TFPT scientific source excerpt Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/OS-VACUUM.txt Original file SHA-256: 469b77e3a452f777ad90abbc363a12eca7d84193b6acded6443c79fe83026218 Inclusive original lines: 201-324 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 | already specified repairs, Omega=[1] follows; there is no further state 000202 | fit after those original hypotheses hold. The admissible sector remains 000203 | the actual one because its supplied reflection/projector operations 000204 | commute and its actual source map is retained. 000205 | 000206 | The smallest remaining RELATIVISTIC application identity, where needed, 000207 | can be written for the same normalized full original flat-branch source: 000208 | 000209 | q_flat[J^g]=q_flat[J] for every actual Euclidean g, (7) 000210 | 000211 | with its actual locality, regularity and reflected operations. A covariance 000212 | law comparing transformed BACKGROUNDS need not be invariance at a fixed 000213 | background unless that background and its state/boundary data are fixed 000214 | by the transformations in question. Parent reviews that actual full-source 000215 | Ward step. Once(7) has the applicable original domain, invariant Omega 000216 | and the forward-cone spectrum follow together. They are not two further 000217 | independent additions to the source. Clustering only strengthens this 000218 | to the unique vacuum within the corresponding generated sector. 000219 | 000220 | 6. DECISIVE TEST ACTUALLY PERFORMED AND VERDICT 000221 | 000222 | No auxiliary model or numerical replay. The decisive constructive test 000223 | was to extend H's SAME actual Gaussian-smearing identity from thermal 000224 | words to contractions in finite physical ground spaces. Exact equations 000225 | GROUND-SOURCE(3)-(7) prove convergence of every bounded original Euclidean 000226 | word on the same state subnet; the uniform entire majorant lifts it to 000227 | the whole normalized source. Its exact reflected Gram maps [1] to the 000228 | already existing Omega_0. The finite Gibbs comparison includes the 000229 | excited numerator at beta-T and the denominator, and therefore controls 000230 | whole words rather than merely finite Gibbs densities. Relational_logic 000231 | independently checked this sign convention and bound. 000232 | 000233 | Thus the full physical Hamiltonian source-to-ground-vacuum connection 000234 | is closed in its actual original class, without a new fit or missing 000235 | moment list. The full Euclidean-covariant original OS branch likewise 000236 | has its canonical relativistic vacuum once its actual full covariance 000237 | identity is invoked. An arbitrary finite-temperature ordinary-Hamiltonian 000238 | KMS state is not silently turned into that vacuum. No uniqueness, 000239 | Lorentz symmetry or all-sector physical closure is claimed from a 000240 | finite transfer spectrum or from groundness alone. 000241 | 000242 | SOURCE REGISTER, HASHES AND ACTUAL READ EXTENTS 000243 | 000244 | A. Original normalized/full parent, old42 FRG: 000245 | research-source:0f0877c5b4346959c8f074a7:3-67, freshly read full range; 000246 | archive--paper-latex--tfpt-42/sections/035-subsection-renormalized- 000247 | physical-and-scheme-readout-laye.tex, 000248 | SHA2562a32bc13e10e2f2c7f7f42890f2065816d3c0289f1b71d23a4797b1bc10ade81. 000249 | 000250 | B. Original45 full/cumulant and old OS chain: 000251 | research-source:5f68beab2336e69cb6e05eb6:144-184; 000252 | research-source:e3a4c851c9b7381edbe7b598:1-122; 000253 | archive--tfpt-45--source_extracts--04_qft_source/sections/005- 000254 | subsection-admissible-schwinger-functions-minkowski-loca.tex, 000255 | SHA2568bf0a37157505ca12b90154dbe41a29c49a503686a8493dffd63945f205e0af6. 000256 | Actual source1-184 was read, including126-142 flatness conditions. 000257 | research-source:3773e2df55f804d81286a192:179-254; 000258 | research-source:ef65163fa990d8ebc30a2ef2:215-255; 000259 | same source family/sections/008-section-relative-reflection- 000260 | positivity-with-fermions.tex, 000261 | SHA256898aa879cf6a3eb6464d3180274bc2fc028408aeec9676af70a862dad9c3f4dc. 000262 | Relevant preceding RP section and179-255 read in full. 000263 | 000264 | C. Existing25October repair, freshly read1-375: 000265 | research-source:80ebe48a5da95a61ff8dbcad:1-200; 000266 | research-source:a7e841d5fe8f267135a523ff:201-375; 000267 | experiments/theory-contracts/primitive-seam-operator-reconstruction- 000268 | 20261025/OS-SOURCE-REPAIR.txt, 000269 | SHA25650bc771398e8a363a617c677f503f556c9f2adccf6e40cfcb460ca4eb9f55ba6. 000270 | Use its actual full-moment and source-isometry proofs. Some old blanket 000271 | source-absence descriptions in its historical audit are superseded by 000272 | the later G/H reconciliation; no such global absence is repeated here. 000273 | 000274 | D. Positive explicit transport gap original, read full1-160: 000275 | paper-source:c38e82c9a06f5aeed1d3e1ad:1-160; 000276 | documents/tfpt_2_standard_model/sections/010-section-the-explicit- 000277 | mass-gap-closes-dynamics-and-cluste.tex, 000278 | SHA2563a31f272d999f1e0b027f25a877068576c6cbdc83150c7b5c0f8a6e17bed1904. 000279 | Same content in paper-source:3a7bbf51fdcf4dfc64371d60:3306-3465, 000280 | experiments/theory-contracts/universalraum-fable-kernfragen-20260910/ 000281 | context/transformationen/source-snapshots/tfpt/tfpt_2_standard_model.tex, 000282 | SHA256bc80e9bb7a37c2cac5e2b0c1bb593adfbf2bcf4bea682fa6d5879d1d37719a75. 000283 | 000284 | E. Transfer/thermo/parent predecessor, freshly read1-381: 000285 | paper-source:e9aab669dac761d3bca03ed1; 000286 | archive--tfpt-45--source_extracts--04_qft_source/sections/004-source.tex, 000287 | SHA256a5d1cc26f80d2f1d5af3d89b94cf8ff8912b572040614d4e1c27f1fe3b747126. 000288 | Existing scoped R075 finding: 000289 | finding:volume-wise-injective-positive-transfer-does-not-prove- 000290 | uniform-parent-gap; reviewed dossier, counterfamily not rerun. 000291 | Positive fixed actual tensor and bounded Hamiltonian continuation retained 000292 | from work/source_continuation/TRANSFER.txt; no repeated gap campaign. 000293 | 000294 | F. Geometric predecessor, freshly read137-178: 000295 | paper-source:4321c3004ffbc46103ca5760; 000296 | archive--tfpt-45--source_extracts--05_metrology_source/sections/005- 000297 | section-absolute-dimensionless-metrology-from-the-bounda.tex, 000298 | SHA256b19c58deb3ee905c16e659dd26b15ca8d1998bab6f703cd350e04e54129a9a4c. 000299 | Primitive later selfadjoint realization and domain upgrade read288-404: 000300 | paper-source:543cbb0e445a456e04ec4efc; 000301 | documents/archive--paper-latex--tfpt-42/sections/003-subsection- 000302 | primitive-relative-spectral-dynamics.tex, 000303 | SHA2568683d7459140a06d5e03a06adefd05bf7e6538356e4e4da4397133aa991b8fe4. 000304 | That seed realization is a different step from complete word reconstruction. 000305 | 000306 | G. Actual v1013/H ground and complete Euclidean source originals: 000307 | see exact sources S1-S3 with hashes and extents in GROUND-SOURCE.txt. 000308 | Those accepted class/constraint results are not replaced by the C6 chain. 000309 | 000310 | PRIMARY MATHEMATICAL SOURCES CHECKED LIVE 000311 | 000312 | Osterwalder and Schrader, Axioms for Euclidean Green's Functions II, 000313 | CMP42(1975)281-305, especially III and IV.1, theorem E'->R': its corrected 000314 | distribution/growth assumption must accompany a Wightman reconstruction. 000315 | https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-42/issue-3/Axioms-for-Euclidean-Greens-functions-II-with-an-Appendix-by/cmp/1103899050.pdf 000316 | 000317 | Schlingemann, From euclidean field theory to quantum field theory, 000318 | hep-th/9802035, Definitions2.1-2.3, Lemma3.1, Theorems3.4 and3.7: 000319 | regular invariant RP Euclidean net gives a positive-energy Poincare 000320 | representation and invariant [1]; the local observable reconstruction 000321 | uses the time-zero condition. Its graded extension retains actual signs. 000322 | https://arxiv.org/html/hep-th/9802035 000323 | These primary results supply the stated reconstruction implications, 000324 | not a proof that an arbitrary given TFPT lattice already has full E(4).