Recorded data and provenance for the associated calculation.
| utc | 2026-10-01T04:28:46.165676+00:00 |
|---|---|
| scope | Exact representation and profile identities with numerical Clifford realizations; no stability, particle statistics, mass-frequency selection or complete depth-spin law. |
View complete data
{
"utc": "2026-10-01T04:28:46.165676+00:00",
"scope": "Exact representation and profile identities with numerical Clifford realizations; no stability, particle statistics, mass-frequency selection or complete depth-spin law.",
"checks": {
"clifford_d2": true,
"full_turn_minus_identity_d2": true,
"exact_dirac_profile_d2": true,
"profile_norm_d2": true,
"whole_pattern_rotation_d2": true,
"clifford_d3": true,
"full_turn_minus_identity_d3": true,
"spin_half_casimir_d3": true,
"rotation_algebra_d3": true,
"exact_dirac_profile_d3": true,
"profile_norm_d3": true,
"whole_pattern_rotation_d3": true,
"finite_norm_integral_d3": true,
"clifford_d4": true,
"full_turn_minus_identity_d4": true,
"spin_half_casimir_d4": true,
"rotation_algebra_d4": true,
"exact_dirac_profile_d4": true,
"profile_norm_d4": true,
"whole_pattern_rotation_d4": true,
"finite_norm_integral_d4": true,
"clifford_d5": true,
"full_turn_minus_identity_d5": true,
"spin_half_casimir_d5": true,
"rotation_algebra_d5": true,
"exact_dirac_profile_d5": true,
"profile_norm_d5": true,
"whole_pattern_rotation_d5": true,
"finite_norm_integral_d5": true,
"clifford_d6": true,
"full_turn_minus_identity_d6": true,
"spin_half_casimir_d6": true,
"rotation_algebra_d6": true,
"exact_dirac_profile_d6": true,
"profile_norm_d6": true,
"whole_pattern_rotation_d6": true,
"finite_norm_integral_d6": true,
"spin6_diagonal_embedding_scalar_plus_vector": true,
"clifford_d10": true,
"full_turn_minus_identity_d10": true,
"spin_half_casimir_d10": true,
"rotation_algebra_d10": true,
"exact_dirac_profile_d10": true,
"profile_norm_d10": true,
"whole_pattern_rotation_d10": true,
"finite_norm_integral_d10": true,
"bilinear_scalar_vector_casimir": true,
"single_spinor_bilinear_rank_one_constraint": true,
"orientation_chern_spin_half": true,
"orientation_chern_spin_one": true,
"massless_vector_physical_count": true,
"massive_vector_physical_count": true,
"longitudinal_vector_transversality": true,
"longitudinal_vector_norm": true,
"simplex_rotation_decomposition_d3_n1": true,
"simplex_rotation_decomposition_d3_n4": true,
"simplex_rotation_decomposition_d3_n16": true,
"simplex_rotation_decomposition_d3_n17": true,
"simplex_rotation_decomposition_d4_n3": true,
"simplex_rotation_decomposition_d4_n20": true,
"simplex_rotation_decomposition_d4_n72": true,
"simplex_rotation_decomposition_d5_n10": true,
"simplex_rotation_decomposition_d5_n15": true,
"simplex_rotation_decomposition_d5_n22": true,
"simplex_rotation_decomposition_d6_n13": true,
"simplex_rotation_decomposition_d6_n35": true,
"simplex_rotation_decomposition_d10_n23": true,
"d2_log_norm_derivative": true,
"d2_bilinear_square_norm": true
},
"depths": [
{
"d": 2,
"complex_clifford_rank": 2,
"observer_spin_half_copies": null,
"critical_profile_finite_L2": false,
"norm_over_A2_a_to_d": "diverges logarithmically"
},
{
"d": 3,
"complex_clifford_rank": 2,
"observer_spin_half_copies": 1,
"critical_profile_finite_L2": true,
"norm_over_A2_a_to_d": "pi**2"
},
{
"d": 4,
"complex_clifford_rank": 4,
"observer_spin_half_copies": 2,
"critical_profile_finite_L2": true,
"norm_over_A2_a_to_d": "pi**2/2"
},
{
"d": 5,
"complex_clifford_rank": 4,
"observer_spin_half_copies": 2,
"critical_profile_finite_L2": true,
"norm_over_A2_a_to_d": "pi**3/12"
},
{
"d": 6,
"complex_clifford_rank": 8,
"observer_spin_half_copies": 4,
"critical_profile_finite_L2": true,
"norm_over_A2_a_to_d": "pi**3/24"
},
{
"d": 10,
"complex_clifford_rank": 32,
"observer_spin_half_copies": 16,
"critical_profile_finite_L2": true,
"norm_over_A2_a_to_d": "pi**5/6720"
}
],
"orientation_line_chern_numbers": {
"spin_half": "1",
"spin_one": "2"
},
"simplex_carrier_decomposition": [
{
"d": 3,
"n": 1,
"N": 0,
"simplex_count": 1,
"spin_half_copies_per_one_spinor_doublet": 1,
"maximum_total_spin": "1/2"
},
{
"d": 3,
"n": 4,
"N": 3,
"simplex_count": 20,
"spin_half_copies_per_one_spinor_doublet": 4,
"maximum_total_spin": "7/2"
},
{
"d": 3,
"n": 16,
"N": 15,
"simplex_count": 816,
"spin_half_copies_per_one_spinor_doublet": 16,
"maximum_total_spin": "31/2"
},
{
"d": 3,
"n": 17,
"N": 16,
"simplex_count": 969,
"spin_half_copies_per_one_spinor_doublet": 17,
"maximum_total_spin": "33/2"
},
{
"d": 4,
"n": 3,
"N": 2,
"simplex_count": 15,
"spin_half_copies_per_one_spinor_doublet": 6,
"maximum_total_spin": "5/2"
},
{
"d": 4,
"n": 20,
"N": 19,
"simplex_count": 8855,
"spin_half_copies_per_one_spinor_doublet": 210,
"maximum_total_spin": "39/2"
},
{
"d": 4,
"n": 72,
"N": 71,
"simplex_count": 1215450,
"spin_half_copies_per_one_spinor_doublet": 2628,
"maximum_total_spin": "143/2"
},
{
"d": 5,
"n": 10,
"N": 9,
"simplex_count": 2002,
"spin_half_copies_per_one_spinor_doublet": 220,
"maximum_total_spin": "19/2"
},
{
"d": 5,
"n": 15,
"N": 14,
"simplex_count": 11628,
"spin_half_copies_per_one_spinor_doublet": 680,
"maximum_total_spin": "29/2"
},
{
"d": 5,
"n": 22,
"N": 21,
"simplex_count": 65780,
"spin_half_copies_per_one_spinor_doublet": 2024,
"maximum_total_spin": "43/2"
},
{
"d": 6,
"n": 13,
"N": 12,
"simplex_count": 18564,
"spin_half_copies_per_one_spinor_doublet": 1820,
"maximum_total_spin": "25/2"
},
{
"d": 6,
"n": 35,
"N": 34,
"simplex_count": 3838380,
"spin_half_copies_per_one_spinor_doublet": 73815,
"maximum_total_spin": "69/2"
},
{
"d": 10,
"n": 23,
"N": 22,
"simplex_count": 64512240,
"spin_half_copies_per_one_spinor_doublet": 5852925,
"maximum_total_spin": "45/2"
}
],
"sources": {
"experiments/depth-spin-checks.py": "5a0e8c43e0ee073c9926df7ed7dbf23417fb93399b9cbc98f72ec133d0d6828e"
}
}