TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-ADMISSIBILITY-AND-TOTAL-CHIRAL-TRACE.json
Original file SHA-256: efcb46e6b47b8cd5a6a8a17af772e2be32402c9c224c16b634b589d44d2e21e2
Inclusive original lines: 1-50
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 |   "contract": "ORIGINAL-ADMISSIBILITY-TOTAL-CHIRAL-TRACE-20261031",
000003 |   "all_passed": true,
000004 |   "checks": {
000005 |     "H_scalar_and_derivative_terms_have_zero_chiral_spin_trace": true,
000006 |     "H_kinetic_pair_has_no_local_chiral_index_component": true,
000007 |     "H_mixed_curvature_terms_have_no_local_chiral_index_component": true,
000008 |     "pure_gauge_index_density_cannot_be_dropped_just_from_H_test": true,
000009 |     "two_halves_have_same_rank_but_different_actual_action": true,
000010 |     "total_chiral_half_is_not_spin_commuting_internal_half": true,
000011 |     "original_whole96_Phi_is_odd_in_fixed_finite_grading": true,
000012 |     "actual_whole_product_is_odd_in_total_grading": true,
000013 |     "actual_total_chiral_half_reduces_square_not_first_order_operator": true,
000014 |     "actual_total_chiral_square_moment_half_1": true,
000015 |     "actual_total_chiral_square_moment_half_2": true,
000016 |     "actual_variable_H_direction_0_survives_total_not_internal_half": true,
000017 |     "actual_variable_H_kinetic_moment_half_0": true,
000018 |     "actual_variable_H_direction_1_survives_total_not_internal_half": true,
000019 |     "actual_variable_H_kinetic_moment_half_1": true,
000020 |     "actual_variable_H_direction_2_survives_total_not_internal_half": true,
000021 |     "actual_variable_H_kinetic_moment_half_2": true,
000022 |     "actual_variable_H_direction_3_survives_total_not_internal_half": true,
000023 |     "actual_variable_H_kinetic_moment_half_3": true,
000024 |     "whole_rectangular_positive_spectra_pair_with_multiplicity": true,
000025 |     "index_term_is_present_for_every_rectangular_parameter": true,
000026 |     "whole_heat_supertrace_including_zero_is_index": true,
000027 |     "absolute_chiral_heat_needs_half_index_term": true,
000028 |     "zero_excluded_whole_spectral_trace_is_exact_half": true,
000029 |     "positive_zeta_half_has_no_unpaired_zero_added": true,
000030 |     "combined_chirality_and_highpass_has_no_index_term": true,
000031 |     "combined_highpass_removes_unpaired_zero_without_new_grading": true,
000032 |     "zero_appearance_jumps_cancel_in_cut_FP_without_threshold_crossing": true,
000033 |     "bound_reference_is_odd_when_lift_preserves_grading": true,
000034 |     "bound_reference_is_odd_when_lift_swaps_grading": true,
000035 |     "multiplying_by_internal_grading_does_not_make_it_odd": true,
000036 |     "actual_selector_form_reduces_its_own_positive_operator": true,
000037 |     "own_operator_positive_spectral_cut_kills_its_zero_mode": true,
000038 |     "whole_weighted_heat_equals_restricted_heat_for_same_spectral_cut": true,
000039 |     "first_order_compression_need_not_match_restricted_square": true,
000040 |     "finite_low_removal_is_entire_at_Einstein_pole": true,
000041 |     "finite_low_removal_changes_FP0_by_count_not_eigenvalue": true,
000042 |     "logdet_low_mode_has_H2_and_H4_jets_unlike_FP0": true,
000043 |     "heat_count_includes_zero_while_positive_zeta_count_does_not": true,
000044 |     "moving_spectral_projector_has_offdiagonal_derivative": true,
000045 |     "first_trace_derivative_from_moving_projection_is_zero": true,
000046 |     "whole_moving_cutoff_trace_has_original_eigenvalue_derivative": true,
000047 |     "H_mass_curvature_ratio_unchanged_under_common_chiral_halving": true
000048 |   },
000049 |   "scope": "Actual96 finite constructor and existing conditional spin4 product; generic spectral-cut,rectangular index and moving-projection identity controls. No chosen physical normal module,trace or source. No new Lean proof,original Dadm/Ksigma identification,physical chirality selection or whole TFPT closure."
000050 | }