TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/native-f20-joint-clock-results.json
Original file SHA-256: 3d32adb64f3cb03f93f6b2d4c5e79c06d16b3442177937ca7c9e2cce5d73955b
Inclusive original lines: 1-186
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 |   "abstract_four_dimensional_joint_relation": {
000003 |     "minus": [
000004 |       {
000005 |         "exponents": [
000006 |           0,
000007 |           0,
000008 |           0,
000009 |           0
000010 |         ],
000011 |         "trace_in_basis_1_omega": [
000012 |           4,
000013 |           0
000014 |         ]
000015 |       },
000016 |       {
000017 |         "exponents": [
000018 |           1,
000019 |           2,
000020 |           1,
000021 |           2
000022 |         ],
000023 |         "trace_in_basis_1_omega": [
000024 |           -2,
000025 |           0
000026 |         ]
000027 |       },
000028 |       {
000029 |         "exponents": [
000030 |           2,
000031 |           1,
000032 |           2,
000033 |           1
000034 |         ],
000035 |         "trace_in_basis_1_omega": [
000036 |           -2,
000037 |           0
000038 |         ]
000039 |       }
000040 |     ],
000041 |     "plus": [
000042 |       {
000043 |         "exponents": [
000044 |           0,
000045 |           0,
000046 |           0,
000047 |           0
000048 |         ],
000049 |         "trace_in_basis_1_omega": [
000050 |           4,
000051 |           0
000052 |         ]
000053 |       },
000054 |       {
000055 |         "exponents": [
000056 |           1,
000057 |           1,
000058 |           1,
000059 |           1
000060 |         ],
000061 |         "trace_in_basis_1_omega": [
000062 |           0,
000063 |           4
000064 |         ]
000065 |       },
000066 |       {
000067 |         "exponents": [
000068 |           2,
000069 |           2,
000070 |           2,
000071 |           2
000072 |         ],
000073 |         "trace_in_basis_1_omega": [
000074 |           -4,
000075 |           -4
000076 |         ]
000077 |       }
000078 |     ]
000079 |   },
000080 |   "actual_native_four": {
000081 |     "rank_C5_sigma_commutator": 4,
000082 |     "rank_G_sigma_Ginv_minus_sigma": 4,
000083 |     "rank_G_sigma_Ginv_minus_sigma_inv": 4,
000084 |     "sigma": [
000085 |       [
000086 |         "0",
000087 |         "0",
000088 |         "1",
000089 |         "0"
000090 |       ],
000091 |       [
000092 |         "1",
000093 |         "0",
000094 |         "0",
000095 |         "0"
000096 |       ],
000097 |       [
000098 |         "0",
000099 |         "1",
000100 |         "0",
000101 |         "0"
000102 |       ],
000103 |       [
000104 |         "0",
000105 |         "0",
000106 |         "0",
000107 |         "1"
000108 |       ]
000109 |     ],
000110 |     "sigma_charpoly": "(lambda - 1)**2*(lambda**2 + lambda + 1)",
000111 |     "sigma_trace": "1"
000112 |   },
000113 |   "checks": [
000114 |     "source pin verification/v315_coxeter_coupling.py",
000115 |     "source pin verification/v417_eisenstein_cp_operator.py",
000116 |     "source pin verification/v419_seam_galois_carrier.py",
000117 |     "source pin verification/v634_st31_structure.py",
000118 |     "source pin experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PAULI-SPIN-CENTRAL-LIFT.txt",
000119 |     "selected native carrier has order five",
000120 |     "selected native F20 relations",
000121 |     "actual v634 sigma has order three and trace one",
000122 |     "actual v634 sigma characteristic polynomial",
000123 |     "actual selected C5 does not commute with sigma",
000124 |     "actual selected G does not fix sigma",
000125 |     "actual selected G does not invert sigma",
000126 |     "F20 symplectic normalization has order eight",
000127 |     "F20 quarter lift has nonscalar square and projective order four",
000128 |     "no commuting F20 four sigma has order three trace one under plus or minus",
000129 |     "plus relation forces scalar sigma",
000130 |     "minus relation gives trace four or minus two",
000131 |     "Q(zeta30) carrier family and Galois orders",
000132 |     "Q(zeta30) cyclic carrier and family clocks commute",
000133 |     "Q(zeta30) carrier Frobenius relation",
000134 |     "Q(zeta30) carrier Galois generator fixes the family clock",
000135 |     "Q(zeta30) family trace is minus four not native trace one"
000136 |   ],
000137 |   "checks_pass": true,
000138 |   "original_Qzeta30_rank_eight": {
000139 |     "G_C5_Ginv_equals_C5_squared": true,
000140 |     "G_sigma_Ginv_equals_sigma": true,
000141 |     "carrier_family_commute": true,
000142 |     "minimal_polynomial": "x**8 + x**7 - x**5 - x**4 - x**3 + x + 1",
000143 |     "sigma_trace": "-4"
000144 |   },
000145 |   "quarter_lift_distinction": {
000146 |     "new_F20_Ghat_projective_order": 4,
000147 |     "new_F20_Ghat_square": [
000148 |       [
000149 |         "0",
000150 |         "1",
000151 |         "0",
000152 |         "0"
000153 |       ],
000154 |       [
000155 |         "-1",
000156 |         "0",
000157 |         "0",
000158 |         "0"
000159 |       ],
000160 |       [
000161 |         "0",
000162 |         "0",
000163 |         "0",
000164 |         "I"
000165 |       ],
000166 |       [
000167 |         "0",
000168 |         "0",
000169 |         "I",
000170 |         "0"
000171 |       ]
000172 |     ],
000173 |     "new_F20_Ghat_square_trace": "0",
000174 |     "old_theta_alpha_projective_order": 2,
000175 |     "old_theta_alpha_square": "+i I4"
000176 |   },
000177 |   "scope": "The gap is for the selected native F20 four with the actual v634 sigma and for any irreducible F20 four under either stated extra joint relation. The original Q(zeta30) arithmetic rank-eight module does carry the commuting carrier and family clocks. No physical no-go or identification of the theta alpha with the F20 Ghat follows.",
000178 |   "source_pins": {
000179 |     "experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PAULI-SPIN-CENTRAL-LIFT.txt": "e5ef50c899eba80dca03e1b7023edf816df3b45a669534fccf2fef215b0ae8e6",
000180 |     "verification/v315_coxeter_coupling.py": "490969af0827cf8829f236e3999710bb526396dc9eb2ee0672d8bdd5c6af7b0c",
000181 |     "verification/v417_eisenstein_cp_operator.py": "c5f1fe26b9e6fd30bf2ad45354de6819a184c4a86b491f19ab21cb53b21c2b7e",
000182 |     "verification/v419_seam_galois_carrier.py": "cc6152ad7ea68c67725020e386e49eec32810ab25bb483c76bae99964399c2fd",
000183 |     "verification/v634_st31_structure.py": "5ff53ed031ca03103187ac22edf723aabce88bee3df1085c52486ecb0044d37c"
000184 |   },
000185 |   "verdict": "JOINT_CLOCK_GAP_ON_SELECTED_NATIVE_F20_FOUR"
000186 | }