Recorded data and provenance for the associated calculation.
| title | A Hodge-Gated Gauss Constraint Retains Complete Spatial Singlet Branches |
|---|---|
| checks_passed | 1121 |
| case_count | 12 |
| status | conditional common action, not a derived master-field coefficient or complete color force |
| conclusion | Putting the existing positive Hodge-current norm in the actual connection dielectric gives exact inactive-sector source constraints. Complete singlet branches of the surviving normal gauge algebra retain every active spatial Clifford direction. Active three/four triplets retain independent color. An ordinary dielectric floor removes the exact constraint. |
View complete data
{
"title": "A Hodge-Gated Gauss Constraint Retains Complete Spatial Singlet Branches",
"sources": {
"experiments/hodge-gated-gauss-checks.py": "d24406f940aea7e81ee65cb9596a57a3dc88e0f5d03c07106db93cc948ff1faa",
"content/notes/topics/gauge-topology/hodge-color-current.md": "398703f0f46f508d0b1e1952c7ededc2792bb9fe15bee4ed96c4eaf27d1d4fcc",
"content/notes/topics/gauge-topology/normal-color-kinetics.md": "33e558e6945c95c9bae48a734f6292c6ca9871b25caa969b5dd1d656f6f54098"
},
"checks_passed": 1121,
"case_count": 12,
"occupied_depths": [
2,
3,
4,
5,
6,
10
],
"status": "conditional common action, not a derived master-field coefficient or complete color force",
"conclusion": "Putting the existing positive Hodge-current norm in the actual connection dielectric gives exact inactive-sector source constraints. Complete singlet branches of the surviving normal gauge algebra retain every active spatial Clifford direction. Active three/four triplets retain independent color. An ordinary dielectric floor removes the exact constraint.",
"cases": [
{
"case": "hodge-gauss-sector-depth-2",
"depth": 2,
"even_source_carrier": 2,
"hodge_prefactor_active": false,
"independent_normal_algebra_dimension": 8,
"joint_singlet_rank": 8,
"all_active_kinetic_directions_preserved": true,
"allowed_active_triplet_rank": null,
"example_current_prefactor": 0.0,
"zero_dielectric_enforces_source_constraint": true,
"all_higher_forces_excluded": false
},
{
"case": "hodge-gauss-sector-depth-3",
"depth": 3,
"even_source_carrier": 4,
"hodge_prefactor_active": true,
"independent_normal_algebra_dimension": 8,
"joint_singlet_rank": 8,
"all_active_kinetic_directions_preserved": true,
"allowed_active_triplet_rank": 12,
"example_current_prefactor": 0.4994227446764154,
"zero_dielectric_enforces_source_constraint": false,
"all_higher_forces_excluded": false
},
{
"case": "hodge-gauss-sector-depth-4",
"depth": 4,
"even_source_carrier": 4,
"hodge_prefactor_active": true,
"independent_normal_algebra_dimension": 8,
"joint_singlet_rank": 8,
"all_active_kinetic_directions_preserved": true,
"allowed_active_triplet_rank": 12,
"example_current_prefactor": 0.6329246618359791,
"zero_dielectric_enforces_source_constraint": false,
"all_higher_forces_excluded": false
},
{
"case": "hodge-gauss-sector-depth-5",
"depth": 5,
"even_source_carrier": 6,
"hodge_prefactor_active": false,
"independent_normal_algebra_dimension": 3,
"joint_singlet_rank": 16,
"all_active_kinetic_directions_preserved": true,
"allowed_active_triplet_rank": null,
"example_current_prefactor": 0.0,
"zero_dielectric_enforces_source_constraint": true,
"all_higher_forces_excluded": false
},
{
"case": "hodge-gauss-sector-depth-6",
"depth": 6,
"even_source_carrier": 6,
"hodge_prefactor_active": false,
"independent_normal_algebra_dimension": 3,
"joint_singlet_rank": 16,
"all_active_kinetic_directions_preserved": true,
"allowed_active_triplet_rank": null,
"example_current_prefactor": 0.0,
"zero_dielectric_enforces_source_constraint": true,
"all_higher_forces_excluded": false
},
{
"case": "hodge-gauss-sector-depth-10",
"depth": 10,
"even_source_carrier": 10,
"hodge_prefactor_active": false,
"independent_normal_algebra_dimension": 0,
"joint_singlet_rank": 32,
"all_active_kinetic_directions_preserved": true,
"allowed_active_triplet_rank": null,
"example_current_prefactor": 0.0,
"zero_dielectric_enforces_source_constraint": false,
"all_higher_forces_excluded": false
},
{
"case": "finite-floor-source-depth-2",
"depth": 2,
"sigma": 1.3,
"unit_floor_energy": 0.005224178395317106,
"independent_integral": 0.005224178395317106,
"floors": [
1.0,
0.1,
0.01,
0.001
],
"energies": [
0.005224178395317106,
0.052241783953171056,
0.5224178395317106,
5.2241783953171055
],
"source_total_charge_zero": true,
"source_dipole_zero": true,
"source_constraint_requires_exact_zero_prefactor": true
},
{
"case": "finite-floor-source-depth-3",
"depth": 3,
"sigma": 1.3,
"unit_floor_energy": 0.000906900625610198,
"independent_integral": 0.000906900625610198,
"floors": [
1.0,
0.1,
0.01,
0.001
],
"energies": [
0.000906900625610198,
0.00906900625610198,
0.09069006256101979,
0.9069006256101979
],
"source_total_charge_zero": true,
"source_dipole_zero": true,
"source_constraint_requires_exact_zero_prefactor": true
},
{
"case": "finite-floor-source-depth-4",
"depth": 4,
"sigma": 1.3,
"unit_floor_energy": 0.0001639948353468645,
"independent_integral": 0.0001639948353468645,
"floors": [
1.0,
0.1,
0.01,
0.001
],
"energies": [
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0.001639948353468645,
0.01639948353468645,
0.16399483534686451
],
"source_total_charge_zero": true,
"source_dipole_zero": true,
"source_constraint_requires_exact_zero_prefactor": true
},
{
"case": "finite-floor-source-depth-5",
"depth": 5,
"sigma": 1.3,
"unit_floor_energy": 3.0502476217031978e-05,
"independent_integral": 3.0502476217031975e-05,
"floors": [
1.0,
0.1,
0.01,
0.001
],
"energies": [
3.0502476217031978e-05,
0.0003050247621703198,
0.003050247621703198,
0.030502476217031976
],
"source_total_charge_zero": true,
"source_dipole_zero": true,
"source_constraint_requires_exact_zero_prefactor": true
},
{
"case": "finite-floor-source-depth-6",
"depth": 6,
"sigma": 1.3,
"unit_floor_energy": 5.791550744155688e-06,
"independent_integral": 5.791550744155685e-06,
"floors": [
1.0,
0.1,
0.01,
0.001
],
"energies": [
5.791550744155688e-06,
5.791550744155688e-05,
0.0005791550744155688,
0.005791550744155688
],
"source_total_charge_zero": true,
"source_dipole_zero": true,
"source_constraint_requires_exact_zero_prefactor": true
},
{
"case": "finite-floor-source-depth-10",
"depth": 10,
"sigma": 1.3,
"unit_floor_energy": 8.56072348835995e-09,
"independent_integral": 8.560723488359948e-09,
"floors": [
1.0,
0.1,
0.01,
0.001
],
"energies": [
8.56072348835995e-09,
8.56072348835995e-08,
8.56072348835995e-07,
8.56072348835995e-06
],
"source_total_charge_zero": true,
"source_dipole_zero": true,
"source_constraint_requires_exact_zero_prefactor": true
}
]
}