TFPT scientific source excerpt Original repository path: experiments/theory-contracts/historical-dynamics-source-recovery-20261103/verbindung-und-ganze-quelle-D.json Original file SHA-256: 6e604cbb25ac061ab0710cae446f2e2e9781f882874762c5e50bb2cd816c260d Inclusive original lines: 1-104 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000001 | { 000002 | "result_id": "TORSION20261104D", 000003 | "passed": 70, 000004 | "checks": { 000005 | "whole_metric_connection_dirac_image_rank8": true, 000006 | "formal_symmetry_has_four_independent_conditions": true, 000007 | "symmetric_connection_fiber_dimension20": true, 000008 | "symmetric_dirac_image_rank4": true, 000009 | "dirac_invisible_connection_kernel_dimension16": true, 000010 | "orthogonal_spin_connection_skew_0": true, 000011 | "connection_clifford_compatibility_requires_moving_tangent_connection_0_0": true, 000012 | "connection_clifford_compatibility_requires_moving_tangent_connection_0_1": true, 000013 | "connection_clifford_compatibility_requires_moving_tangent_connection_0_2": true, 000014 | "connection_clifford_compatibility_requires_moving_tangent_connection_0_3": true, 000015 | "orthogonal_spin_connection_skew_1": true, 000016 | "connection_clifford_compatibility_requires_moving_tangent_connection_1_0": true, 000017 | "connection_clifford_compatibility_requires_moving_tangent_connection_1_1": true, 000018 | "connection_clifford_compatibility_requires_moving_tangent_connection_1_2": true, 000019 | "connection_clifford_compatibility_requires_moving_tangent_connection_1_3": true, 000020 | "orthogonal_spin_connection_skew_2": true, 000021 | "connection_clifford_compatibility_requires_moving_tangent_connection_2_0": true, 000022 | "connection_clifford_compatibility_requires_moving_tangent_connection_2_1": true, 000023 | "connection_clifford_compatibility_requires_moving_tangent_connection_2_2": true, 000024 | "connection_clifford_compatibility_requires_moving_tangent_connection_2_3": true, 000025 | "orthogonal_spin_connection_skew_3": true, 000026 | "connection_clifford_compatibility_requires_moving_tangent_connection_3_0": true, 000027 | "connection_clifford_compatibility_requires_moving_tangent_connection_3_1": true, 000028 | "connection_clifford_compatibility_requires_moving_tangent_connection_3_2": true, 000029 | "connection_clifford_compatibility_requires_moving_tangent_connection_3_3": true, 000030 | "actual_axial_spin_connection_contraction": true, 000031 | "real_axial_hermitian": true, 000032 | "real_axial_J_real": true, 000033 | "real_axial_spin_odd": true, 000034 | "actual_axial_extraction_0": true, 000035 | "axial_does_not_commute_with_full_Clifford_0": true, 000036 | "actual_axial_extraction_1": true, 000037 | "axial_does_not_commute_with_full_Clifford_1": true, 000038 | "actual_axial_extraction_2": true, 000039 | "axial_does_not_commute_with_full_Clifford_2": true, 000040 | "actual_axial_extraction_3": true, 000041 | "axial_does_not_commute_with_full_Clifford_3": true, 000042 | "whole_Clifford_commutant_is_scalar_dimension_one": true, 000043 | "axial_image_is_whole_symmetric_metric_connection_dirac_image": true, 000044 | "central_scalar_commutator_unchanged": true, 000045 | "whole_collar_split": true, 000046 | "tangent_axial_part_is_skew_normal_connection": true, 000047 | "normal_axial_part_is_hermitian_boundary_potential": true, 000048 | "normal_connection_preserves_normal_clifford": true, 000049 | "boundary_potential_anticommutes_with_normal": true, 000050 | "operator_normal_connection_is_three_times_axial_representative_connection": true, 000051 | "naive_boundary_generator_hermiticity_defect": true, 000052 | "naive_hermitian_iff_all_three_tangent_components_zero": true, 000053 | "original_whole_boundary_B0_hermitian": true, 000054 | "original_whole_boundary_B0_normal_odd": true, 000055 | "original_whole_boundary_square": true, 000056 | "new_boundary_potential_is_hermitian": true, 000057 | "whole_fermion_source_coefficient_two_integration_orders_15": true, 000058 | "whole_fermion_source_coefficient_two_integration_orders_63": true, 000059 | "whole_fermion_source_coefficient_two_integration_orders_95": true, 000060 | "whole_fermion_source_coefficient_two_integration_orders_111": true, 000061 | "whole_fermion_source_coefficient_two_integration_orders_159": true, 000062 | "whole_fermion_source_coefficient_two_integration_orders_175": true, 000063 | "whole_fermion_source_coefficient_two_integration_orders_207": true, 000064 | "whole_fermion_source_coefficient_two_integration_orders_255": true, 000065 | "all_external_eta_sectors_retained": true, 000066 | "exact_auxiliary_contact_2kappa_squared_over3": true, 000067 | "exact_current_response_kappa_squared_over2": true, 000068 | "exact_transverse_current_spectral_weight_kappa_fourth_over4": true, 000069 | "extra_weight_first_source_force_0": true, 000070 | "extra_weight_second_source_contacts_0_0": true, 000071 | "extra_weight_second_source_contacts_0_1": true, 000072 | "extra_weight_first_source_force_1": true, 000073 | "extra_weight_second_source_contacts_1_0": true, 000074 | "extra_weight_second_source_contacts_1_1": true 000075 | }, 000076 | "connection_fiber": { 000077 | "real_metric_dimension": 24, 000078 | "dirac_image_rank": 8, 000079 | "selfadjoint_constraints_rank": 4, 000080 | "symmetric_fiber_dimension": 20, 000081 | "symmetric_dirac_image_rank": 4, 000082 | "invisible_kernel_dimension": 16 000083 | }, 000084 | "collar": { 000085 | "A_normal": "-3/4 sum_i S_i gamma4 gammai gamma5", 000086 | "B_selfadjoint": "B0-3/4 S4 gamma5", 000087 | "naive_shift": "A_normal-3/4 S4 gamma5", 000088 | "frame_ode": "partial_r U=-A_normal U, U(0)=I", 000089 | "frame_carry": "U* B_selfadjoint U including its tangential derivatives; both endpoints and original reference/state/domain" 000090 | }, 000091 | "source_identity": { 000092 | "Q": "r+c0 J5", 000093 | "gaussian_factor": "(pi/A)^(number_of_real_S_coordinates/2) exp(sum(ell+r)^2/(4A))", 000094 | "all_fermion_source_coefficients_checked": 8, 000095 | "exact_relation": "G_SS,c=(2A)^-1 I+(2A)^-2 G_QQ,c", 000096 | "transverse_relation": "G_STST,c=(2kappa_phys^2/3) P_T+(kappa_phys^4/4) G_JTJT,c", 000097 | "extra_weight_unnormalized_identity": "4A^2 Z_SS=2A delta Z+Z[Q Q F+Q Fprime+Fprime Q+Fsecond] at ell0; connected subtraction retained; no division by F", 000098 | "scope": "actual regulated minimal historical P25 Gaussian parent; same original remaining fields, reference and sources; any extra S-dependent factor requires its own force/contact terms" 000099 | }, 000100 | "primitive_original_torsion_field_image_selected": false, 000101 | "full_Sadm_derived": false, 000102 | "physical_Htrpos_derived": false, 000103 | "common_physical_spectrum_computed": false 000104 | }