Recorded data and provenance for the associated calculation.
| title | Spatial spinor bilinears generate the full middle-Hodge carrier |
|---|---|
| created_utc | 2026-10-09T22:36:08.818858+00:00 |
| checks_passed | 5578 |
| scope | Exact algebraic field-source construction across maintained and neighboring depths; no particle simulations. |
| statistics | Commuting classical amplitudes; identical Grassmann spinor squares require a different slot symmetry. |
View complete data
{
"title": "Spatial spinor bilinears generate the full middle-Hodge carrier",
"created_utc": "2026-10-09T22:36:08.818858+00:00",
"checks_passed": 5578,
"cases": [
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 1,
"parameters": {
"even_carrier_depth": 2,
"middle_degree": 1,
"minimal_spinor_rank": 1,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": true
},
"measurements": {
"middle_channel_rank": 1,
"symmetric_square_rank": 1,
"lower_symmetric_grades": [],
"Hodge_eigenvalue": "(-0-1j)",
"symmetric_Hodge_filter_active": false,
"middle_source_is_full_symmetric_square": true
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 2,
"parameters": {
"even_carrier_depth": 2,
"middle_degree": 1,
"minimal_spinor_rank": 1,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": false
},
"measurements": {
"middle_channel_rank": 1,
"symmetric_square_rank": 1,
"lower_symmetric_grades": [],
"Hodge_eigenvalue": "(-0-1j)",
"symmetric_Hodge_filter_active": false,
"middle_source_is_full_symmetric_square": true
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 3,
"parameters": {
"even_carrier_depth": 4,
"middle_degree": 2,
"minimal_spinor_rank": 2,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": true
},
"measurements": {
"middle_channel_rank": 3,
"symmetric_square_rank": 3,
"lower_symmetric_grades": [],
"Hodge_eigenvalue": "(1-0j)",
"symmetric_Hodge_filter_active": true,
"middle_source_is_full_symmetric_square": true
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 4,
"parameters": {
"even_carrier_depth": 4,
"middle_degree": 2,
"minimal_spinor_rank": 2,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": false
},
"measurements": {
"middle_channel_rank": 3,
"symmetric_square_rank": 3,
"lower_symmetric_grades": [],
"Hodge_eigenvalue": "(1-0j)",
"symmetric_Hodge_filter_active": true,
"middle_source_is_full_symmetric_square": true
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 5,
"parameters": {
"even_carrier_depth": 6,
"middle_degree": 3,
"minimal_spinor_rank": 4,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": true
},
"measurements": {
"middle_channel_rank": 10,
"symmetric_square_rank": 10,
"lower_symmetric_grades": [],
"Hodge_eigenvalue": "(-0-1j)",
"symmetric_Hodge_filter_active": false,
"middle_source_is_full_symmetric_square": true
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 6,
"parameters": {
"even_carrier_depth": 6,
"middle_degree": 3,
"minimal_spinor_rank": 4,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": false
},
"measurements": {
"middle_channel_rank": 10,
"symmetric_square_rank": 10,
"lower_symmetric_grades": [],
"Hodge_eigenvalue": "(-0-1j)",
"symmetric_Hodge_filter_active": false,
"middle_source_is_full_symmetric_square": true
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 7,
"parameters": {
"even_carrier_depth": 8,
"middle_degree": 4,
"minimal_spinor_rank": 8,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": true
},
"measurements": {
"middle_channel_rank": 35,
"symmetric_square_rank": 36,
"lower_symmetric_grades": [
0
],
"Hodge_eigenvalue": "(1-0j)",
"symmetric_Hodge_filter_active": true,
"middle_source_is_full_symmetric_square": false
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 8,
"parameters": {
"even_carrier_depth": 8,
"middle_degree": 4,
"minimal_spinor_rank": 8,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": false
},
"measurements": {
"middle_channel_rank": 35,
"symmetric_square_rank": 36,
"lower_symmetric_grades": [
0
],
"Hodge_eigenvalue": "(1-0j)",
"symmetric_Hodge_filter_active": true,
"middle_source_is_full_symmetric_square": false
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 9,
"parameters": {
"even_carrier_depth": 10,
"middle_degree": 5,
"minimal_spinor_rank": 16,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": true
},
"measurements": {
"middle_channel_rank": 126,
"symmetric_square_rank": 136,
"lower_symmetric_grades": [
1
],
"Hodge_eigenvalue": "-1j",
"symmetric_Hodge_filter_active": false,
"middle_source_is_full_symmetric_square": false
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 10,
"parameters": {
"even_carrier_depth": 10,
"middle_degree": 5,
"minimal_spinor_rank": 16,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": false
},
"measurements": {
"middle_channel_rank": 126,
"symmetric_square_rank": 136,
"lower_symmetric_grades": [
1
],
"Hodge_eigenvalue": "-1j",
"symmetric_Hodge_filter_active": false,
"middle_source_is_full_symmetric_square": false
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 11,
"parameters": {
"even_carrier_depth": 12,
"middle_degree": 6,
"minimal_spinor_rank": 32,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": true
},
"measurements": {
"middle_channel_rank": 462,
"symmetric_square_rank": 528,
"lower_symmetric_grades": [
2
],
"Hodge_eigenvalue": "(1+0j)",
"symmetric_Hodge_filter_active": true,
"middle_source_is_full_symmetric_square": false
}
},
{
"name": "spinor-generated-Hodge-channel",
"real_depth": 12,
"parameters": {
"even_carrier_depth": 12,
"middle_degree": 6,
"minimal_spinor_rank": 32,
"source": "F_I=psi^T C gamma_I psi",
"odd_shadow_requires_declared_even_carrier": false
},
"measurements": {
"middle_channel_rank": 462,
"symmetric_square_rank": 528,
"lower_symmetric_grades": [
2
],
"Hodge_eigenvalue": "(1+0j)",
"symmetric_Hodge_filter_active": true,
"middle_source_is_full_symmetric_square": false
}
},
{
"name": "triplet-source-geometry",
"real_depth": 4,
"parameters": {
"carrier": "Sym^2 C^2",
"one_spinor_source": "(x^2,sqrt(2)xy,y^2)"
},
"measurements": {
"source_constraint": "c_2^2-2 c_1 c_3=0",
"three_slot_volume": "sqrt(2) product_{i<j} det(w_i,w_j)",
"independent_color_derived": false,
"two_distinct_spinor_pairs_can_fill_carrier": true,
"uniform_unit_spinor_triplet_covariance": "I_3/3",
"unit_spinor_pair_energy_after_third_average": "(1-|u^dagger v|^4)/3",
"full_Dirac_kinetic_carrier_must_be_retained": true
}
}
],
"scope": "Exact algebraic field-source construction across maintained and neighboring depths; no particle simulations.",
"statistics": "Commuting classical amplitudes; identical Grassmann spinor squares require a different slot symmetry.",
"limitations": [
"The bilinear is a geometric source, not an independently derived color multiplet.",
"One spinor square obeys algebraic constraints not preserved by arbitrary full-channel unitary mixing.",
"Odd depths use the declared even-carrier shadow.",
"The full kinetic spinor carrier is retained; a pointwise chiral compression would kill its symbol."
],
"sources": {
"experiments/spinor-hodge-source-checks.py": "c1a9212b8dd1f0e9e525e36db80c322b9487986ca656aa028c2a4cbb8456b38e"
}
}