TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/source-observation-identifiability-20261013/PROOF.txt
Original file SHA-256: b37b7cc9d0454954938fc348337f4da4d2d5c56f178127ad65d94df887ad672d
Inclusive original lines: 10-30
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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000010 | New combination of Universalraum future equivalence and gravity source audit:
000011 | Let W[g,J]=logZ. Fixed-background normalized matter functional is
000012 | Wnorm[g,J]=W[g,J]-W[g,0]. Replace W by W+lambda Q[g]. Wnorm is identical
000013 | for every matter source J. At each fixed g, Hamiltonian scalar shifts produce
000014 | only a global phase and density normalization cancels the scalar Boltzmann
000015 | factor. Thus all matter-only instrument records and the same state's modular
000016 | flow are identical, provided metric branches/deformations are absent from the
000017 | operations menu. All self-consistency constraints depending only on these
000018 | observations are equally satisfied; adding more such constraints cannot fix
000019 | lambda. A common fixed-background state-preserving GNS map cannot recover it.
000020 | 
000021 | Under the already-declared replica convention
000022 | Q[g_n]-nQ[g_1]=4pi(1-n)A, replica entropy
000023 | S=-partial_n(W[g_n,0]-nW[g_1,0]) at n=1 shifts by4pi lambda A.
000024 | Hence the area response is not a function on the matter-only future quotient.
000025 | This extends the existing source audit by an operational-identifiability
000026 | statement; it does not establish that TFPT admits every such metric term.
000027 | The resolution needs an enlarged common source including metric/replica
000028 | responses and an original principle fixing permissible geometric cocycles.
000029 | Even all mixed J-g derivatives of order>=1 in J kill a pure Q[g] term, so a
000030 | purely geometric/source normalization response is necessary for this freedom.