Recorded data and provenance for the associated calculation.
| title | Compact Non-Abelian Gauss Data Limit the Commuting Flux-Confinement Claim |
|---|---|
| checks_passed | 846 |
| dependency_checks_passed | 18 |
| case_count | 8 |
| scope | admissible full classical Gauss phase-space data for fixed extended sources; not a static solution, quantum center screening or particle construction |
| conclusion | The full proposed classical connection Hamiltonian permits finite compact Gauss data for a one-signed mean-color source. Two opposite fixed cores give a separation-independent energy upper bound. Thus the commuting-channel linear lower bound cannot be transferred to this full classical source problem. Inactive Hodge source constraints remain unchanged. |
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{
"title": "Compact Non-Abelian Gauss Data Limit the Commuting Flux-Confinement Claim",
"sources": {
"experiments/nonabelian-gauss-compact-checks.py": "2c13b8126f7afea6011dadd8eb3265b7b4bb3e80e00fd1c1dea326ac70d39123",
"experiments/hodge-gated-gauss-checks.py": "d24406f940aea7e81ee65cb9596a57a3dc88e0f5d03c07106db93cc948ff1faa"
},
"checks_passed": 846,
"dependency_checks_passed": 18,
"case_count": 8,
"occupied_depths": [
2,
3,
4,
5,
6,
10
],
"scope": "admissible full classical Gauss phase-space data for fixed extended sources; not a static solution, quantum center screening or particle construction",
"conclusion": "The full proposed classical connection Hamiltonian permits finite compact Gauss data for a one-signed mean-color source. Two opposite fixed cores give a separation-independent energy upper bound. Thus the commuting-channel linear lower bound cannot be transferred to this full classical source problem. Inactive Hodge source constraints remain unchanged.",
"cases": [
{
"case": "compact-source-gate-depth-2",
"real_depth": 2,
"hodge_coefficient_active": false,
"nonzero_finite_energy_displacement_permitted": false,
"independent_normal_algebra_dimension": 8,
"exact_inactive_source_constraint_retained": true
},
{
"case": "compact-nonabelian-gauss-depth-3",
"real_depth": 3,
"source_core_radius": 1,
"source_charge_scale": 1.1,
"gauge_coupling": 0.7,
"dielectric_coefficient": 1.3,
"neutral_restoring_frequency": 0.9,
"scalar_amplitudes": [
0.3,
1.0,
2.0
],
"complete_single_core_trial_energies": [
22.99063661401704,
24.53165341297574,
29.611928574378055
],
"exact_integrals": {
"source": "633825300114114700748351602688*pi/2444789209684704726957840711075",
"electric": "147573952589676412928*pi/205152091333295551445",
"magnetic": "3128556081471108233082266140727676936126464*pi/158520660078501016449518387697974681757375",
"gradient": "262144*pi/255255",
"restoring": "131072*pi/2078505"
},
"independent_integrals": [
0.8144754969507778,
2.259870919686268,
62.00232068820594,
3.2263801476274416,
0.19811106169642184
],
"connection_energy_after_balance": 22.838228359174966,
"maximum_gauss_error": 3.552763266907874e-15,
"pair_energy_upper_bound_for_all_separations_above_two": 49.06330682595148,
"exterior_field_strength": "0",
"ordinary_source_integral": "Q H != 0 in the chosen source gauge",
"static_solution_constructed": false,
"localized_master_field_source_derived": false,
"quantum_fundamental_triality_screened": false
},
{
"case": "compact-source-gate-depth-3",
"real_depth": 3,
"hodge_coefficient_active": true,
"nonzero_finite_energy_displacement_permitted": true,
"independent_normal_algebra_dimension": 8,
"exact_inactive_source_constraint_retained": false
},
{
"case": "compact-nonabelian-gauss-depth-4",
"real_depth": 4,
"source_core_radius": 1,
"source_charge_scale": 1.1,
"gauge_coupling": 0.7,
"dielectric_coefficient": 1.3,
"neutral_restoring_frequency": 0.9,
"scalar_amplitudes": [
0.3,
1.0,
2.0
],
"complete_single_core_trial_energies": [
25.011113897283202,
26.1920175469871,
30.085106502054895
],
"exact_integrals": {
"source": "48*pi**2/2303",
"electric": "24*pi**2/341",
"magnetic": "20504*pi**2/13237",
"gradient": "16*pi**2/63",
"restoring": "pi**2/90"
},
"independent_integrals": [
0.2057060404916584,
0.6946349138596616,
15.287932963657648,
2.5065661971020594,
0.10966227112321508
],
"connection_energy_after_balance": 24.89432122863117,
"maximum_gauss_error": 1.776512849088884e-14,
"pair_energy_upper_bound_for_all_separations_above_two": 52.3840350939742,
"exterior_field_strength": "0",
"ordinary_source_integral": "Q H != 0 in the chosen source gauge",
"static_solution_constructed": false,
"localized_master_field_source_derived": false,
"quantum_fundamental_triality_screened": false
},
{
"case": "compact-source-gate-depth-4",
"real_depth": 4,
"hodge_coefficient_active": true,
"nonzero_finite_energy_displacement_permitted": true,
"independent_normal_algebra_dimension": 8,
"exact_inactive_source_constraint_retained": false
},
{
"case": "compact-source-gate-depth-5",
"real_depth": 5,
"hodge_coefficient_active": false,
"nonzero_finite_energy_displacement_permitted": false,
"independent_normal_algebra_dimension": 3,
"exact_inactive_source_constraint_retained": true
},
{
"case": "compact-source-gate-depth-6",
"real_depth": 6,
"hodge_coefficient_active": false,
"nonzero_finite_energy_displacement_permitted": false,
"independent_normal_algebra_dimension": 3,
"exact_inactive_source_constraint_retained": true
},
{
"case": "compact-source-gate-depth-10",
"real_depth": 10,
"hodge_coefficient_active": false,
"nonzero_finite_energy_displacement_permitted": false,
"independent_normal_algebra_dimension": 0,
"exact_inactive_source_constraint_retained": false
}
]
}