Recorded data and provenance for the associated calculation.
| timestamp | 20260914T053528_685814Z |
|---|---|
| scope | Full normal Dirac control with complete grades and reciprocal translation. |
| passed | true |
View complete data
{
"timestamp": "20260914T053528_685814Z",
"scope": "Full normal Dirac control with complete grades and reciprocal translation.",
"passed": true,
"checks": [
{
"name": "complete normal grades have no Dirac action outside their boundary K=8",
"error": 3.3820826609804605e-15,
"tolerance": 3e-10,
"passed": true
},
{
"name": "complete exact graded normal square K=8",
"error": 1.8061767059839926e-14,
"tolerance": 2e-09,
"passed": true
},
{
"name": "normal canonical chirality K=8",
"error": 0.0,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K8_Lambda30",
"error": 1.7400138653040998e-14,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K8_Lambda30",
"error": 1.5543122344752192e-15,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K8_Lambda30",
"error": 4.713652208778487e-09,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K8_Lambda30",
"error": 9.353650582938322e-17,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K8_Lambda100",
"error": 1.937232861340362e-14,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K8_Lambda100",
"error": 1.3322676295501878e-15,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K8_Lambda100",
"error": 1.25864388189926e-10,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K8_Lambda100",
"error": 3.659422292276241e-18,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K8_Lambda300",
"error": 1.8824782874349324e-13,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K8_Lambda300",
"error": 8.881784197001252e-16,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K8_Lambda300",
"error": 4.64352449501644e-12,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K8_Lambda300",
"error": 1.8437113331390654e-16,
"tolerance": 2e-09,
"passed": true
},
{
"name": "unperturbed entire normal inertia equals its frequency",
"error": 8.79251776862914e-15,
"tolerance": 2e-09,
"passed": true
},
{
"name": "unperturbed full normal equation source",
"error": 4.380264395613923e-15,
"tolerance": 2e-10,
"passed": true
},
{
"name": "complete normal grades have no Dirac action outside their boundary K=12",
"error": 5.65233285126159e-15,
"tolerance": 3e-10,
"passed": true
},
{
"name": "complete exact graded normal square K=12",
"error": 5.434235062241892e-14,
"tolerance": 2e-09,
"passed": true
},
{
"name": "normal canonical chirality K=12",
"error": 0.0,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K12_Lambda30",
"error": 2.520922394584868e-14,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K12_Lambda30",
"error": 1.2212453270876722e-15,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K12_Lambda30",
"error": 4.0906604654413137e-10,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K12_Lambda30",
"error": 7.505573762667568e-18,
"tolerance": 2e-09,
"passed": true
},
{
"name": "independent complete moving normal frame K12_Lambda30,axis=0,v=0.001",
"error": 5.522513371047921e-07,
"tolerance": 3e-05,
"passed": true
},
{
"name": "independent complete moving normal frame K12_Lambda30,axis=0,v=0.002",
"error": 2.0077537223883724e-06,
"tolerance": 3e-05,
"passed": true
},
{
"name": "independent complete moving normal frame K12_Lambda30,axis=1,v=0.001",
"error": 5.364266237872783e-07,
"tolerance": 3e-05,
"passed": true
},
{
"name": "independent complete moving normal frame K12_Lambda30,axis=1,v=0.002",
"error": 2.002809194712185e-06,
"tolerance": 3e-05,
"passed": true
},
{
"name": "full canonical eigenstate K12_Lambda100",
"error": 7.126293982884714e-14,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K12_Lambda100",
"error": 1.5543122344752192e-15,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K12_Lambda100",
"error": 1.0853903230707021e-11,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K12_Lambda100",
"error": 1.8917005409075792e-16,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K12_Lambda300",
"error": 1.2500322386545024e-13,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K12_Lambda300",
"error": 6.661338147750939e-16,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K12_Lambda300",
"error": 4.015913401180751e-13,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K12_Lambda300",
"error": 9.281583902836796e-17,
"tolerance": 2e-09,
"passed": true
},
{
"name": "complete normal grades have no Dirac action outside their boundary K=16",
"error": 7.242875823676482e-15,
"tolerance": 3e-10,
"passed": true
},
{
"name": "complete exact graded normal square K=16",
"error": 9.633234831379939e-14,
"tolerance": 2e-09,
"passed": true
},
{
"name": "normal canonical chirality K=16",
"error": 0.0,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K16_Lambda30",
"error": 3.2011389115015387e-14,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K16_Lambda30",
"error": 1.1102230246251565e-15,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K16_Lambda30",
"error": 5.7134017899442283e-11,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K16_Lambda30",
"error": 2.847074852199242e-16,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K16_Lambda100",
"error": 5.3690047018807095e-14,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K16_Lambda100",
"error": 1.2212453270876722e-15,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K16_Lambda100",
"error": 1.516815356467652e-12,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K16_Lambda100",
"error": 5.71798815854356e-18,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K16_Lambda300",
"error": 2.2274437378179067e-13,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K16_Lambda300",
"error": 4.440892098500626e-16,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K16_Lambda300",
"error": 6.848286539225855e-14,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K16_Lambda300",
"error": 1.0464712719017072e-16,
"tolerance": 2e-09,
"passed": true
},
{
"name": "complete normal grades have no Dirac action outside their boundary K=20",
"error": 8.067281120720504e-15,
"tolerance": 3e-10,
"passed": true
},
{
"name": "complete exact graded normal square K=20",
"error": 1.620440017233737e-13,
"tolerance": 2e-09,
"passed": true
},
{
"name": "normal canonical chirality K=20",
"error": 0.0,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K20_Lambda30",
"error": 1.8558986788688976e-14,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K20_Lambda30",
"error": 2.220446049250313e-16,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K20_Lambda30",
"error": 1.0604152075374585e-11,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K20_Lambda30",
"error": 9.274025701764191e-17,
"tolerance": 2e-09,
"passed": true
},
{
"name": "independent complete moving normal frame K20_Lambda30,axis=0,v=0.001",
"error": 5.340134325848567e-07,
"tolerance": 3e-05,
"passed": true
},
{
"name": "independent complete moving normal frame K20_Lambda30,axis=0,v=0.002",
"error": 1.992957509244775e-06,
"tolerance": 3e-05,
"passed": true
},
{
"name": "independent complete moving normal frame K20_Lambda30,axis=1,v=0.001",
"error": 4.885914393071289e-07,
"tolerance": 3e-05,
"passed": true
},
{
"name": "independent complete moving normal frame K20_Lambda30,axis=1,v=0.002",
"error": 2.001159288056442e-06,
"tolerance": 3e-05,
"passed": true
},
{
"name": "full canonical eigenstate K20_Lambda100",
"error": 6.88035228360903e-14,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K20_Lambda100",
"error": 9.992007221626409e-16,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K20_Lambda100",
"error": 2.870264740582559e-13,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K20_Lambda100",
"error": 1.9951998866884605e-16,
"tolerance": 2e-09,
"passed": true
},
{
"name": "full canonical eigenstate K20_Lambda300",
"error": 2.1977600648659955e-13,
"tolerance": 2e-08,
"passed": true
},
{
"name": "complete ordinary spatial canonical norm K20_Lambda300",
"error": 4.440892098500626e-16,
"tolerance": 2e-10,
"passed": true
},
{
"name": "stationary normal mean momentum K20_Lambda300",
"error": 1.325426250186214e-14,
"tolerance": 2e-07,
"passed": true
},
{
"name": "symmetric full translation stress K20_Lambda300",
"error": 5.2210297392424116e-18,
"tolerance": 2e-09,
"passed": true
},
{
"name": "normal frequency refinement improves at Lambda=30.0",
"error": 0.0,
"tolerance": 1e-11,
"passed": true
},
{
"name": "last complete normal frequency refinement Lambda=30.0",
"error": 9.858709848487024e-07,
"tolerance": 0.0002,
"passed": true
},
{
"name": "normal frequency refinement improves at Lambda=100.0",
"error": 0.0,
"tolerance": 1e-11,
"passed": true
},
{
"name": "last complete normal frequency refinement Lambda=100.0",
"error": 9.85531656283456e-07,
"tolerance": 0.0002,
"passed": true
},
{
"name": "normal frequency refinement improves at Lambda=300.0",
"error": 0.0,
"tolerance": 1e-11,
"passed": true
},
{
"name": "last complete normal frequency refinement Lambda=300.0",
"error": 9.985812177149e-07,
"tolerance": 0.0002,
"passed": true
},
{
"name": "independent complete spatial quadrature of normal frequency",
"error": 9.485745522397337e-13,
"tolerance": 2e-10,
"passed": true
},
{
"name": "independent complete spatial quadrature of normal stress",
"error": 2.6804438643530502e-12,
"tolerance": 2e-09,
"passed": true
}
],
"results": [
{
"frequency": 1.9971521883124255,
"source_residual": 0.029129014221514316,
"projected_normal_weight": 0.9988485446366457,
"inertia": [
[
1.998417955417895,
3.156096332748386e-16
],
[
3.817499308352905e-16,
1.997947828161308
]
],
"stress": [
[
0.0012657671054694657,
3.156096332748386e-16
],
[
3.817499308352905e-16,
0.0007956398488824859
]
],
"momentum": [
2.968473163510866e-18,
4.713652208778487e-09
],
"cutoff": 8,
"Lambda": 30.0,
"frequency_coefficient": -2.5630305188170777,
"scaled_stress": [
[
1.139190394922519,
2.840486699473547e-13
],
[
3.4357493775176143e-13,
0.7160758639942373
]
]
},
{
"frequency": 1.999743517968457,
"source_residual": 0.029059359202608548,
"projected_normal_weight": 0.9998967157409133,
"inertia": [
[
1.9998574794493829,
1.71090417534688e-15
],
[
1.7083165730287862e-15,
1.9998153213084748
]
],
"stress": [
[
0.00011396148092573683,
1.71090417534688e-15
],
[
1.7083165730287862e-15,
7.18033400176751e-05
]
],
"momentum": [
-5.863150476445349e-18,
1.2586438818992588e-10
],
"cutoff": 8,
"Lambda": 100.0,
"frequency_coefficient": -2.5648203154293725,
"scaled_stress": [
[
1.1396148092573684,
1.71090417534688e-11
],
[
1.7083165730287864e-11,
0.718033400176751
]
]
},
{
"frequency": 1.9999715002517982,
"source_residual": 0.02905323035490922,
"projected_normal_weight": 0.9999885273696807,
"inertia": [
[
1.9999841630446749,
1.019890989998176e-14
],
[
1.0329279978603073e-14,
1.9999794803135058
]
],
"stress": [
[
1.2662792876663286e-05,
1.019890989998176e-14
],
[
1.0329279978603073e-14,
7.980061707732445e-06
]
],
"momentum": [
1.7165636314159577e-17,
4.643524494984712e-12
],
"cutoff": 8,
"Lambda": 300.0,
"frequency_coefficient": -2.5649773381664076,
"scaled_stress": [
[
1.1396513588996957,
9.179018909983585e-10
],
[
9.296351980742765e-10,
0.71820555369592
]
]
},
{
"frequency": 1.997152102792462,
"source_residual": 0.010877830959863279,
"projected_normal_weight": 0.9988485017838986,
"inertia": [
[
1.998418226652162,
4.0193720760879688e-16
],
[
3.966299655045188e-16,
1.997947886278441
]
],
"stress": [
[
0.0012661238596999459,
4.0193720760879688e-16
],
[
3.966299655045188e-16,
0.0007957834859791818
]
],
"momentum": [
-5.178572743757273e-18,
4.090660465441313e-10
],
"cutoff": 12,
"Lambda": 30.0,
"frequency_coefficient": -2.5631074867842774,
"scaled_stress": [
[
1.1395114737299512,
3.617434868479172e-13
],
[
3.5696696895406694e-13,
0.7162051373812637
]
],
"moving_frame": [
{
"axis": 0,
"speed": 0.001,
"inertia": 1.998418778903499
},
{
"axis": 0,
"speed": 0.002,
"inertia": 1.9984202344058843
},
{
"axis": 1,
"speed": 0.001,
"inertia": 1.9979484227050648
},
{
"axis": 1,
"speed": 0.002,
"inertia": 1.9979498890876357
}
]
},
{
"frequency": 1.9997435102646741,
"source_residual": 0.010850199967924329,
"projected_normal_weight": 0.9998967118882727,
"inertia": [
[
1.999857503898105,
-4.0413537467306e-15
],
[
-3.907590318685599e-15,
1.9998153266098493
]
],
"stress": [
[
0.00011399363343095022,
-4.0413537467306e-15
],
[
-3.907590318685599e-15,
7.181634517524878e-05
]
],
"momentum": [
2.5340001711516493e-18,
1.0853903230706726e-11
],
"cutoff": 12,
"Lambda": 100.0,
"frequency_coefficient": -2.5648973532588215,
"scaled_stress": [
[
1.1399363343095021,
-4.0413537467306e-11
],
[
-3.907590318685599e-11,
0.7181634517524879
]
]
},
{
"frequency": 1.9999714993957103,
"source_residual": 0.010847768529953292,
"projected_normal_weight": 0.9999885269416506,
"inertia": [
[
1.9999841657615052,
-8.636041717799603e-15
],
[
-8.570411008621125e-15,
1.9999794809031914
]
],
"stress": [
[
1.266636579487783e-05,
-8.636041717799603e-15
],
[
-8.570411008621125e-15,
7.981507481254506e-06
]
],
"momentum": [
-1.2577884368096182e-18,
4.015913401161054e-13
],
"cutoff": 12,
"Lambda": 300.0,
"frequency_coefficient": -2.5650543860744612,
"scaled_stress": [
[
1.1399729215390049,
-7.772437546019643e-10
],
[
-7.713369907759013e-10,
0.7183356733129055
]
]
},
{
"frequency": 1.9971520949882158,
"source_residual": 0.004780524438968711,
"projected_normal_weight": 0.9988484978790706,
"inertia": [
[
1.998418247909948,
-9.112723259933326e-16
],
[
-7.099537325397554e-16,
1.9979478905128725
]
],
"stress": [
[
0.0012661529217320756,
-9.112723259933326e-16
],
[
-7.099537325397554e-16,
0.0007957955246567497
]
],
"momentum": [
-3.821609926577727e-18,
5.7134017899442154e-11
],
"cutoff": 16,
"Lambda": 30.0,
"frequency_coefficient": -2.5631145106058018,
"scaled_stress": [
[
1.1395376295588682,
-8.201450933939993e-13
],
[
-6.389583592857798e-13,
0.7162159721910747
]
]
},
{
"frequency": 1.9997435095623857,
"source_residual": 0.004767888410587128,
"projected_normal_weight": 0.9998967115371145,
"inertia": [
[
1.9998575058101231,
-5.07629264508895e-15
],
[
-5.080335873290601e-15,
1.999815326995241
]
],
"stress": [
[
0.00011399624773743202,
-5.07629264508895e-15
],
[
-5.080335873290601e-15,
7.181743285535752e-05
]
],
"momentum": [
-7.381278756282513e-18,
1.5168153564496922e-12
],
"cutoff": 16,
"Lambda": 100.0,
"frequency_coefficient": -2.5649043761433177,
"scaled_stress": [
[
1.1399624773743202,
-5.07629264508895e-11
],
[
-5.0803358732906006e-11,
0.7181743285535752
]
]
},
{
"frequency": 1.9999714993177897,
"source_residual": 0.0047667764647346435,
"projected_normal_weight": 0.9999885269026362,
"inertia": [
[
1.9999841659740492,
-8.344434291835872e-15
],
[
-8.418430985103733e-15,
1.9999794809461653
]
],
"stress": [
[
1.2666656259510971e-05,
-8.344434291835872e-15
],
[
-8.418430985103733e-15,
7.981628375499641e-06
]
],
"momentum": [
1.4176532637844404e-17,
6.848286392492742e-14
],
"cutoff": 16,
"Lambda": 300.0,
"frequency_coefficient": -2.5650613989247617,
"scaled_stress": [
[
1.1399990633559873,
-7.509990862652285e-10
],
[
-7.57658788659336e-10,
0.7183465537949677
]
]
},
{
"frequency": 1.9971520938928036,
"source_residual": 0.002329412089560174,
"projected_normal_weight": 0.9988484973313829,
"inertia": [
[
1.9984182506632262,
-1.3430502447918202e-15
],
[
-1.2774729801656623e-15,
1.9979478910369721
]
],
"stress": [
[
0.0012661567704227387,
-1.3430502447918202e-15
],
[
-1.2774729801656623e-15,
0.0007957971441684619
]
],
"momentum": [
-2.6139068170069486e-18,
1.0604152075374261e-11
],
"cutoff": 20,
"Lambda": 30.0,
"frequency_coefficient": -2.5631154964767866,
"scaled_stress": [
[
1.1395410933804648,
-1.2087452203126382e-12
],
[
-1.149725682149096e-12,
0.7162174297516157
]
],
"moving_frame": [
{
"axis": 0,
"speed": 0.001,
"inertia": 1.9984187846766588
},
{
"axis": 0,
"speed": 0.002,
"inertia": 1.9984202436207354
},
{
"axis": 1,
"speed": 0.001,
"inertia": 1.9979483796284114
},
{
"axis": 1,
"speed": 0.002,
"inertia": 1.9979498921962602
}
]
},
{
"frequency": 1.9997435094638325,
"source_residual": 0.0023230797548954556,
"projected_normal_weight": 0.9998967114878365,
"inertia": [
[
1.9998575060575996,
-2.774881257303078e-15
],
[
-2.915963194273082e-15,
1.9998153270429466
]
],
"stress": [
[
0.000113996593767169,
-2.774881257303078e-15
],
[
-2.915963194273082e-15,
7.18175791141547e-05
]
],
"momentum": [
-9.793186660629764e-18,
2.8702647389118683e-13
],
"cutoff": 20,
"Lambda": 100.0,
"frequency_coefficient": -2.564905361674974,
"scaled_stress": [
[
1.13996593767169,
-2.774881257303078e-11
],
[
-2.915963194273082e-11,
0.718175791141547
]
]
},
{
"frequency": 1.9999714993066944,
"source_residual": 0.0023225225213780966,
"projected_normal_weight": 0.9999885268971608,
"inertia": [
[
1.9999841660013982,
-1.0652048777309335e-14
],
[
-1.065574060284273e-14,
1.9999794809513258
]
],
"stress": [
[
1.2666694703823808e-05,
-1.0652048777309335e-14
],
[
-1.065574060284273e-14,
7.981644631522861e-06
]
],
"momentum": [
1.863977348573878e-18,
1.3254262370794435e-14
],
"cutoff": 20,
"Lambda": 300.0,
"frequency_coefficient": -2.5650623975059794,
"scaled_stress": [
[
1.1400025233441426,
-9.586843899578402e-10
],
[
-9.590166542558457e-10,
0.7183480168370575
]
]
}
],
"raw_data": {
"path": "linear-normal-grades-20260914T053528_685814Z.npz",
"sha256": "12594c9d504e455b2b74bdbf631c8dd25fb1cfc755f9622db53bd8dc0c146767"
},
"sources": {
"linear_normal_grades.py": "b2be7d35e98d480fcdf909c7b16a1bc9cbd21ac819bf2d5d8e8d6c15ae5315d0",
"linear_normal_grade_checks.py": "83779360d4c7498127a09ec4bd260c98a7beafdfb72a98c6245ebc359a10966a",
"holomorphic_normal_dirac.py": "31a49f0f37f863669ae70cb43279dc585bf2d6682378ccc92219dc94c0654b0e"
}
}