TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/ORIGINAL-STATE-MAP.txt
Original file SHA-256: 0fb21f2038204bdef0314d3c1bcad8a20a9ac4deb1ef6f0f2ef3e444bac44905
Inclusive original lines: 201-282
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 | For the existing elliptic Gibbs state rho_beta proportional exp(-beta
000202 | H_alpha), q=exp(-beta) in(0,1), its actual one-current entry is
000203 |  [rho_beta,P]_(1,2) Z=-sqrt(2)(q-q^2)/2 !=0.              (3)
000204 | It is therefore not the P-invariant vacuum just constructed. This does
000205 | not negate the vacuum theorem; it forbids replacing a specified Gibbs
000206 | caller by that vacuum while claiming all words/time were unchanged.
000207 | Its Q0 two-point value 1/(1-exp(-beta)) also differs from vacuum value1.
000208 | 
000209 | Original v526:1–180 and:742–827 likewise constructs the free-circle
000210 | half-algebra rho_OS and its full Tomita ratio spectrum from the SAME
000211 | Omega=[1], but explicitly finds transfer != modular flow on its specified
000212 | domains. This illustrates why [1] by itself is not a zero-temperature
000213 | vacuum theorem: the faithful thermal standard representation has a
000214 | two-sided modular/standard Liouvillian. The genuine vacuum branch also
000215 | uses its positive reconstructed physical H and the full OS conditions.
000216 | 
000217 | The seed time tau_t, geometric deck involution, Cauchy polarization,
000218 | thermal Hamiltonian time, and wedge modular boosts are not equated by
000219 | their names. BW modular conjugation also need not literally equal the
000220 | raw P1 Theta: its actual PCT/rotation/graded relation must be retained.
000221 | Equations(1)–(2) transport a proved relation without inventing such an
000222 | identification. The H ordinary Hamiltonian KMS source and a BW-KMS wedge
000223 | restriction of a vacuum are not interchanged.
000224 | 
000225 | The later full-CAR positive-time reduction also removes a redundant state
000226 | postulate in ITS actual class: a full odd CAR embedding with the same
000227 | gapped Bogoliubov time and H>=0,H Omega=0 forces its sea covariance and
000228 | Wick state. That established theorem is retained. It is not a theorem
000229 | that the coupled S_adm source has linear Bogoliubov time, or that every
000230 | neutral/even current state fixes all charged words. It is not imposed
000231 | as a new universal source-selection obligation.
000232 | 
000233 | CONCLUSION FOR THE ORIGINAL TASK
000234 | 
000235 | The positive neutral local vacuum/BW problem is already solved on the
000236 | actual Q0 source. The complete original P1 source already includes its
000237 | state/time/reflection, and G's full carrier representation inherits its
000238 | OS vacuum and modular data without another independent choice. Where
000239 | the SAME whole source satisfies the original Euclidean/vacuum hypotheses,
000240 | vacuum invariance is its reconstruction consequence. The proposed missing
000241 | post-reconstruction vacuum selection is therefore redundant in that scope.
000242 | 
000243 | No equality between the neutral vacuum, elliptic/H Gibbs callers and
000244 | the whole interacting source is inferred from dimension, group order,
000245 | one covariance or the label KMS. The actual source-map applicability
000246 | remains the concrete task Root checks; this is not a blanket new measure
000247 | requirement or an all-corpus absence claim. No complete physical TFPT
000248 | promotion is made.
000249 | 
000250 | EXACT SOURCE MANIFEST
000251 | 
000252 | Boundary002100–248: research-source:c06319bc3e605029f5678ca9,
000253 |  sha1de90a4a7379bef804cc7815d72c0f86bb398a5771e9b00997c4bb15e8815f9e.
000254 | G REFERENCE-SOURCE-COMPLETION1–165:
000255 |  research-source:0bca6e0297af549d011c9715,
000256 |  sha5ddc9c63c5f20f42befba6ae32fc57fdecb61c4b70dd9ab2d7b26fe667380cbb.
000257 | 17September modular audit RESULTS1–174: source:bb84009c16a7dc57f4c7,
000258 |  sha2d93e640cb38f69c9f2e633f0f624c169c8637579431ffad464c544a714e14c8.
000259 | Neutral PROOF1–193: research-source:09f123d8a14174c6a5960c2c,
000260 |  shad738013d8775f9769747a5cd97f60cfc6b2ff0d2122c4fbfd20b2d65ebe9f4e0.
000261 | Neutral INDEPENDENT-REVIEW1–46: research-source:c87d9115e7644c1d82dc57d0,
000262 |  sha9ec8338d04030b5930703c3bea93fbc7b1790e93246d8d0dd98f1ad18cc77da6.
000263 | Actual checker1–123: research-source:0122e3b0aab89dadb4473f10,
000264 |  sha4016adce04cd143935c6eb7b94fc34c06ab6f2e0baaf89bf8dd3ee0e12444319.
000265 | Original recovery33–115: research-source:dee9317dffa25c5c183326d6,
000266 |  sha5861c8516e38bd1ed303622e019c7bef182d9312a25142bc754456beac573141.
000267 | Original quarter166–180: research-source:7de3b6cc375bc9332cb32c35,
000268 |  sha62a9eeb4519b59d4514445f9d4dd5d2059e29179956a4c97ec94b7bae9ae3094.
000269 | Neutral recorded result1–15: research-source:a47fe485aa825b8b77318f2c,
000270 |  sha06b20dfee86d8cae69de37817e6ac47b6fe82b573a36e4cf0c3bafb43f32f8a0.
000271 | v5261–180,742–827: source:a7fc28ee575c918fe0ab,
000272 |  sha250a6c344c028159ac3965abb67ca5717c9e1ad59d5fb6a8304a3d2065820347.
000273 | Full-CAR state theorem100–266:
000274 |  research-source:75e8260aa0dd042d49813333 /66c658f0f385ed1b4304a791,
000275 |  sha908420944efb265dbb57f5fc53e2331a416170f76a626f75e14f3445299046cb.
000276 | Historical BW ledger421: source:64575236e5003d4a74a3,
000277 |  sha8723b921bdc50a6157acc6bee4342b40586eb89bec6d7dcc0abc3309562c78b4.
000278 | v4551–146: source:d6aed5231ca1da4f9806,
000279 |  sha99bec2c8d51c3b04007281d199b72be59e9565da1575a4cfa6d3ec690b0a1610.
000280 | All above registered excerpts were read after source/hash validation.
000281 | The origin_theory.tex historical excerpt source:2c582ccf837bd2f94d55 was
000282 | rejected by read_source as stale and is NOT used as current evidence.