TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/historical-dynamics-source-recovery-20261103/originaler-spinlift-und-waermekern.json
Original file SHA-256: 0abb6874e6128b320eab1591f306b2b71412aa1b66e9bb1a747f0cb3ca11410f
Inclusive original lines: 1-105
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": "ACTUAL-REAL-EUCLIDEAN-TORSION-SOURCE-20261104",
000003 |   "checks": {
000004 |     "original_full96_Phi_odd": true,
000005 |     "normal_spin_reflection_flips_gamma5": true,
000006 |     "original_real_Euclidean_spinlift_0": true,
000007 |     "real_geometric_torsion_is_Hermitian_0": true,
000008 |     "real_geometric_torsion_is_J_real_0": true,
000009 |     "real_geometric_torsion_is_total_odd_0": true,
000010 |     "tauS_real_geometric_direction_is_odd_0": true,
000011 |     "tauT_real_geometric_direction_is_odd_0": true,
000012 |     "tauS_odd_coordinate_theta_geometric_direction_is_even_0": true,
000013 |     "tauT_odd_coordinate_theta_geometric_direction_is_even_0": true,
000014 |     "tauS_internal_unitary_direction_is_even_0": true,
000015 |     "tauT_internal_unitary_direction_is_even_0": true,
000016 |     "geometric_mass_cross_anticommutator_zero_0": true,
000017 |     "fiber_-1_geometric_is_i_times_unitary_phase_0": true,
000018 |     "fiber_-1_geometric_not_same_real_unitary_phase_0": true,
000019 |     "fiber_1_geometric_is_i_times_unitary_phase_0": true,
000020 |     "fiber_1_geometric_not_same_real_unitary_phase_0": true,
000021 |     "original_real_Euclidean_spinlift_1": true,
000022 |     "real_geometric_torsion_is_Hermitian_1": true,
000023 |     "real_geometric_torsion_is_J_real_1": true,
000024 |     "real_geometric_torsion_is_total_odd_1": true,
000025 |     "tauS_real_geometric_direction_is_odd_1": true,
000026 |     "tauT_real_geometric_direction_is_odd_1": true,
000027 |     "tauS_odd_coordinate_theta_geometric_direction_is_even_1": true,
000028 |     "tauT_odd_coordinate_theta_geometric_direction_is_even_1": true,
000029 |     "tauS_internal_unitary_direction_is_even_1": true,
000030 |     "tauT_internal_unitary_direction_is_even_1": true,
000031 |     "geometric_mass_cross_anticommutator_zero_1": true,
000032 |     "fiber_-1_geometric_is_i_times_unitary_phase_1": true,
000033 |     "fiber_-1_geometric_not_same_real_unitary_phase_1": true,
000034 |     "fiber_1_geometric_is_i_times_unitary_phase_1": true,
000035 |     "fiber_1_geometric_not_same_real_unitary_phase_1": true,
000036 |     "original_real_Euclidean_spinlift_2": true,
000037 |     "real_geometric_torsion_is_Hermitian_2": true,
000038 |     "real_geometric_torsion_is_J_real_2": true,
000039 |     "real_geometric_torsion_is_total_odd_2": true,
000040 |     "tauS_real_geometric_direction_is_odd_2": true,
000041 |     "tauT_real_geometric_direction_is_odd_2": true,
000042 |     "tauS_odd_coordinate_theta_geometric_direction_is_even_2": true,
000043 |     "tauT_odd_coordinate_theta_geometric_direction_is_even_2": true,
000044 |     "tauS_internal_unitary_direction_is_even_2": true,
000045 |     "tauT_internal_unitary_direction_is_even_2": true,
000046 |     "geometric_mass_cross_anticommutator_zero_2": true,
000047 |     "fiber_-1_geometric_is_i_times_unitary_phase_2": true,
000048 |     "fiber_-1_geometric_not_same_real_unitary_phase_2": true,
000049 |     "fiber_1_geometric_is_i_times_unitary_phase_2": true,
000050 |     "fiber_1_geometric_not_same_real_unitary_phase_2": true,
000051 |     "original_real_Euclidean_spinlift_3": true,
000052 |     "real_geometric_torsion_is_Hermitian_3": true,
000053 |     "real_geometric_torsion_is_J_real_3": true,
000054 |     "real_geometric_torsion_is_total_odd_3": true,
000055 |     "tauS_real_geometric_direction_is_odd_3": true,
000056 |     "tauT_real_geometric_direction_is_odd_3": true,
000057 |     "tauS_odd_coordinate_theta_geometric_direction_is_even_3": true,
000058 |     "tauT_odd_coordinate_theta_geometric_direction_is_even_3": true,
000059 |     "tauS_internal_unitary_direction_is_even_3": true,
000060 |     "tauT_internal_unitary_direction_is_even_3": true,
000061 |     "geometric_mass_cross_anticommutator_zero_3": true,
000062 |     "fiber_-1_geometric_is_i_times_unitary_phase_3": true,
000063 |     "fiber_-1_geometric_not_same_real_unitary_phase_3": true,
000064 |     "fiber_1_geometric_is_i_times_unitary_phase_3": true,
000065 |     "fiber_1_geometric_not_same_real_unitary_phase_3": true,
000066 |     "whole_geometric_W_square": true,
000067 |     "full_spin_vertex_trace": true,
000068 |     "full_Gaussian_vertex_trace": true,
000069 |     "quadratic_W_contact_trace": true,
000070 |     "complete_geometric_heat_kernel_including_contact": true,
000071 |     "geometric_G_has_no_linear_x_term": true,
000072 |     "geometric_G_zero_is_one": true,
000073 |     "full_independent_torsion_parallel_transverse_vertex": true,
000074 |     "full_independent_torsion_contact": true,
000075 |     "integration_by_parts_identity_series": true,
000076 |     "transverse_form_factor_reduction": true,
000077 |     "longitudinal_form_factor_reduction": true,
000078 |     "transverse_a4_curl_coefficient": true,
000079 |     "gradient_a4_curl_zero": true,
000080 |     "independent_Bochner_curvature_trace": true,
000081 |     "independent_Bochner_a4_parallel_cancels": true,
000082 |     "independent_Bochner_a4_transverse_negative": true
000083 |   },
000084 |   "passed": 79,
000085 |   "original_symbolic_internal_dimension": 96,
000086 |   "ordinary_product_dimension": 384,
000087 |   "all_original_Yukawa_and_Majorana_blocks_retained": true,
000088 |   "original_constructor_sha256": "6acaa9bc2c7a157a30730d7d6de75e944266afbf69b18a31c6fba654b8bd1c04",
000089 |   "actual_geometric_spinlift": "delta D=3i/4 S_mu gamma_mu gamma5 for the stated original K and Euclidean epsilon conventions",
000090 |   "real_geometric_torsion_not_internal_unitary_phase": true,
000091 |   "even_theta_geometric_reference_jet": "delta D_ref=0;delta D_rel=W_geometric, for both existing lifts",
000092 |   "general_coordinate_parity_jet": "delta D_ref=W[theta_o];delta D_rel=W[theta_e], for both existing lifts; this does not select intrinsic physical reflection parity",
000093 |   "heat_theta_squared_coefficient": "p^2/(8*pi^2*t) G(t*p^2) Tr_F exp(-t*Phi^2)",
000094 |   "G_positive_integral": "integral_0^1 (1+x*a*(1-a))*exp(-x*a*(1-a)) da",
000095 |   "G_series": "-x**4/5040 + x**3/420 - x**2/60 + 1",
000096 |   "a2_theta_coefficient": "dim(F)/(8*pi^2) integral |dtheta|^2",
000097 |   "a4_theta_coefficient_flat_constant_Phi": "-Tr_F(Phi^2)/(8*pi^2) integral |dtheta|^2",
000098 |   "full_independent_torsion_heat_jet": "Tr_F exp(-t Phi^2)/(2*pi^2*t) [G(x)|b_parallel|^2+F(x)|b_transverse|^2], b=3S/4",
000099 |   "a4_independent_torsion_flat_constant_Phi": "-3 dim(F)/(64*pi^2) integral |dS|_form^2 -9 Tr_F(Phi^2)/(32*pi^2) integral |S|^2",
000100 |   "historical_parent_not_identified_with_geometric_residue": "P25 auxiliary action is algebraic in S; ordinary geometric a4 has a nonzero curl term before source/domain/reference reduction. The actual bound source must decide any cancellation or restriction. No free kinetic coupling introduced.",
000101 |   "Wick_or_contour_identity_inferred": false,
000102 |   "complete_Sadm_identified": false,
000103 |   "physical_Htrpos_or_spectrum_claimed": false,
000104 |   "scope": "Actual original ordinary Spin4 matrices and full96 family; real geometric Euclidean torsion and its bound-reference parity. Exact flat constant-full-Phi heat jet, second order in theta and all external momentum. No physical profile, field measure, vacuum, spacetime origin or whole quantum source chosen."
000105 | }