Recorded data and provenance for the associated calculation.
| title | An Exact-Zero Dielectric Leaves a Vacuum-History Ambiguity |
|---|---|
| checks_passed | 472 |
| dependency_checks_passed | 18 |
| case_count | 16 |
| scope | exact local homogeneous driven classical solutions with smooth raw vacuum connection histories; energy-density controls, not finite-total-energy particles |
| conclusion | In active sectors, different smooth zero-energy vacuum connection histories sharing identical initial raw data yield different responses to the same later neutral drive. A positive floor rejects those histories but removes the exact source constraints. A geometric vacuum-flatness or connection-reduction rule requires derivation. Inactive sectors keep their zero source and neutral harmonic controls. |
View complete data
{
"title": "An Exact-Zero Dielectric Leaves a Vacuum-History Ambiguity",
"sources": {
"experiments/vacuum-connection-checks.py": "95e318a98b676905fd9146002f73918ae0b87d13ba6d564ce690c0248ce4cf7b",
"experiments/hodge-gated-gauss-checks.py": "d24406f940aea7e81ee65cb9596a57a3dc88e0f5d03c07106db93cc948ff1faa"
},
"checks_passed": 472,
"dependency_checks_passed": 18,
"case_count": 16,
"occupied_depths": [
2,
3,
4,
5,
6,
10
],
"scope": "exact local homogeneous driven classical solutions with smooth raw vacuum connection histories; energy-density controls, not finite-total-energy particles",
"conclusion": "In active sectors, different smooth zero-energy vacuum connection histories sharing identical initial raw data yield different responses to the same later neutral drive. A positive floor rejects those histories but removes the exact source constraints. A geometric vacuum-flatness or connection-reduction rule requires derivation. Inactive sectors keep their zero source and neutral harmonic controls.",
"cases": [
{
"case": "vacuum-response-depth-2-B-0",
"real_depth": 2,
"hodge_coefficient_active": false,
"settled_magnetic_curvature": 0.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
"identical_neutral_probe": "smooth pulse supported in 2<t<3",
"response_at_t4": 0.4128976872814609,
"maximum_energy_work_error": 3.0059288391726113e-14,
"maximum_independent_scalar_PDE_error": 5.4657472436936416e-08,
"post_probe_complete_energy_density": 0.07252479676807998,
"unforced_common_initial_velocity_period": 6.981317007977318,
"unforced_turning_amplitude": -0.0035577020538688294,
"local_homogeneous_control": true,
"finite_total_energy_global_solution": false
},
{
"case": "vacuum-response-depth-2-B-1",
"real_depth": 2,
"hodge_coefficient_active": false,
"settled_magnetic_curvature": 1.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
"identical_neutral_probe": "smooth pulse supported in 2<t<3",
"response_at_t4": 0.4128976872814609,
"maximum_energy_work_error": 3.0059288391726113e-14,
"maximum_independent_scalar_PDE_error": 5.4657472436936416e-08,
"post_probe_complete_energy_density": 0.07252479676807998,
"unforced_common_initial_velocity_period": 6.981317007977318,
"unforced_turning_amplitude": -0.0035577020538688294,
"local_homogeneous_control": true,
"finite_total_energy_global_solution": false
},
{
"case": "vacuum-response-depth-2-B-3",
"real_depth": 2,
"hodge_coefficient_active": false,
"settled_magnetic_curvature": 3.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
"identical_neutral_probe": "smooth pulse supported in 2<t<3",
"response_at_t4": 0.4128976872814609,
"maximum_energy_work_error": 3.0059288391726113e-14,
"maximum_independent_scalar_PDE_error": 5.4657472436936416e-08,
"post_probe_complete_energy_density": 0.07252479676807998,
"unforced_common_initial_velocity_period": 6.981317007977318,
"unforced_turning_amplitude": -0.0035577020538688294,
"local_homogeneous_control": true,
"finite_total_energy_global_solution": false
},
{
"case": "vacuum-response-depth-3-B-0",
"real_depth": 3,
"hodge_coefficient_active": true,
"settled_magnetic_curvature": 0.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
"identical_neutral_probe": "smooth pulse supported in 2<t<3",
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"maximum_energy_work_error": 3.0059288391726113e-14,
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"post_probe_complete_energy_density": 0.07252479676807998,
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"local_homogeneous_control": true,
"finite_total_energy_global_solution": false
},
{
"case": "vacuum-response-depth-3-B-1",
"real_depth": 3,
"hodge_coefficient_active": true,
"settled_magnetic_curvature": 1.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
"identical_neutral_probe": "smooth pulse supported in 2<t<3",
"response_at_t4": 0.3833787434220946,
"maximum_energy_work_error": 3.209932319947484e-14,
"maximum_independent_scalar_PDE_error": 5.468203634340085e-08,
"post_probe_complete_energy_density": 0.07251764543751306,
"unforced_common_initial_velocity_period": 4.9173822305399515,
"unforced_turning_amplitude": -0.17205289820856973,
"local_homogeneous_control": true,
"finite_total_energy_global_solution": false
},
{
"case": "vacuum-response-depth-3-B-3",
"real_depth": 3,
"hodge_coefficient_active": true,
"settled_magnetic_curvature": 3.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
"identical_neutral_probe": "smooth pulse supported in 2<t<3",
"response_at_t4": 0.22686144342728434,
"maximum_energy_work_error": 4.835021272242557e-14,
"maximum_independent_scalar_PDE_error": 5.487742082976865e-08,
"post_probe_complete_energy_density": 0.07246051405469903,
"unforced_common_initial_velocity_period": 3.111923495369455,
"unforced_turning_amplitude": -0.26193038339572744,
"local_homogeneous_control": true,
"finite_total_energy_global_solution": false
},
{
"case": "vacuum-response-depth-4-B-0",
"real_depth": 4,
"hodge_coefficient_active": true,
"settled_magnetic_curvature": 0.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
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"unforced_turning_amplitude": -0.0035577020538688294,
"local_homogeneous_control": true,
"finite_total_energy_global_solution": false
},
{
"case": "vacuum-response-depth-4-B-1",
"real_depth": 4,
"hodge_coefficient_active": true,
"settled_magnetic_curvature": 1.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
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"local_homogeneous_control": true,
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},
{
"case": "vacuum-response-depth-4-B-3",
"real_depth": 4,
"hodge_coefficient_active": true,
"settled_magnetic_curvature": 3.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
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"maximum_energy_work_error": 4.835021272242557e-14,
"maximum_independent_scalar_PDE_error": 5.487742082976865e-08,
"post_probe_complete_energy_density": 0.07246051405469903,
"unforced_common_initial_velocity_period": 3.111923495369455,
"unforced_turning_amplitude": -0.26193038339572744,
"local_homogeneous_control": true,
"finite_total_energy_global_solution": false
},
{
"case": "vacuum-response-depth-5-B-0",
"real_depth": 5,
"hodge_coefficient_active": false,
"settled_magnetic_curvature": 0.0,
"initial_raw_connection_and_curvature": "0",
"initial_neutral_amplitude_and_velocity": "0",
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"finite_total_energy_global_solution": false
},
{
"case": "vacuum-response-depth-5-B-1",
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"hodge_coefficient_active": false,
"settled_magnetic_curvature": 1.0,
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},
{
"case": "vacuum-response-depth-5-B-3",
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"initial_raw_connection_and_curvature": "0",
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},
{
"case": "vacuum-response-depth-6-B-0",
"real_depth": 6,
"hodge_coefficient_active": false,
"settled_magnetic_curvature": 0.0,
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},
{
"case": "vacuum-response-depth-6-B-1",
"real_depth": 6,
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},
{
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},
{
"case": "vacuum-response-depth-10",
"real_depth": 10,
"independent_normal_connection_exists": false,
"neutral_clock_period": 6.981317007977318
}
]
}