TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/theta_lattice_closure_20261027/fields/vertex-lifts.json
Original file SHA-256: 51a243b5a2674dc08e67edd279e2b2c262482d536a97d4112b8f4a997348dc31
Inclusive original lines: 1-64
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_zero_on_basis_J_extends_strictly": false,
000003 |   "characters_enumerated_per_generator": 256,
000004 |   "explicit_T_commutes_with_beta0": false,
000005 |   "explicit_T_square_is_identity": false,
000006 |   "groupoid_does_not_use": [
000007 |     "T^2=1",
000008 |     "[T,beta0]=1",
000009 |     "full G31 splitting"
000010 |   ],
000011 |   "lifted_group_order": 24,
000012 |   "native_clock": [
000013 |     "order(c)=12",
000014 |     "c^4=sigma",
000015 |     "c^9=J"
000016 |   ],
000017 |   "power_normalized_candidate_counts": {
000018 |     "J_order_4": 256,
000019 |     "V_order_2": 16,
000020 |     "sigma_order_3": 16
000021 |   },
000022 |   "relations": [
000023 |     "J^4=1",
000024 |     "V^2=1",
000025 |     "[V,J]=1",
000026 |     "sigma^3=1",
000027 |     "[sigma,J]=1",
000028 |     "V sigma V^-1=sigma^-1"
000029 |   ],
000030 |   "scope": "standard cocycle on the actual theta E8 basis; proves the marked order-24 subgroup and two-object alpha groupoid only, not a splitting of the full G31 extension",
000031 |   "selected_character_masks": {
000032 |     "J": "0x03",
000033 |     "V": "0x35",
000034 |     "sigma": "0x2a"
000035 |   },
000036 |   "selected_character_supports_zero_based": {
000037 |     "J": [
000038 |       0,
000039 |       1
000040 |     ],
000041 |     "V": [
000042 |       0,
000043 |       2,
000044 |       4,
000045 |       5
000046 |     ],
000047 |     "sigma": [
000048 |       1,
000049 |       3,
000050 |       5
000051 |     ]
000052 |   },
000053 | [OMITTED: non-scientific conversation or execution metadata]
000054 |   "standard_cocycle": "epsilon(m,n)=(-1)^(m^T F n), lower-triangular Gram section",
000055 |   "strict_solution_count": 256,
000056 |   "two_object_alpha": [
000057 |     "alpha_01=T",
000058 |     "alpha_10=beta0 T^-1",
000059 |     "alpha^2=diag(beta0,beta1)",
000060 |     "alpha^8=1",
000061 |     "sigma1=T sigma0^-1 T^-1"
000062 |   ],
000063 |   "verdict": "TWO_OBJECT_VERTEX_GROUPOID_EXISTS_AND_STRICT_ORDER24_SECTION_IS_OPTIONAL"
000064 | }