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2432 bytes, as of the version from 2026-10-30 02:35 (current). Recorded here, not run.
{
"table": "T615",
"scope": "Analytic checks for two prose repairs only; no nonlinear ODE recomputation or precision upgrade.",
"skill_manifest": "agents/runs/20261030T022722Z-repair-skills/manifest.json",
"skill_sha256": {
"local": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
"live": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199"
},
"source": "https://arxiv.org/html/1611.07202v1#S2, equations (7)-(10)",
"n1": {
"ODE_residual": "0",
"central_second_derivative": "-1/3",
"mass": "pi",
"ratio": "1/3*pi^2",
"absolute_error_ulps": "[0.39199136207532561864074255062598998442412979410733826744633653338126447478980950 +/- 6.18e-81]",
"stored_interval_contains_ball": true,
"shifted_control_rejected": true
},
"n5": {
"ODE_residual": "0",
"mass_at_infinity": "sqrt(3)",
"finite_surface": false,
"positivity_reason": "theta5=(1+x^2/3)^(-1/2)>0 for every finite real x; the positive denominator never vanishes.",
"absolute_error_ulps": "[0.32437385858459329697003005490500104752118834448790562635147190676809769441793203 +/- 5.86e-81]",
"stored_interval_contains_ball": true,
"shifted_control_rejected": true
},
"generator": {
"enumeration": [
{
"n": "0"
},
{
"n": "1/2"
},
{
"n": "1"
},
{
"n": "3/2"
},
{
"n": "2"
},
{
"n": "5/2"
},
{
"n": "3"
},
{
"n": "7/2"
},
{
"n": "4"
},
{
"n": "9/2"
}
],
"analytic_controls_pass": true,
"n1_comment": "The index-one profile $\\theta_1(\\xi)=\\sin(\\xi)/\\xi$ gives $C_1=\\pi^2/3$.",
"sha256": "a4648d33566a1bddd340aba4ca634e674a1bb2e664718ad0e75d23dd279d2d26"
},
"argument_uncertainty": "Exact rational indices. Pi and sqrt(3) are 600-bit Arb enclosures; all arithmetic propagates their uncertainty.",
"versions": {
"sage": "10.9",
"python": "3.12.3"
},
"skill_manifest_sha256": "f3ffe644f05a2d8ba38978976adde3737ab5de3d1ebeb214066f311233b3080e",
"check_script_sha256": "af366aa1650cc3afb89d9a7ecf99995d88b1600bf5753922bd1e9e576be23abf",
"document_sha256": {
"T615": "97a92defc890fc705aafba076915f0e89bcf4b09f314280629ad776b10bcba25",
"T614": "9c5c2d3a120ca0ec0f27feb721a1da9984ee746329490c692f1b6dcd93954401"
}
}