TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/clock/e8-common-clock-results.json
Original file SHA-256: d7973aaffe0be66455e1aa6f267b76d1f1ade6b6207d09f50c929cc693679c3a
Inclusive original lines: 1-178
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 |   "canonical_selection": false,
000003 |   "exact_arithmetic": true,
000004 |   "galois_lift_census": {
000005 |     "fourth_power_W_exponents": {
000006 |       "24": {
000007 |         "25": 10,
000008 |         "5": 10
000009 |       },
000010 |       "8": {
000011 |         "15": 10
000012 |       }
000013 |     },
000014 |     "orders": {
000015 |       "24": 20,
000016 |       "8": 10
000017 |     },
000018 |     "total": 30
000019 |   },
000020 |   "gram_det": 1,
000021 |   "krylov_det": -1,
000022 |   "native_normalizer_counts_among_30_lifts": {
000023 |     "J_to_J": 0,
000024 |     "J_to_J_inverse": 0,
000025 |     "sigma_to_coxeter_family": 0,
000026 |     "sigma_to_coxeter_family_inverse": 0,
000027 |     "sigma_to_sigma": 0,
000028 |     "sigma_to_sigma_inverse": 0
000029 |   },
000030 |   "relations": {
000031 |     "G4": "W^15=-I",
000032 |     "G_C3_Ginv": "C3",
000033 |     "G_C5_Ginv": "C5^2",
000034 |     "G_W_Ginv": "W^7",
000035 |     "compiler": "c=J*sigma, c^4=sigma, c^9=J",
000036 |     "native_J_coordinate_sign": "J(x,y)=(-y,x), multiplication by +i"
000037 |   },
000038 |   "representative_G8_matrix": [
000039 |     [
000040 |       -1,
000041 |       -1,
000042 |       0,
000043 |       2,
000044 |       -1,
000045 |       -1,
000046 |       0,
000047 |       1
000048 |     ],
000049 |     [
000050 |       -2,
000051 |       -1,
000052 |       0,
000053 |       2,
000054 |       0,
000055 |       -2,
000056 |       0,
000057 |       2
000058 |     ],
000059 |     [
000060 |       -2,
000061 |       -1,
000062 |       0,
000063 |       3,
000064 |       -1,
000065 |       -2,
000066 |       -1,
000067 |       3
000068 |     ],
000069 |     [
000070 |       -3,
000071 |       -2,
000072 |       0,
000073 |       4,
000074 |       0,
000075 |       -4,
000076 |       -1,
000077 |       4
000078 |     ],
000079 |     [
000080 |       -2,
000081 |       -2,
000082 |       -1,
000083 |       4,
000084 |       0,
000085 |       -3,
000086 |       -1,
000087 |       3
000088 |     ],
000089 |     [
000090 |       -2,
000091 |       -1,
000092 |       -1,
000093 |       3,
000094 |       0,
000095 |       -2,
000096 |       -1,
000097 |       2
000098 |     ],
000099 |     [
000100 |       -2,
000101 |       -1,
000102 |       0,
000103 |       2,
000104 |       0,
000105 |       -1,
000106 |       -1,
000107 |       1
000108 |     ],
000109 |     [
000110 |       -1,
000111 |       -1,
000112 |       0,
000113 |       1,
000114 |       0,
000115 |       0,
000116 |       -1,
000117 |       1
000118 |     ]
000119 |   ],
000120 |   "root_count": 240,
000121 |   "root_orbits": {
000122 |     "all_named_operators": {
000123 |       "240": 1
000124 |     },
000125 |     "compiler_and_coxeter": {
000126 |       "240": 1
000127 |     }
000128 |   },
000129 |   "scope": [
000130 |     "common integral E8 lattice and 240-root carrier",
000131 |     "no equality of native and cyclotomic order-three clocks",
000132 |     "no source-derived P1/P2 sewing functor",
000133 |     "no identification of the scalar-square theta alpha with G8"
000134 |   ],
000135 |   "spectra": {
000136 |     "coxeter_W": {
000137 |       "charpoly": "x**8 + x**7 - x**5 - x**4 - x**3 + x + 1",
000138 |       "order": 30,
000139 |       "trace": -1
000140 |     },
000141 |     "coxeter_carrier_C5": {
000142 |       "charpoly": "(x**4 + x**3 + x**2 + x + 1)**2",
000143 |       "order": 5,
000144 |       "trace": -2
000145 |     },
000146 |     "coxeter_family_C3": {
000147 |       "charpoly": "(x**2 + x + 1)**4",
000148 |       "order": 3,
000149 |       "trace": -4
000150 |     },
000151 |     "galois_lift_G8": {
000152 |       "charpoly": "(x**4 + 1)**2",
000153 |       "order": 8,
000154 |       "trace": 0
000155 |     },
000156 |     "galois_lift_G8_square": {
000157 |       "charpoly": "(x**2 + 1)**4",
000158 |       "order": 4,
000159 |       "trace": 0
000160 |     },
000161 |     "native_J": {
000162 |       "charpoly": "(x**2 + 1)**4",
000163 |       "order": 4,
000164 |       "trace": 0
000165 |     },
000166 |     "native_compiler": {
000167 |       "charpoly": "(x**2 + 1)**2*(x**4 - x**2 + 1)",
000168 |       "order": 12,
000169 |       "trace": 0
000170 |     },
000171 |     "native_sigma": {
000172 |       "charpoly": "(x - 1)**4*(x**2 + x + 1)**2",
000173 |       "order": 3,
000174 |       "trace": 2
000175 |     }
000176 |   },
000177 |   "verdict": "COMMON_E8_CARRIER_WITH_DISTINCT_CLOCK_SUBALGEBRAS"
000178 | }