Recorded data and provenance for the associated calculation.
| generated_at | 2026-09-23T04:05:06.243394+00:00 |
|---|---|
| status | diagnostic_pass |
| checks | 108 |
| scope | shared algebraic controls for current positive-response routes |
View complete data
{
"generated_at": "2026-09-23T04:05:06.243394+00:00",
"status": "diagnostic_pass",
"checks": 108,
"scope": "shared algebraic controls for current positive-response routes",
"assumptions": {
"source": "(i+ell+d)/(i+2ell+d+1), even ell >= 2",
"inverse_stiffness": "d/((ell-1)(ell+d))",
"size_law": "E=Q*c*mu/L-g^2*Q^2*K/(2*L^(d-2))",
"fixed_profile": true,
"bias": "minimum-norm solution on maintained selected modes",
"background_schur": "unit v and the same source/control inverse; reported G bound omits the nonnegative field-mixing Schur term"
},
"route_findings": {
"unbiased_positive_response": "The fixed-norm shift is not proportional to the simplex count at any multi-mode depth.",
"finite_common_bias": "Selected modes are algebraically compatible, but the next mode has a nonzero residual and the response amplitude curvature is negative.",
"scale_covariant_size": "No maintained depth has a finite positive-curvature size extremum from these two energy terms alone.",
"nonzero_background": "The shared unit-normalization geometric stiffness must exceed the maximum reported Schur penalty at each depth before field mixing; radial stability and the full action remain untested."
},
"limits": [
"The source vectors are controls, not derived spatial particle profiles.",
"A passing diagnostic does not establish a complete stable particle or pair coupling.",
"Depth ten has one maintained mode and cannot test within-depth proportionality.",
"A fixed norm removes radial variations but does not derive the norm value."
],
"sources": {
"experiments/route-decision-checks.py": "531158df3ecce9d20e7ade159340c73b26fcc8574c75ff828d341970212db50d"
},
"records": [
{
"depth": 2,
"indices": [
76,
81,
95
],
"simplex_counts": [
2926,
3321,
4560
],
"response_norms": [
"0.69749012355472711390101923776468736",
"0.70182709004672823762348772378112482",
"0.71198816279324300540738418583977382"
],
"response_per_simplex": [
"0.00023837666560311931438859167387720005",
"0.00021133004819233009262977649014788462",
"0.00015613775499851820294021583022802057"
],
"background_unit_schur_penalties": [
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"0.70182709004672823762348772378112482",
"0.71198816279324300540738418583977382"
],
"background_shared_geometric_stiffness_lower_bound": "0.71198816279324300540738418583977382",
"response_ratio_spread": "1.526707397614251498117974",
"bias_minimum_norm_squared": "4.97618064900007247649920217784",
"bias_gram_condition_estimate": "1185463869.3465507083",
"bias_selected_max_residual": "1.37048573262e-80",
"bias_next_index": 96,
"bias_next_residual": "0.00000111384682091369598343901997867",
"bias_amplitude_curvatures": [
"-2.78996049421890845560407695106",
"-2.80730836018691295049395089512",
"-2.84795265117297202162953674336"
],
"size_response_power": 0,
"size_stationary_frequency_fraction": null,
"size_stationary_curvature_sign": "no finite stationary size",
"angular_jacobi": {
"0": "-1.0",
"1": "0.0",
"2": "2.0"
}
},
{
"depth": 3,
"indices": [
1,
4,
16,
17
],
"simplex_counts": [
1,
20,
816,
969
],
"response_norms": [
"0.39983756997098636224886790246395956",
"0.49655935255021424257801517266842855",
"0.68179927945951416061987753354264133",
"0.69064027668203223582089860488696825"
],
"response_per_simplex": [
"0.39983756997098636224886790246395956",
"0.024827967627510712128900758633421427",
"0.00083553833267097323605377148718460948",
"0.00071273506365534802458297069647777941"
],
"background_unit_schur_penalties": [
"0.39983756997098636224886790246395956",
"0.49655935255021424257801517266842855",
"0.68179927945951416061987753354264133",
"0.69064027668203223582089860488696825"
],
"background_shared_geometric_stiffness_lower_bound": "0.69064027668203223582089860488696825",
"response_ratio_spread": "560.9904582501820506404855",
"bias_minimum_norm_squared": "79.7666984369902854736959449297",
"bias_gram_condition_estimate": "421015148.93467080456",
"bias_selected_max_residual": "9.11900122089e-80",
"bias_next_index": 18,
"bias_next_residual": "0.0000243434165573608154403295120663",
"bias_amplitude_curvatures": [
"-1.59935027988394544899547160986",
"-1.98623741020085697031206069067",
"-2.72719711783805664247951013417",
"-2.76256110672812894328359441955"
],
"size_response_power": 1,
"size_stationary_frequency_fraction": "-1.0",
"size_stationary_curvature_sign": "flat only at equality",
"angular_jacobi": {
"0": "-1.0",
"1": "0.0",
"2": "1.6666666666666666666666666666666666666666666666666666666666666666666666666666667"
}
},
{
"depth": 4,
"indices": [
3,
20,
72
],
"simplex_counts": [
15,
8855,
1215450
],
"response_norms": [
"0.56752926716497497398243984485456033",
"0.82432116938975218928104242423516566",
"0.99543094716890210585311264217170313"
],
"response_per_simplex": [
"0.037835284477664998265495989656970689",
"0.00009309104115073429579684273565614519",
"0.00000081898140373433880937357574739537054"
],
"background_unit_schur_penalties": [
"0.56752926716497497398243984485456033",
"0.82432116938975218928104242423516566",
"0.99543094716890210585311264217170313"
],
"background_shared_geometric_stiffness_lower_bound": "0.99543094716890210585311264217170313",
"response_ratio_spread": "46197.97751834913210990735",
"bias_minimum_norm_squared": "43.4310328095309925794055393665",
"bias_gram_condition_estimate": "18678.209257489024615",
"bias_selected_max_residual": "0.0",
"bias_next_index": 73,
"bias_next_residual": "0.000446067882280155034157241105503",
"bias_amplitude_curvatures": [
"-2.27011706865989989592975937942",
"-3.29728467755900875712416969694",
"-3.98172378867560842341245056869"
],
"size_response_power": 2,
"size_stationary_frequency_fraction": "0.0",
"size_stationary_curvature_sign": "negative",
"angular_jacobi": {
"0": "-1.0",
"1": "0.0",
"2": "1.5"
}
},
{
"depth": 5,
"indices": [
10,
15,
22
],
"simplex_counts": [
2002,
11628,
65780
],
"response_norms": [
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"0.86589113356203925728158398629574145",
"0.92841221591330343631611549090791189"
],
"response_per_simplex": [
"0.00040029619830541862541282884385810885",
"0.000074466041758001312115719297067057228",
"0.000014113898083206193923930001381999269"
],
"background_unit_schur_penalties": [
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"0.86589113356203925728158398629574145",
"0.92841221591330343631611549090791189"
],
"background_shared_geometric_stiffness_lower_bound": "0.92841221591330343631611549090791189",
"response_ratio_spread": "28.36184560392440132783541",
"bias_minimum_norm_squared": "35.0232927564610507155227546121",
"bias_gram_condition_estimate": "2973364.9537611132114",
"bias_selected_max_residual": "1.05421979432e-81",
"bias_next_index": 23,
"bias_next_residual": "0.000121131941950498495500393189928",
"bias_amplitude_curvatures": [
"-3.20557195602979235230593338162",
"-3.46356453424815702912633594518",
"-3.71364886365321374526446196363"
],
"size_response_power": 3,
"size_stationary_frequency_fraction": "0.3333333333333333333333333",
"size_stationary_curvature_sign": "negative",
"angular_jacobi": {
"0": "-1.0",
"1": "0.0",
"2": "1.4"
}
},
{
"depth": 6,
"indices": [
13,
35
],
"simplex_counts": [
18564,
3838380
],
"response_norms": [
"0.91566133011910104758139820377474791",
"1.0783014394539006722882650040090457"
],
"response_per_simplex": [
"0.000049324570680839315211236705654748325",
"0.00000028092618225759322221569125620940233"
],
"background_unit_schur_penalties": [
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"1.0783014394539006722882650040090457"
],
"background_shared_geometric_stiffness_lower_bound": "1.0783014394539006722882650040090457",
"response_ratio_spread": "175.5784038513416610335083",
"bias_minimum_norm_squared": "13.3677164333573869608001683958",
"bias_gram_condition_estimate": "7497.5297778389075091",
"bias_selected_max_residual": "0.0",
"bias_next_index": 36,
"bias_next_residual": "-0.000702411175544740834562977331403",
"bias_amplitude_curvatures": [
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],
"size_response_power": 4,
"size_stationary_frequency_fraction": "0.5",
"size_stationary_curvature_sign": "negative",
"angular_jacobi": {
"0": "-1.0",
"1": "0.0",
"2": "1.3333333333333333333333333333333333333333333333333333333333333333333333333333333"
}
},
{
"depth": 10,
"indices": [
23
],
"simplex_counts": [
64512240
],
"response_norms": [
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],
"response_per_simplex": [
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],
"background_unit_schur_penalties": [
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],
"background_shared_geometric_stiffness_lower_bound": "1.2249750622167611610588472352200678",
"response_ratio_spread": null,
"bias_minimum_norm_squared": "1.22497506221676116105884723522",
"bias_gram_condition_estimate": "1.0",
"bias_selected_max_residual": "0.0",
"bias_next_index": 24,
"bias_next_residual": "0.00361044022890621980587624078647",
"bias_amplitude_curvatures": [
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],
"size_response_power": 8,
"size_stationary_frequency_fraction": "0.75",
"size_stationary_curvature_sign": "negative",
"angular_jacobi": {
"0": "-1.0",
"1": "0.0",
"2": "1.2"
}
}
]
}