": 8,
    "wrong": 0,
    "unsupported": 0,
    "abstained": 4,
    "needlesMissed": 0
   }
  ]
 },
 "attacker": {
  "rungs": [
   {
    "id": "c0",
    "label": "wide band",
    "note": "absolute tolerance 1e-6 against an enclosure ~1e-13 wide — the band is ~10 million times the enclosure",
    "attackable": true,
    "fact": "erdos1038.upper",
    "grader": "absolute-tolerance",
    "tolerance": 0.000001,
    "noAttackScore": -1,
    "mintedAttackScore": 1,
    "attackBandWidth": 5.000001710442348e-7
   },
   {
    "id": "c1",
    "label": "narrow band",
    "note": "absolute tolerance 1e-9 — same trick, four orders less room",
    "attackable": true,
    "fact": "erdos1038.upper",
    "grader": "relative-tolerance",
    "tolerance": 1e-9,
    "noAttackScore": -1,
    "mintedAttackScore": 1,
    "attackBandWidth": 5.001710157159778e-10
   },
   {
    "id": "c2",
    "label": "tolerance under the enclosure",
    "note": "absolute tolerance 1e-3 against an enclosure WIDER than the tolerance — the band of accepted-but-wrong values is empty, as arithmetic",
    "attackable": false,
    "fact": "erdos1038.inf",
    "grader": "absolute-tolerance",
    "tolerance": 0.001,
    "noAttackScore": 1,
    "mintedAttackScore": -1,
    "attackBandWidth": 0
   },
   {
    "id": "c3",
    "label": "sound grader",
    "note": "the grader compares against the certificate; no accepted-but-wrong value exists",
    "attackable": false,
    "fact": "erdos1038.upper",
    "grader": "enclosure",
    "tolerance": null,
    "noAttackScore": 1,
    "mintedAttackScore": -1,
    "attackBandWidth": 0
   }
  ]
 },
 "forgeries": {
  "planted": 26,
  "leaked": 0
 },
 "ledgerRows": 36,
 "ledgerModels": [
  "stub:sampler-1e3",
  "stub:bluffer",
  "stub:sound",
  "stub:sound-2e3",
  "stub:prose",
  "stub:always-attack",
  "stub:always-noattack",
  "stub:calibrated"
 ],
 "meta": {
  "date": "2026-09-03",
  "git": "6750a59",
  "ms": 2408
 }
}