{"skill": {"manifest": "agents/runs/20261030T042402Z-repair-skills/manifest.json", "manifest_sha256": "f3ffe644f05a2d8ba38978976adde3737ab5de3d1ebeb214066f311233b3080e", "versions": [{"source": "local", "file": "skill-local.md", "sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199", "path": "agents/runs/20261030T042402Z-repair-skills/skill-local.md"}, {"source": "live", "file": "skill-live.md", "sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199", "path": "agents/runs/20261030T042402Z-repair-skills/skill-live.md"}]}, "sage": "10.9", "scipy": "1.17.1", "python": "3.12.3 (main, Mar 23 2026, 19:04:32) [GCC 13.3.0]", "input_sha256": "4d74d7bf8f1ebd139b4a973830f21c1de35db1c97358639c1f9399e7943ab253", "program_sha256": "da8deda4513560a07dbe582f93c606beb5cd285fa94814b8afa0b0a7682b9182"}
{"original_program_rejection": "13/4", "message": "Use a selected integer or half-integer in [0,9/2]."}
{"original_program_rejection": "1/3", "message": "Use a selected integer or half-integer in [0,9/2]."}
{"enumeration_matches": true, "count": 10}
{"n": "0", "reference": "stored 100-digit value", "actual": "0.11936620731892169655630198121798457577824592590332031250000000000000000", "relative_error": "1.6313632101790064736596502729299948474261087879820150430344275381502505e-15", "tolerance_start_change": "1.0463605494025889577200667393899225578902869167198394866296287213961522e-15"}
{"n": "1/2", "reference": "stored 100-digit value", "actual": "0.21220906688478854973389786664483835920691490173339843750000000000000000", "relative_error": "3.8987534179039473035439640690186537585571371068985391266590882260078312e-13", "tolerance_start_change": "3.0736482495406214635342172453546806184104515303319231340202358357416821e-13"}
{"n": "1", "reference": "stored 100-digit value", "actual": "0.39269908169880041182153718182235024869441986083984375000000000000000000", "relative_error": "1.9418689082971355678480981371167324967286955291304892233447458597475598e-13", "tolerance_start_change": "2.0779623918895258291517318062423134847566072962524964799621028116913018e-13"}
{"n": "3/2", "reference": "stored 100-digit value", "actual": "0.77014037135011403911732941196532920002937316894531250000000000000000000", "relative_error": "1.0490905061596790346043761978428844537095747131958672803661923273417735e-12", "tolerance_start_change": "9.0675714255099326857381595955475909242673423450466889918053304192991906e-13"}
{"n": "2", "reference": "stored 100-digit value", "actual": "1.6381833457741721282729940867284312844276428222656250000000000000000000", "relative_error": "1.0017465509105701752011888199194967137581419116067859446953631214415418e-13", "tolerance_start_change": "4.5420524694229804409354048139894767219051372254263710356701046105491682e-13"}
{"n": "5/2", "reference": "stored 100-digit value", "actual": "3.9090617225041497384552258154144510626792907714843750000000000000000000", "relative_error": "3.1775958635391003922452481756434218279760031083011384733146150422526310e-12", "tolerance_start_change": "5.4394104972370602085643964288891783238789658935561909295816408473202012e-12"}
{"n": "3", "reference": "stored 100-digit value", "actual": "11.050681023416345283294504042714834213256835937500000000000000000000000", "relative_error": "4.2352783189816727436467853934995441044066935480933985584334678098071867e-12", "tolerance_start_change": "4.1491852530745169547522027972783395709575246773126864857351230166435677e-12"}
{"n": "7/2", "reference": "stored 100-digit value", "actual": "40.909816957815756666150264209136366844177246093750000000000000000000000", "relative_error": "5.8453974508624231930528608864267127438419695083972464905486969554078128e-12", "tolerance_start_change": "6.5449771968136895133562939269725427613745455424456088515641046123633745e-12"}
{"n": "4", "reference": "stored 100-digit value", "actual": "247.55943951834564131786464713513851165771484375000000000000000000000000", "relative_error": "2.0125314624231862646362559152713911044924000835542956313785704071966472e-14", "tolerance_start_change": "2.8988923408202784776045474937453616895403190081717545150689668187466876e-13"}
{"n": "9/2", "reference": "stored 100-digit value", "actual": "4921.8422298338464315747842192649841308593750000000000000000000000000000", "relative_error": "2.7809696046330411028685280684578129301885127644936079564147863392748622e-14", "tolerance_start_change": "1.2011184604191741171383987908799648816782365947714944909075739335760674e-14"}
{"analytic_controls_pass": true, "displaced_controls_rejected": true}
{"n": "13/4", "reference": "70-digit radial Taylor pressure integral; heuristic endpoint correction", "reference_value": "20.365103816176341958865851535226575876840459405339185912645125974299841", "relative_error": "3.8432702640836764582277320853771675487061562084908380964209296728841863e-11", "tight_relative_error": "1.2746234730865601072041747002308124621653846144417699388607390757523924e-12", "metadata": {"radius": "8.0189375272715114161980038148312206806674835545407926639412271929216047630", "steps": 292, "terminal_theta": "8.3622396161752365137357883441550054313854684160413267542152063885849313212e-31", "dps": 70, "degree": 80, "mass_tail": "7.3783376360984005231772324810186482005816121753258063221563959514824109396e-126", "pressure_integral": "1.1513727565774753071827046655426274426596257097432107160378644230410463584", "virial_relative_error": "2.2658290134272288851034230273687094299901622659482008030731894839380335064e-73"}, "seconds": 7.227879342623055}
{"n": "1/3", "reference": "70-digit radial Taylor pressure integral; heuristic endpoint correction", "reference_value": "0.17453641075030055360456945640475479486071426904595270418881488101502168", "relative_error": "8.6605161020149968633255218896805970226106392527906639654233781776594727e-12", "tight_relative_error": "1.2832078208979368800468890965191858088768990219476662237231494529876591e-12", "metadata": {"radius": "2.6434817755567563809158636893277361981534445985943842291181570496190567868", "steps": 320, "terminal_theta": "9.5483808668795516853310490720533071036234083714190510123472841391800081449e-31", "dps": 70, "degree": 80, "mass_tail": "8.4269587987136574177733723260056807950286745075380142451945119675108355271e-40", "pressure_integral": "1.8047883394170834389357008891312154435945537724941690157934022106155319111", "virial_relative_error": "5.0936696231142911927652244845439852380803129679077192485306635264833324001e-70"}, "seconds": 7.943770305253565}
{"ok": true, "stored_values_changed": false, "stored_worst_relative_error": "5.8453974508624231930528608864267127438419695083972464905486969554078128e-12", "accuracy_claim": "8 displayed significant digits, empirically checked, not certified; no table values computed by this example"}