back to table · edit · history · where entries came from · files · download
23185 bytes, as of the version from 2026-11-02 01:06 (current). Recorded here, not run.
{
"table": "T664",
"run": "20261102T005728Z",
"stage": "repair",
"skill": {
"manifest": "agents/runs/20261102T005728Z-repair-skills/manifest.json",
"versions": [
{
"source": "local",
"file": "skill-local.md",
"sha256": "a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278"
},
{
"source": "live",
"file": "skill-live.md",
"sha256": "a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278"
}
],
"canonical_snapshot_sha256": "a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278"
},
"document_revision": "62a96c00a520207d5aa4a39f9fe4817d93f117aba86b04ff7a106a3e56ab8195",
"finding_status": {
"1": "done",
"2": "done",
"3": "done"
},
"changes": [
"Added aligned and gathered line breaks without changing any mathematical token or identity.",
"Removed redundant definition wording; the displayed unit-cube integral continues to specify normalized Haar measure and natural logarithms remain explicit.",
"Removed unsupported Data properties.digits while retaining all values, generator precision and rigour details.",
"Added seven readable captions without changing targets or relation text."
],
"unchanged": [
"All 26 stored value strings and entry annotations",
"Parameter declarations, identities and order",
"Completeness note",
"Generator enumeration and Programs",
"All reviewed generator/source bytes",
"Independent critique and argument sidecar"
],
"checks": {
"all_generator_entries": "26/26 matched; 0 differing, missing or extra. Checked with the unchanged generator at its existing 150/210-digit protocol.",
"independent_numerical": "640-bit Arb computation of 7*zeta(3)/pi^2 at k=-4 is finite, has radius < 1e-180 and lies strictly inside the stored 100-digit interval.",
"exact_algebra": "Both Laurent polynomial torus-substitution identities verified over QQ.",
"precision": "All 26 stored decimal values contain exactly 100 significant digits.",
"arguments": "Exact integer inputs; no selected arguments or definitions of inputs changed. No new values were calculated for storage.",
"comparison": "Before/after ordered document comparison proves unchanged numeric values, parameter order, program, complete-note, links and source bytes.",
"limitations": "Generator verification is not an independent recomputation of all 26 values. Only k=-4 was independently recomputed here; the common heuristic agreement rigour is unchanged.",
"script": "repair_checks.py",
"log": "repair-checks.log",
"sage": "10.9",
"python": "3.12.3",
"initial_checker_error": "Preserved repair_checks.initial.py and repair-checks.initial.log; the mixed RealNumber/RealBall radius comparison was corrected with an explicit conversion. This was a checker error, not a table discrepancy."
},
"browser": {
"playwright": "1.64.1",
"chromium": "156.0.8078.4",
"screens": [
{
"width": 1440,
"height": 1100,
"sections": [
{
"name": "Numbers",
"width": 648,
"scrollWidth": 648,
"math": [
{
"width": 8.703125,
"text": "k"
},
{
"width": 48.4375,
"text": "m(Qk)"
},
{
"width": 8.34375,
"text": "0"
},
{
"width": 132.9375,
"text": "m(Q12)=4m(Q0)"
},
{
"width": 187.578125,
"text": "m(Q−3)=85m(1+x+y)"
},
{
"width": 366.25,
"text": "Q−4=(1+x+xy+xyz)(1+z+zy+zyx)/(xyz)"
},
{
"width": 142.4375,
"text": "m(Q−4)=7ζ(3)/π2"
},
{
"width": 60.703125,
"text": "k=−36"
},
{
"width": 52.34375,
"text": "k=−6"
}
]
},
{
"name": "Definition",
"width": 648,
"scrollWidth": 648,
"math": [
{
"width": 455.09375,
"text": "Qk(x,y,z)=x+x−1+y+y−1+z+z−1+xy+(xy)−1+yz+(yz)−1+xyz+(xyz)−1−k"
},
{
"width": 354.40625,
"text": "m(Qk)=∫[0,1]3log|Qk(e2πiu,e2πiv,e2πiw)|dudvdw"
}
]
},
{
"name": "Parameters",
"width": 648,
"scrollWidth": 648,
"math": [
{
"width": 8.703125,
"text": "k"
},
{
"width": 41.203125,
"text": "k∈R"
}
]
},
{
"name": "Formulas",
"width": 648,
"scrollWidth": 648,
"math": [
{
"width": 446.75,
"text": "Qk(x,y,z)=(1+x+xy+xyz)(1+z+zy+zyx)xyz−(k+4),m(Qk)=Elog|R42−(k+4)|."
},
{
"width": 139.0625,
"text": "|1+x+xy+xyz|2"
},
{
"width": 174.03125,
"text": "(U,V,W)=(x,xy,xyz)"
},
{
"width": 19.96875,
"text": "R42"
},
{
"width": 324.234375,
"text": "Qk(xz,y/z,z/x)=(x+x−1)(y+y−1)+(x+x−1)(z+z−1)+(y+y−1)(z+z−1)−k."
},
{
"width": 136.484375,
"text": "m(Qk)=g2(k+4)"
},
{
"width": 236.59375,
"text": "m(Qk)=log|u|−∑n=1∞Dnnun,u=k+4,|u|>16,Dn=∑j=0n(nj)2(2jj)(2n−2jn−j)."
},
{
"width": 51.765625,
"text": "D0=1"
},
{
"width": 51.765625,
"text": "D1=4"
},
{
"width": 274.15625,
"text": "n3Dn=2(2n−1)(5n2−5n+2)Dn−1−64(n−1)3Dn−2"
},
{
"width": 40.671875,
"text": "n≥2"
},
{
"width": 322.40625,
"text": "m(Q−4)=2m(1+x+y+z)=7ζ(3)π2,m(Q−3)=85m(1+x+y)=635πL(2,χ−3)."
},
{
"width": 29.21875,
"text": "ζ(3)"
},
{
"width": 67.125,
"text": "L(2,χ−3)"
},
{
"width": 52.921875,
"text": "0,1,−1"
},
{
"width": 39.921875,
"text": "0,1,2"
},
{
"width": 8.34375,
"text": "3"
},
{
"width": 21.34375,
"text": "−4"
},
{
"width": 21.34375,
"text": "−3"
},
{
"width": 189.625,
"text": "m(Q12)=4m(Q0)=hfcc,12ddkm(Qk)|k=12+=WA3."
},
{
"width": 25.109375,
"text": "hfcc"
},
{
"width": 31.1875,
"text": "WA3"
},
{
"width": 347.578125,
"text": "1/(1−(cosucosv+cosvcosw+coswcosu)/3)"
}
]
},
{
"name": "Comments",
"width": 1344,
"scrollWidth": 1344,
"math": [
{
"width": 8.703125,
"text": "k"
},
{
"width": 21.703125,
"text": "−k"
},
{
"width": 48.4375,
"text": "m(Qk)"
},
{
"width": 91.34375,
"text": "−4≤k≤12"
},
{
"width": 18.265625,
"text": "Pk"
},
{
"width": 13.21875,
"text": "Q"
},
{
"width": 61.28125,
"text": "−4,0,12"
},
{
"width": 16.703125,
"text": "20"
},
{
"width": 19.96875,
"text": "R4"
},
{
"width": 8.34375,
"text": "1"
},
{
"width": 110.328125,
"text": "W4(s)=E(R4s)"
},
{
"width": 99.046875,
"text": "Dn=W4(2n)"
}
]
},
{
"name": "Programs",
"width": 1344,
"scrollWidth": 1344,
"math": []
},
{
"name": "References",
"width": 1344,
"scrollWidth": 1344,
"math": []
},
{
"name": "Links",
"width": 1344,
"scrollWidth": 1344,
"math": []
},
{
"name": "Similar tables",
"width": 1344,
"scrollWidth": 1344,
"math": [
{
"width": 18.265625,
"text": "Pk"
},
{
"width": 57.390625,
"text": "m(Q−3)"
},
{
"width": 57.390625,
"text": "m(Q−4)"
},
{
"width": 11.375,
"text": "L"
},
{
"width": 67.125,
"text": "L(2,χ−3)"
},
{
"width": 57.390625,
"text": "m(Q−3)"
},
{
"width": 29.21875,
"text": "ζ(3)"
},
{
"width": 57.390625,
"text": "m(Q−4)"
},
{
"width": 48.4375,
"text": "m(Qk)"
},
{
"width": 47.703125,
"text": "k=12"
}
]
},
{
"name": "Data properties",
"width": 1344,
"scrollWidth": 1344,
"math": [
{
"width": 91.34375,
"text": "−8≤k≤16"
},
{
"width": 60.703125,
"text": "k=−36"
},
{
"width": 61.28125,
"text": "−4,0,12"
},
{
"width": 87.28125,
"text": "−3,−6,−36"
},
{
"width": 29.703125,
"text": "−36"
},
{
"width": 52.34375,
"text": "k=−4"
},
{
"width": 48.5625,
"text": "u=32"
},
{
"width": 48.5625,
"text": "u=64"
},
{
"width": 63.5,
"text": "k=0,12"
},
{
"width": 81.140625,
"text": "k=−4,−3"
},
{
"width": 85.78125,
"text": "|k+4|>16"
}
]
}
],
"errors": [],
"math_errors": 0,
"unknown_key": 0
},
{
"width": 390,
"height": 844,
"sections": [
{
"name": "Numbers",
"width": 359,
"scrollWidth": 390,
"math": [
{
"width": 8.484375,
"text": "k"
},
{
"width": 47.21875,
"text": "m(Qk)"
},
{
"width": 8.140625,
"text": "0"
},
{
"width": 129.609375,
"text": "m(Q12)=4m(Q0)"
},
{
"width": 182.890625,
"text": "m(Q−3)=85m(1+x+y)"
},
{
"width": 357.09375,
"text": "Q−4=(1+x+xy+xyz)(1+z+zy+zyx)/(xyz)"
},
{
"width": 138.875,
"text": "m(Q−4)=7ζ(3)/π2"
},
{
"width": 59.1875,
"text": "k=−36"
},
{
"width": 51.03125,
"text": "k=−6"
}
]
},
{
"name": "Definition",
"width": 359,
"scrollWidth": 466,
"math": [
{
"width": 443.71875,
"text": "Qk(x,y,z)=x+x−1+y+y−1+z+z−1+xy+(xy)−1+yz+(yz)−1+xyz+(xyz)−1−k"
},
{
"width": 345.546875,
"text": "m(Qk)=∫[0,1]3log|Qk(e2πiu,e2πiv,e2πiw)|dudvdw"
}
]
},
{
"name": "Parameters",
"width": 359,
"scrollWidth": 359,
"math": [
{
"width": 8.484375,
"text": "k"
},
{
"width": 40.171875,
"text": "k∈R"
}
]
},
{
"name": "Formulas",
"width": 359,
"scrollWidth": 482,
"math": [
{
"width": 435.578125,
"text": "Qk(x,y,z)=(1+x+xy+xyz)(1+z+zy+zyx)xyz−(k+4),m(Qk)=Elog|R42−(k+4)|."
},
{
"width": 135.59375,
"text": "|1+x+xy+xyz|2"
},
{
"width": 169.671875,
"text": "(U,V,W)=(x,xy,xyz)"
},
{
"width": 19.46875,
"text": "R42"
},
{
"width": 316.125,
"text": "Qk(xz,y/z,z/x)=(x+x−1)(y+y−1)+(x+x−1)(z+z−1)+(y+y−1)(z+z−1)−k."
},
{
"width": 133.078125,
"text": "m(Qk)=g2(k+4)"
},
{
"width": 230.671875,
"text": "m(Qk)=log|u|−∑n=1∞Dnnun,u=k+4,|u|>16,Dn=∑j=0n(nj)2(2jj)(2n−2jn−j)."
},
{
"width": 50.46875,
"text": "D0=1"
},
{
"width": 50.46875,
"text": "D1=4"
},
{
"width": 267.3125,
"text": "n3Dn=2(2n−1)(5n2−5n+2)Dn−1−64(n−1)3Dn−2"
},
{
"width": 39.65625,
"text": "n≥2"
},
{
"width": 314.34375,
"text": "m(Q−4)=2m(1+x+y+z)=7ζ(3)π2,m(Q−3)=85m(1+x+y)=635πL(2,χ−3)."
},
{
"width": 28.5,
"text": "ζ(3)"
},
{
"width": 65.4375,
"text": "L(2,χ−3)"
},
{
"width": 51.609375,
"text": "0,1,−1"
},
{
"width": 38.921875,
"text": "0,1,2"
},
{
"width": 8.140625,
"text": "3"
},
{
"width": 20.8125,
"text": "−4"
},
{
"width": 20.8125,
"text": "−3"
},
{
"width": 184.875,
"text": "m(Q12)=4m(Q0)=hfcc,12ddkm(Qk)|k=12+=WA3."
},
{
"width": 24.484375,
"text": "hfcc"
},
{
"width": 30.40625,
"text": "WA3"
},
{
"width": 338.890625,
"text": "1/(1−(cosucosv+cosvcosw+coswcosu)/3)"
}
]
},
{
"name": "Comments",
"width": 359,
"scrollWidth": 359,
"math": [
{
"width": 8.484375,
"text": "k"
},
{
"width": 21.15625,
"text": "−k"
},
{
"width": 47.21875,
"text": "m(Qk)"
},
{
"width": 89.0625,
"text": "−4≤k≤12"
},
{
"width": 17.8125,
"text": "Pk"
},
{
"width": 12.890625,
"text": "Q"
},
{
"width": 59.75,
"text": "−4,0,12"
},
{
"width": 16.28125,
"text": "20"
},
{
"width": 19.46875,
"text": "R4"
},
{
"width": 8.140625,
"text": "1"
},
{
"width": 107.5625,
"text": "W4(s)=E(R4s)"
},
{
"width": 96.578125,
"text": "Dn=W4(2n)"
}
]
},
{
"name": "Programs",
"width": 359,
"scrollWidth": 523,
"math": []
},
{
"name": "References",
"width": 359,
"scrollWidth": 359,
"math": []
},
{
"name": "Links",
"width": 359,
"scrollWidth": 359,
"math": []
},
{
"name": "Similar tables",
"width": 359,
"scrollWidth": 359,
"math": [
{
"width": 17.8125,
"text": "Pk"
},
{
"width": 55.953125,
"text": "m(Q−3)"
},
{
"width": 55.953125,
"text": "m(Q−4)"
},
{
"width": 11.09375,
"text": "L"
},
{
"width": 65.4375,
"text": "L(2,χ−3)"
},
{
"width": 55.953125,
"text": "m(Q−3)"
},
{
"width": 28.5,
"text": "ζ(3)"
},
{
"width": 55.953125,
"text": "m(Q−4)"
},
{
"width": 47.21875,
"text": "m(Qk)"
},
{
"width": 46.5,
"text": "k=12"
}
]
},
{
"name": "Data properties",
"width": 359,
"scrollWidth": 359,
"math": [
{
"width": 89.0625,
"text": "−8≤k≤16"
},
{
"width": 59.1875,
"text": "k=−36"
},
{
"width": 59.75,
"text": "−4,0,12"
},
{
"width": 85.109375,
"text": "−3,−6,−36"
},
{
"width": 28.96875,
"text": "−36"
},
{
"width": 51.03125,
"text": "k=−4"
},
{
"width": 47.34375,
"text": "u=32"
},
{
"width": 47.34375,
"text": "u=64"
},
{
"width": 61.90625,
"text": "k=0,12"
},
{
"width": 79.109375,
"text": "k=−4,−3"
},
{
"width": 83.640625,
"text": "|k+4|>16"
}
]
}
],
"errors": [],
"math_errors": 0,
"unknown_key": 0
}
]
},
"browser_scope": "Fresh live HTML was fetched with authentication, then rendered at its original NumberDB origin by Playwright using public assets. Desktop Definition and Formulas now fit 648 pixels. At 390 pixels, some long math still requires section scrolling: Definition 466/359, Formulas 482/359, reduced from 644/359 and 720/359; Similar tables now fits. No MathJax or JavaScript errors.",
"audit": {
"tid": "T664",
"title": "Mahler measures of the Bertin $Q_k$ family",
"findings": [],
"clean": true
},
"initial_audit_warning": "Added LaTeX markup raised the definition above the 320-character audit threshold. Redundant wording was shortened; final definition is 310 characters and final audit is clean.",
"original_selection_sha256": "32ad01d0924490fd806344d74977eff4896c986d328fb414a33d1b2ce1ebb8e5",
"final_fingerprint": {
"table": "T664",
"selection_sha256": "3cebf12d4d245959be9eac8617fd2baf6c98f6e12ce4a1a03d78570ed1db0c19",
"generator_files": {
"generate.py": "387aec89e33143a684168188e9a7f0f644934aa2f886a351a4db0d955e20727a",
"argument-selection.md": "c182e26d5f8484e203cf1f5c7972fb6c6e7fdeee6b791d1e78c2fa7065da20d7"
}
},
"independent_sidecar_sha256": "815dfaf4718c8beb9bb6ad5b8ca93d6ecba0f484a11799d78bec7448505cdb8e",
"fresh_independent_critique_required": true,
"reason": "The gate includes Definition and Formulas text in its fingerprint, so formatting alone makes the old fingerprint stale. No verdict or sidecar was rewritten or accepted by this repair.",
"controller_action": "Retain T664 and obtain a fresh independent critique of this same draft before any controller offer. No new draft, offer, review or publication was performed."
}