TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/automated_source_search_20261029/weyl-reflection-type-results.json
Original file SHA-256: e0f346fb85a9580a3672949e8c9eae5c4a1a86bd6f12810435c98566c02f0440
Inclusive original lines: 752-862
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.

000752 |       "independently_multiplied_weyl_words_match": true,
000753 |       "product_type": "order_reversing",
000754 |       "required_cocycle_sign": 1,
000755 |       "scalar_type": "conjugate_linear",
000756 |       "spatial_map": "reflection",
000757 |       "weyl_relation_preserved": true
000758 |     },
000759 |     {
000760 |       "actual_cocycle_sign": 1,
000761 |       "channel_case": "oppositely_oriented_face_pair_with_swap",
000762 |       "conditional_target": true,
000763 |       "field_sign": -1,
000764 |       "independently_multiplied_weyl_words_match": true,
000765 |       "product_type": "order_reversing",
000766 |       "required_cocycle_sign": 1,
000767 |       "scalar_type": "conjugate_linear",
000768 |       "spatial_map": "reflection",
000769 |       "weyl_relation_preserved": true
000770 |     }
000771 |   ],
000772 |   "central_phase_witness": {
000773 |     "choose_original_group_commutator": "exp(-i*pi/2) = -i",
000774 |     "conjugate_linear_image_required": "+i",
000775 |     "contradiction": true,
000776 |     "order_reversal_plus_single_spatial_reflection_gives": "-i"
000777 |   },
000778 |   "complete_TFPT_solution": false,
000779 |   "conditional_opposite_face_os_reflection_variants": [
000780 |     {
000781 |       "actual_cocycle_sign": 1,
000782 |       "channel_case": "oppositely_oriented_face_pair_with_swap",
000783 |       "conditional_target": true,
000784 |       "field_sign": 1,
000785 |       "independently_multiplied_weyl_words_match": true,
000786 |       "product_type": "order_reversing",
000787 |       "required_cocycle_sign": 1,
000788 |       "scalar_type": "conjugate_linear",
000789 |       "spatial_map": "reflection",
000790 |       "weyl_relation_preserved": true
000791 |     },
000792 |     {
000793 |       "actual_cocycle_sign": 1,
000794 |       "channel_case": "oppositely_oriented_face_pair_with_swap",
000795 |       "conditional_target": true,
000796 |       "field_sign": -1,
000797 |       "independently_multiplied_weyl_words_match": true,
000798 |       "product_type": "order_reversing",
000799 |       "required_cocycle_sign": 1,
000800 |       "scalar_type": "conjugate_linear",
000801 |       "spatial_map": "reflection",
000802 |       "weyl_relation_preserved": true
000803 |     }
000804 |   ],
000805 |   "constant_field_sign_and_weyl_character_do_not_repair": true,
000806 |   "enumerated_variants": 64,
000807 |   "formula": "sigma(Lf,Lg) = scalar_conjugation_sign * product_order_sign * sigma(f,g)",
000808 |   "ledger_changed": false,
000809 |   "passed_algebraic_type_test": 32,
000810 |   "scope": "Necessary algebraic type test; no original P1 source, state, OS positivity, time or spacetime reconstruction proved.",
000811 |   "single_chiral_os_reflection_variants": [
000812 |     {
000813 |       "actual_cocycle_sign": -1,
000814 |       "channel_case": "original_cover_level1",
000815 |       "conditional_target": false,
000816 |       "field_sign": 1,
000817 |       "independently_multiplied_weyl_words_match": false,
000818 |       "product_type": "order_reversing",
000819 |       "required_cocycle_sign": 1,
000820 |       "scalar_type": "conjugate_linear",
000821 |       "spatial_map": "reflection",
000822 |       "weyl_relation_preserved": false
000823 |     },
000824 |     {
000825 |       "actual_cocycle_sign": -1,
000826 |       "channel_case": "original_cover_level1",
000827 |       "conditional_target": false,
000828 |       "field_sign": -1,
000829 |       "independently_multiplied_weyl_words_match": false,
000830 |       "product_type": "order_reversing",
000831 |       "required_cocycle_sign": 1,
000832 |       "scalar_type": "conjugate_linear",
000833 |       "spatial_map": "reflection",
000834 |       "weyl_relation_preserved": false
000835 |     },
000836 |     {
000837 |       "actual_cocycle_sign": -1,
000838 |       "channel_case": "folded_total_level8",
000839 |       "conditional_target": false,
000840 |       "field_sign": 1,
000841 |       "independently_multiplied_weyl_words_match": false,
000842 |       "product_type": "order_reversing",
000843 |       "required_cocycle_sign": 1,
000844 |       "scalar_type": "conjugate_linear",
000845 |       "spatial_map": "reflection",
000846 |       "weyl_relation_preserved": false
000847 |     },
000848 |     {
000849 |       "actual_cocycle_sign": -1,
000850 |       "channel_case": "folded_total_level8",
000851 |       "conditional_target": false,
000852 |       "field_sign": -1,
000853 |       "independently_multiplied_weyl_words_match": false,
000854 |       "product_type": "order_reversing",
000855 |       "required_cocycle_sign": 1,
000856 |       "scalar_type": "conjugate_linear",
000857 |       "spatial_map": "reflection",
000858 |       "weyl_relation_preserved": false
000859 |     }
000860 |   ],
000861 |   "verdict": "SINGLE_CHIRAL_OS_ANTI_ANTI_FORMULA_EXCLUDED_FOR_ORDINARY_WEYL_PRODUCT"
000862 | }