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23871 bytes, as of the version from 2026-10-29 09:12 (current). Recorded here, not run.
{
"table": "T605",
"stored_readback": false,
"entries": 36,
"skill_manifest": "agents/runs/20261029T085909Z-build-skills/manifest.json",
"skill_sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
"working_bits": 429,
"relative_radius_bound": "< 1e-125 for every inexact computed value",
"quadrature_dps": 150,
"controls": {
"gaussian_moment_0": "7.6373409e-152",
"gaussian_moment_2": "7.6373409e-152",
"gaussian_moment_4": "0.0",
"sign_average": "p=1 at (1,1) and p=2 at (1,2,3) passed",
"ten_ulp_mutation_rejected": true
},
"groups": {
"intrinsic": [
"1",
"2"
],
"documented_application": [
"4/3",
"3/2",
"8/5",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"20/11",
"11/6",
"24/13",
"13/7",
"28/15",
"15/8",
"32/17",
"17/9",
"36/19",
"19/10",
"40/21"
],
"reference_sample": [
"1/6",
"1/5",
"1/4",
"1/3",
"2/5",
"1/2",
"3/5",
"2/3",
"3/4",
"4/5",
"5/6",
"7/6",
"6/5",
"5/4",
"7/5"
]
},
"versions": {
"python": "3.12.3",
"sage": "10.9",
"mpmath": "1.4.1",
"numberdb": "0.1.10"
},
"records": [
{
"params": {
"p": "1/6"
},
"number": "0.02209708691207961013752638631577653247765112305276481364338562090610519497597042248203730522386939957"
},
{
"params": {
"p": "1/5"
},
"number": "0.04419417382415922027505277263155306495530224610552962728677124181221038995194084496407461044773879915"
},
{
"params": {
"p": "1/4"
},
"number": "0.08838834764831844055010554526310612991060449221105925457354248362442077990388168992814922089547759830"
},
{
"params": {
"p": "1/3"
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},
{
"params": {
"p": "2/5"
},
"number": "1/4",
"comment": "The exponent $1/2-1/p$ is an integer, so this value is exact."
},
{
"params": {
"p": "1/2"
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"number": "0.3535533905932737622004221810524245196424179688442370182941699344976831196155267597125968835819103932"
},
{
"params": {
"p": "3/5"
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"number": "0.4454493590701696523701131027952562539936063079390802016918784961259654016578812463187628836252785988"
},
{
"params": {
"p": "2/3"
},
"number": "1/2",
"comment": "The exponent $1/2-1/p$ is an integer, so this value is exact."
},
{
"params": {
"p": "3/4"
},
"number": "0.5612310241546864907167665248395897581162055553069933767202047729414520027829306235439616135562545404"
},
{
"params": {
"p": "4/5"
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"number": "0.5946035575013605333587499852802379576464860462319087065095011123597333341134585799353906722690688369"
},
{
"params": {
"p": "5/6"
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"number": "0.6155722066724581422496965345838715549380688805504088971685327691230503598596792292020113748254470708"
},
{
"params": {
"p": "1"
},
"number": "0.7071067811865475244008443621048490392848359376884740365883398689953662392310535194251937671638207864",
"comment": "$A_1=1/\\sqrt{2}$, the sharp first-moment constant."
},
{
"params": {
"p": "7/6"
},
"number": "0.7807091821557100915662087529289000436214944705186434469579333067692475167773281278851758207261616409"
},
{
"params": {
"p": "6/5"
},
"number": "0.7937005259840997373758528196361541301957466639499265049041428809126082528121095866367721066311104785"
},
{
"params": {
"p": "5/4"
},
"number": "0.8122523963562355226097093827752816512852049744321594425324937130542207434350148856247361298160288275"
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{
"params": {
"p": "4/3"
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},
{
"params": {
"p": "7/5"
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"number": "0.8619728212469777242192933639474666076981029217257664217377692602612058740832835515905859187530500644"
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{
"params": {
"p": "3/2"
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"number": "0.8908987181403393047402262055905125079872126158781604033837569922519308033157624926375257672505571975"
},
{
"params": {
"p": "8/5"
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"p": "5/3"
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"p": "12/7"
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},
{
"params": {
"p": "7/4"
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{
"params": {
"p": "16/9"
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{
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},
{
"params": {
"p": "20/11"
},
"number": "0.9659363289248455510651443129204638993907373128792525806668938605719411049010477379328897192088814122"
},
{
"params": {
"p": "11/6"
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"number": "0.9689844739012624397729118463988302081651568351548343054109579610446185447934186065004533732272721303"
},
{
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"number": "0.9715319411536058687432894158212517892246100222689675445485405243173435782241536123786191394289894835"
},
{
"params": {
"p": "13/7"
},
"number": "0.9736036977213536290124855437548547709550572365629593036884540797452144368839072375015532370583532738"
},
{
"params": {
"p": "28/15"
},
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},
{
"params": {
"p": "15/8"
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"number": "0.9769410103450688937163896279578018043250041544226659985951805480651303390606497187346625459995543241"
},
{
"params": {
"p": "32/17"
},
"number": "0.9783119947882982064803860990976214385153146866951214883934180829160320697276372329894025410700847835"
},
{
"params": {
"p": "17/9"
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"number": "0.9795290879738267692823876927213407963780631791576844902332331787976922588027708342878692187324804997"
},
{
"params": {
"p": "36/19"
},
"number": "0.9806168262222609757629723157693266445976457011025458983438387911620582894392677191579212676449857872"
},
{
"params": {
"p": "19/10"
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"number": "0.9815947926151019485784989874356835284058993370873439506032481637617784327406511338886988733044836879"
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{
"params": {
"p": "40/21"
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"number": "0.9824788069415334396371616836963881628196114283983013858797994757473824218714680381297921707099701618"
},
{
"params": {
"p": "2"
},
"number": "1",
"comment": "$A_2=1$ follows from $\\mathbb E(\\sum_j a_j\\varepsilon_j)^2=\\sum_j a_j^2$."
}
],
"evidence": [
{
"p": "1/6",
"number": "0.02209708691207961013752638631577653247765112305276481364338562090610519497597042248203730522386939957",
"branch": "two-point",
"radius": "9.7345513e-131",
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"independent_error_in_last_places": "0.398459134736"
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{
"p": "1/5",
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"independent_error_in_last_places": "0.203081730528"
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{
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{
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"independent_error_in_last_places": "0.0812326922114"
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{
"p": "2/5",
"number": "1/4",
"branch": "two-point-exact",
"radius": "0",
"relative_radius": "0",
"independent_error_in_last_places": "exact"
},
{
"p": "1/2",
"number": "0.3535533905932737622004221810524245196424179688442370182941699344976831196155267597125968835819103932",
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"independent_error_in_last_places": "0.162465384423"
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{
"p": "3/5",
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"independent_error_in_last_places": "0.414434793255"
},
{
"p": "2/3",
"number": "1/2",
"branch": "two-point-exact",
"radius": "0",
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"independent_error_in_last_places": "exact"
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{
"p": "3/4",
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"independent_error_in_last_places": "0.428472234375"
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{
"p": "4/5",
"number": "0.5946035575013605333587499852802379576464860462319087065095011123597333341134585799353906722690688369",
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"independent_error_in_last_places": "0.419813026126"
},
{
"p": "5/6",
"number": "0.6155722066724581422496965345838715549380688805504088971685327691230503598596792292020113748254470708",
"branch": "two-point",
"radius": "1.2928100e-129",
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"independent_error_in_last_places": "0.193950760523"
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{
"p": "1",
"number": "0.7071067811865475244008443621048490392848359376884740365883398689953662392310535194251937671638207864",
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"independent_error_in_last_places": "0.324930768845"
},
{
"p": "7/6",
"number": "0.7807091821557100915662087529289000436214944705186434469579333067692475167773281278851758207261616409",
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"independent_error_in_last_places": "0.0228507611007"
},
{
"p": "6/5",
"number": "0.7937005259840997373758528196361541301957466639499265049041428809126082528121095866367721066311104785",
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"independent_error_in_last_places": "0.114673808407"
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{
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"independent_error_in_last_places": "0.466446642241"
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{
"p": "4/3",
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"independent_error_in_last_places": "0.271984262565"
},
{
"p": "7/5",
"number": "0.8619728212469777242192933639474666076981029217257664217377692602612058740832835515905859187530500644",
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"independent_error_in_last_places": "0.0647379255824"
},
{
"p": "3/2",
"number": "0.8908987181403393047402262055905125079872126158781604033837569922519308033157624926375257672505571975",
"branch": "two-point",
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"independent_error_in_last_places": "0.171130413491"
},
{
"p": "8/5",
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"independent_error_in_last_places": "0.276589403311"
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{
"p": "5/3",
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"independent_error_in_last_places": "0.149597021811"
},
{
"p": "12/7",
"number": "0.9438743126816934966419131566675343760075683033387428137421251423182864877387067030451984546106177082",
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"independent_error_in_last_places": "0.371014648981"
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{
"p": "7/4",
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"branch": "two-point",
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"independent_error_in_last_places": "0.427467251244"
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{
"p": "16/9",
"number": "0.9576032806985736469363056351479154439251382065557010735455510589062596528896244369183554159129788244",
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"independent_error_in_last_places": "0.379271138955"
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{
"p": "9/5",
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"branch": "two-point",
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"independent_error_in_last_places": "0.200311225447"
},
{
"p": "20/11",
"number": "0.9659363289248455510651443129204638993907373128792525806668938605719411049010477379328897192088814122",
"branch": "two-point",
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"independent_error_in_last_places": "0.214051115901"
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{
"p": "11/6",
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"branch": "two-point",
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"independent_error_in_last_places": "0.0153636252747"
},
{
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"independent_error_in_last_places": "0.128956261487"
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{
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"independent_error_in_last_places": "0.130007732413"
},
{
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"independent_error_in_last_places": "0.176403962451"
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{
"p": "15/8",
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},
{
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"independent_error_in_last_places": "0.304954668231"
},
{
"p": "17/9",
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},
{
"p": "36/19",
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"independent_error_in_last_places": "0.277181002043"
},
{
"p": "19/10",
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{
"p": "40/21",
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},
{
"p": "2",
"number": "1",
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"radius": "0",
"relative_radius": "0",
"independent_error_in_last_places": "exact"
}
],
"checks_passed": [
"exactness and named imports via dry_run.py",
"strict Arb branch comparisons",
"100-digit written claims contain Arb balls",
"independent four-sign and Gaussian-integral evaluation for every row",
"algebraic power identity on every two-point row",
"five finite coefficient vectors at every p",
"strict monotonicity on selected inputs",
"exact unit-branch controls at p=2,5/2,3,10"
]
}