TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/clustering-admissible-sector-results.json
Original file SHA-256: d939c231f2c60976163450562b9c4383d501e8762e286376270e3bfd9e29770e
Inclusive original lines: 201-247
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.

000201 |     ],
000202 |     "P_sing_eigenvalue": 0,
000203 |     "carrier_name": "e1+e4",
000204 |     "carrier_representation": "(3,2)_(1/6)",
000205 |     "color_center_phase": "omega",
000206 |     "color_triality": 1,
000207 |     "hypercharge_Y": "1/6",
000208 |     "p_star": [
000209 |       "1/2",
000210 |       "1/2",
000211 |       "1/2",
000212 |       "1/2",
000213 |       "-1/2",
000214 |       "-1/2",
000215 |       "-1/2",
000216 |       "-1/2"
000217 |     ],
000218 |     "scaled_hypercharge_X": "1",
000219 |     "transported_source_U1_charge": "0",
000220 |     "vacuum_P_sing_eigenvalue": 1
000221 |   },
000222 |   "ground_classification_proof": {
000223 |     "all_zero_charges": [
000224 |       "0",
000225 |       "p_star"
000226 |     ],
000227 |     "half_coset": "Coordinatewise strict convexity selects +1/2 where d<0 and -1/2 where d>0, hence uniquely p_star; its total energy is zero.",
000228 |     "integer_coset": "For nonzero integer n, n^2/2+d*n=n(n/2+d)>0 when |d|<1/2; the unique minimizer is p=0."
000229 |   },
000230 |   "scope": {
000231 |     "not_proved": [
000232 |       "that raw P1 alone already contains the later carrier projector",
000233 |       "that P_prim and P_Theta retain the vacuum line",
000234 |       "that H8 is the reconstructed physical OS transfer Hamiltonian",
000235 |       "clustering of the full graded field net or a 4D completion"
000236 |     ],
000237 |     "proved": "On the stipulated E8 lattice extension with the fixed Weyl/carrier dictionary, the original color-center projector removes p_star and the center-neutral restriction has a one-dimensional H8 kernel and a positive exact gap."
000238 |   },
000239 |   "sources": {
000240 | [OMITTED: non-scientific conversation or execution metadata]
000241 | [OMITTED: non-scientific conversation or execution metadata]
000242 |     "fold_results_sha256": "253f370a9c84b70c28169ed0aad83d1866245804227e44aa0189e823382f5639",
000243 | [OMITTED: non-scientific conversation or execution metadata]
000244 | [OMITTED: non-scientific conversation or execution metadata]
000245 |   },
000246 |   "verdict": "PASS_CENTER_PROJECTOR_REMOVES_THE_ONLY_EXTRA_H8_ZERO_STATE"
000247 | }