TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/LOCAL-SOURCE-MODULAR-TIME.json
Original file SHA-256: 48f419a5a233e91bb7a7d246e2dc6e019e323082e9ffb468194525e333a3d9c8
Inclusive original lines: 201-400
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 |       "label": "Canonical modular sign with antilinear annihilation alpha=0.25 j=2",
000203 |       "passed": true
000204 |     },
000205 |     {
000206 |       "label": "Full charge factor cannot cancel first derivative of Weyl modulus alpha=0.25",
000207 |       "passed": true
000208 |     },
000209 |     {
000210 |       "label": "Full connected source, including charge variance, has nonzero geometric-class obstruction alpha=0.25",
000211 |       "passed": true
000212 |     },
000213 |     {
000214 |       "label": "Actual source thermal correction norm tail bound alpha=0.75",
000215 |       "passed": true
000216 |     },
000217 |     {
000218 |       "label": "Actual spatial3mode CAR restriction is faithful alpha=0.75",
000219 |       "passed": true
000220 |     },
000221 |     {
000222 |       "label": "Original source two-point vs independent finite density ('0.75', 0, 0)",
000223 |       "passed": true
000224 |     },
000225 |     {
000226 |       "label": "Original source two-point vs independent finite density ('0.75', 0, 1)",
000227 |       "passed": true
000228 |     },
000229 |     {
000230 |       "label": "Original source two-point vs independent finite density ('0.75', 0, 2)",
000231 |       "passed": true
000232 |     },
000233 |     {
000234 |       "label": "Original source two-point vs independent finite density ('0.75', 1, 0)",
000235 |       "passed": true
000236 |     },
000237 |     {
000238 |       "label": "Original source two-point vs independent finite density ('0.75', 1, 1)",
000239 |       "passed": true
000240 |     },
000241 |     {
000242 |       "label": "Original source two-point vs independent finite density ('0.75', 1, 2)",
000243 |       "passed": true
000244 |     },
000245 |     {
000246 |       "label": "Original source two-point vs independent finite density ('0.75', 2, 0)",
000247 |       "passed": true
000248 |     },
000249 |     {
000250 |       "label": "Original source two-point vs independent finite density ('0.75', 2, 1)",
000251 |       "passed": true
000252 |     },
000253 |     {
000254 |       "label": "Original source two-point vs independent finite density ('0.75', 2, 2)",
000255 |       "passed": true
000256 |     },
000257 |     {
000258 |       "label": "Actual supported four-field word from full sea covariance alpha=0.75",
000259 |       "passed": true
000260 |     },
000261 |     {
000262 |       "label": "Whole supported two-number-unitary word alpha=0.75",
000263 |       "passed": true
000264 |     },
000265 |     {
000266 |       "label": "Actual finite-subalgebra modular action preserves source state alpha=0.75",
000267 |       "passed": true
000268 |     },
000269 |     {
000270 |       "label": "Canonical modular sign with antilinear annihilation alpha=0.75 j=0",
000271 |       "passed": true
000272 |     },
000273 |     {
000274 |       "label": "Canonical modular sign with antilinear annihilation alpha=0.75 j=1",
000275 |       "passed": true
000276 |     },
000277 |     {
000278 |       "label": "Canonical modular sign with antilinear annihilation alpha=0.75 j=2",
000279 |       "passed": true
000280 |     },
000281 |     {
000282 |       "label": "Full charge factor cannot cancel first derivative of Weyl modulus alpha=0.75",
000283 |       "passed": true
000284 |     },
000285 |     {
000286 |       "label": "Full connected source, including charge variance, has nonzero geometric-class obstruction alpha=0.75",
000287 |       "passed": true
000288 |     }
000289 |   ],
000290 |   "control_count": 71,
000291 |   "original_beta": "4*pi",
000292 |   "probe": {
000293 |     "delta": "pi/16",
000294 |     "theta0": "pi/4",
000295 |     "b": "normalized exp[-1/(1-(2x/delta)^2)] on |x|<delta/2",
000296 |     "chi": "b*tilde b",
000297 |     "f": "translated derivative of chi",
000298 |     "b_fourier_first": [
000299 |       "1.0",
000300 |       "0.9992382328598229270825211",
000301 |       "0.9969553906331109944944369",
000302 |       "0.993158840588913598681932"
000303 |     ],
000304 |     "f_zero_mode": 0
000305 |   },
000306 |   "local_covariance_derivative": "-0.00001957819169396816171366830910684732205507",
000307 |   "analytic_derivative_tail_bound": "1.23586221164389e-45",
000308 |   "direct_thermal_derivative": "-0.00001957819169396816171366830910684732205507",
000309 |   "log_weyl_modulus_derivative_per_s_squared": "0.000009789095846984080856834154553423661027534",
000310 |   "geometric_class": {
000311 |     "regularity": "C5 real v, continuous at fixed interval endpoints",
000312 |     "action": "unchanged weight1 current point transport plus arbitrary scalar shifts",
000313 |     "exact_upper_bound_charge_variance_plus_2S1": "205360633608020/4095923200479999",
000314 |     "strict_upper_limit": "1/12",
000315 |     "decision": "only v=0 is state preserving at either original quarter"
000316 |   },
000317 |   "actual_interval_car_rows": [
000318 |     {
000319 |       "alpha": "0.25",
000320 |       "occupation_covariance": [
000321 |         [
000322 |           "0.2706955948000365559271808915",
000323 |           "-0.1013157024965558529251097069",
000324 |           "0.06754417521770275351988629307"
000325 |         ],
000326 |         [
000327 |           "-0.1013157024965558529251097069",
000328 |           "0.04735584638506021556884377544",
000329 |           "-0.0337726479388496541146628792"
000330 |         ],
000331 |         [
000332 |           "0.06754417521770275351988629307",
000333 |           "-0.0337726479388496541146628792",
000334 |           "0.02484116344844272645559741133"
000335 |         ]
000336 |       ],
000337 |       "eigenvalues": [
000338 |         0.00018750575218581524,
000339 |         0.014273437321272842,
000340 |         0.32843166156008086
000341 |       ],
000342 |       "finite_subalgebra_k": [
000343 |         [
000344 |           1.3823213676689299,
000345 |           1.3313749751604425,
000346 |           -0.5431577338398664
000347 |         ],
000348 |         [
000349 |           1.3313749751604425,
000350 |           5.772968607618345,
000351 |           2.455229217285391
000352 |         ],
000353 |         [
000354 |           -0.5431577338398667,
000355 |           2.455229217285391,
000356 |           6.376489248597621
000357 |         ]
000358 |       ],
000359 |       "thermal_correction_tail_bound": "3.86897631326e-92",
000360 |       "four_field_word": 0.0025541474320924223,
000361 |       "two_number_word": [
000362 |         0.9332937649646454,
000363 |         0.1560496619140436
000364 |       ],
000365 |       "charge_variance": "0.039788735772973833942220940843128591",
000366 |       "connected_kernel_a0": "-0.043537622802677401849507695635167758",
000367 |       "connected_kernel_a2": "-0.004170154118478073579970479697809261",
000368 |       "geometric_class_obstruction": "-0.015164196794465722108983562537488222"
000369 |     },
000370 |     {
000371 |       "alpha": "0.75",
000372 |       "occupation_covariance": [
000373 |         [
000374 |           "0.2416461231476641534665776917",
000375 |           "-0.09852310911457005168825165848",
000376 |           "0.0658686110601048049521971648"
000377 |         ],
000378 |         [
000379 |           "-0.09852310911457005168825165848",
000380 |           "0.0464249412821058175705776316",
000381 |           "-0.03321411300563955821614267112"
000382 |         ],
000383 |         [
000384 |           "0.0658686110601048049521971648",
000385 |           "-0.03321411300563955821614267112",
000386 |           "0.02450604519798487393029948813"
000387 |         ]
000388 |       ],
000389 |       "eigenvalues": [
000390 |         4.286073394226918e-05,
000391 |         0.010309684478234417,
000392 |         0.3022245644155781
000393 |       ],
000394 |       "finite_subalgebra_k": [
000395 |         [
000396 |           1.664679659447338,
000397 |           1.6425035810710822,
000398 |           -0.4656470466760269
000399 |         ],
000400 |         [