TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-paper-source-reconciliation-20261102/shorttime_20261105K/source_identity/ORIGINAL-OMEGA-AND-SAME-SOURCE-IDENTITY.txt
Original file SHA-256: f608df8aac2e276c57bd8c898ca36c446adf7e3f04481089d9f07ae3274a4ecc
Inclusive original lines: 1-73
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | ORIGINAL OMEGA AND SAME-SOURCE IDENTITY: TARGETED PROOF
000002 | 5 November2026. Atlas9101635de54a0a3e3ea245a8; plan145.
000003 | No canonical/public edit, fresh physics run or new model.
000004 | 
000005 | Decision
000006 | The operative definition takes omega as a component of its input object. That does NOT make omega a second freely variable parameter after the complete original S_adm source has been fixed. In the established same-caller representation, omega is the normalized whole word functional of that source. Existing uniqueness results are conditional on that actual source/kernel/transfer. None of the inspected proofs replaces evaluation of its particular neutral word by the scalar c3 or the empty-word vacuum vector. This is an evaluation distinction, not a new state/measure/field-map gap.
000007 | 
000008 | 1. Earliest owning definitions in the inspected chain
000009 | The earlier retained Archive31 reduced datum already passes (A,H,D,J,Gamma,involution,nu), including the actual Dirac operator and positive profile. Source45's operational seed explicitly passes (A_loc,tau,Theta,omega,[uSigma],Dcoll). Its collar-completion functor is a forward map from each supplied seed to its boundary datum. It does not classify or calculate every possible seed from c3. This says exactly which construction takes omega as input; it does not prove a globally free physical omega or two complete physical P1 sources.
000010 | 
000011 | The stronger source-conditioned definition is QFT007: e^W_k[J] is the actual original S_adm functional with its regulator and all source legs. The fixed-reference definition gives Z_rel[J]=Z_adm[J]/Z_ref[0]. After normalizing the full word functional,
000012 | 
000013 |   q[J]=Z_rel[J]/Z_rel[0]=Z_adm[J]/Z_adm[0],
000014 |   omega(W)=the corresponding full graded word derivative of q.
000015 | 
000016 | Original composite renormalization, smearing, pairing and contacts are retained. This does not freeze H-dependent inner reference contributions; only the displayed fixed outer factor cancels in q. The same S/Z/OS/time/physical-selector transport is already established and is not demanded again.
000017 | 
000018 | Consequently, wherever the same entire original functional is defined, any proposed omega' with that exact source and insertion prescription must satisfy omega'(W)=omega(W) on every source-generated word. Two such functionals differing on UY cannot both be the normalized functional defined by the same original integral. This is the elementary uniqueness of a fixed value operation, not a new existence, positivity or continuum theorem.
000019 | 
000020 | 2. Stronger original uniqueness claims: what they actually fix
000021 | QFT004 Block2 fixes finite volume/cutoff and the blocked transfer T_V obtained from its actual local C6 kernels, actual diagonal admissibility weights and selector. Its primitivity result gives the unique CP-even Perron vacuum. Block3 uses boundary decoupling and a uniform contraction/gap hypothesis along the actual exhaustion to construct a unique local thermodynamic limit. These are genuine state-selection statements for that original transfer family, not merely an arbitrary GNS vector. Their proofs retain the entries/weights and actual observable insertions. They do not output a new numerical mixed value after those data have been suppressed.
000022 | 
000023 | Carrier010's singleton fiber product is expressly FOR EVERY GIVEN admissible boundary primitive kernel. It fixes the discrete datum and continuous electromagnetic/geometric/transport/vacuum solutions over that same upstream tuple. Carrier009's master functional itself contains -log Z_rel with the original retained source. Thus the singleton argument does not evaluate an unknown full Z_rel by citing its own symbol. Here rho_vac may itself denote a density operator/state, so it must not be reduced to a scalar readout. Nevertheless uniqueness of the variational solution is not its executed evaluation: once its actual complete transfer matrix or vacuum functional is supplied, Perron diagonalization or the stated minimization is a real value-producing algorithm for that source. The displayed master-functional proof does not eliminate that operation; it already calls the full Z_rel and Gamma_vac. No existing conditional closure is revoked by this distinction.
000024 | 
000025 | OS reconstruction begins with the whole reflected functional q and gives Omega=[1]. Its uniqueness is uniqueness of the corresponding cyclic representation/vacuum within the given sector, and its intertwiner preserves the supplied whole word values. On that already matched source, using omega directly or using its S_adm integral are two representations of the SAME value operation. A second physical vacuum choice is unnecessary.
000026 | 
000027 | 3. Minimal-deformation check, preserving exact premises
000028 | A state-only deformation omega_epsilon=omega+epsilon ell with ell(1)=0 and ell(UY) nonzero is NOT an admissible counterexample with the same whole original source: its UY derivative contradicts q=Z_adm/Z_adm[0]. Changing the source functional by a source-only contact such as exp(epsilon J_U J_Y) while keeping its zero-source value also changes the original linear source/composite/contact prescription. Keeping only Z[0] does not preserve the full original source datum.
000029 | 
000030 | The already known R098 segment changes its time transfer. It therefore cannot establish nonuniqueness at fixed original S_adm/time, regardless of its preserved selected moments and common vacuum. It is not rerun here. Likewise the3^N quartic moment basis does not provide free physical integration constants: its actual real-domain base integrals, normalization and stable quartic tails select them. Other formal SD solutions or arbitrary initial values do not preserve that complete caller.
000031 | 
000032 | No pair of inequivalent complete primitive physical sources satisfying ALL unchanged original data has been constructed in this review. The operative input definition and conditional uniqueness theorem do not prove such a pair exists. Conversely, this targeted review is not a proof that c3/P2 alone determines every possible complete P1 source. Making either global claim would exceed the original statements.
000033 | 
000034 | 4. Concrete consequence for continuing the actual calculation
000035 | The target remains the fixed original connected response
000036 | 
000037 |   C_UY = omega(U(f)Y(g))-omega(U(f))omega(Y(g)),
000038 | 
000039 | or its already equivalent marked physical time jet, with the actual full word and prescribed smearing/contact. Its value is fixed by the given complete source; the inspected uniqueness proofs do not themselves evaluate that derivative. The smallest remaining statement is simply the actual same-source value of this marked derivative (or its equivalent full joint time word), not a new equality between already transported callers. For the actual finite transfer realization, evaluating its given Perron state on the original UY insertion is sufficient; for the functional realization, evaluating the same original integral with that insertion is sufficient. Continue the actual same-source integration/transfer evaluation using its original coefficients and marks. Do not replace this task with choosing omega, proving another generic reconstruction, or treating an unevaluated operator expression as a second independent physical axiom.
000040 | 
000041 | Original source records and current SHA256
000042 | 
000043 | documents/archive--paper-latex--tfpt-31/sections/002-subsection-primitive-relative-spectral-dynamics.tex
000044 |   read 7–28: earlier owning reduced datum includes its actual D and nu
000045 |   SHA256 6d8813b95a1ef4d82ee9cd48a25efff3f9c20066a06b85ad121bc26e5dbaae77
000046 | 
000047 | documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex
000048 |   read 88–143,228–243,285–320: operative input and forward completion; boundary-conditioned reconstruction
000049 |   SHA256 1de90a4a7379bef804cc7815d72c0f86bb398a5771e9b00997c4bb15e8815f9e
000050 | 
000051 | documents/archive--tfpt-45--source_extracts--04_qft_source/sections/007-subsection-renormalized-physical-and-scheme-readout-laye.tex
000052 |   read 3–26: original whole regulated generating functional
000053 |   SHA256 9c1c587cbd61fc4034649d778d16f1ee0e8c1e1189885babb3d8148a6fe72d7c
000054 | 
000055 | documents/archive--tfpt-45--source_extracts--04_qft_source/sections/002-section-closure-theorems-from-the-admissibility-complex.tex
000056 |   read 256–310: actual fixed relative normalization and RP statement
000057 |   SHA256 61ecee7727bdec47936bbffc028d3dbac5260a025b6dbcce30124a60d635fc9c
000058 | 
000059 | documents/archive--tfpt-45--source_extracts--04_qft_source/sections/004-source.tex
000060 |   read 89–245: finite vacuum, actual blocked transfer uniqueness, boundary decoupling and thermodynamic limit
000061 |   SHA256 a5d1cc26f80d2f1d5af3d89b94cf8ff8912b572040614d4e1c27f1fe3b747126
000062 | 
000063 | documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/009-source.tex
000064 |   read 324–377: projected modular functional already includes full relative Z
000065 |   SHA256 27114e2ce775346dac11c53ecb77871453f3ecf226fe40951f8b3099bdea6b05
000066 | 
000067 | documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/010-partial-alpha-gamma-u-1-alpha-0.tex
000068 |   read 1–163: continuous closure and singleton fiber product over given boundary kernel
000069 |   SHA256 979c84b3208540fcd0ef01eefb173a70d91e79fa363c9d4f3270b65696ceb4c7
000070 | 
000071 | experiments/theory-contracts/original-local-source-variable-background-20261102/OS-VACUUM.txt
000072 |   read 29–80,109–133: full normalized functional, canonical vacuum and same-source transport
000073 |   SHA256 469b77e3a452f777ad90abbc363a12eca7d84193b6acded6443c79fe83026218