TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/historical-dynamics-source-recovery-20261103/HISTORICAL-THREE-HYPOTHESES-AND-WHOLE-SOURCE.txt
Original file SHA-256: 4f38c533646c95dd231019456263cb3aa9ebbdca411d00204e5b4a791f7b8b2b
Inclusive original lines: 1-47
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | TORSION20261104F. Three hypotheses tested at the original whole source.
000002 | 4 November 2026. Anonymous source-reviewed continuation, no new physical model.
000003 | 
000004 | 1. THE ACTUAL ENDPOINT AND ORIGINAL CALLER
000005 | The operational P1 seed already contains state, time and reflection. Preserve
000006 | its four-mark rank3/dimension5 relation, E8, clocks, flavor/Yukawa, alpha and
000007 | gravity results with their own scopes. No extra state choice is introduced.
000008 | The target is the actual complete Sadm, positive physical time generator and
000009 | interacting common spectrum from that SAME seed/field/reference/time map.
000010 | 
000011 | Source45 QFT007:1-70 defines
000012 |  exp Wk[J]=int_Hadm Dvarphi exp[-Sadm[varphi]-varphi.Rk.varphi/2+J.varphi],
000013 |  Gamma_k[phi]=sup_J(J.phi-Wk[J])-phi.Rk.phi/2,
000014 |  Wk''=(Gamma_k''+Rk)^-1.
000015 | Its original loop expansion in lines122-153 is an expansion from the given
000016 | whole Sadm, not its evaluation or a prescription for independently choosing
000017 | the higher vertices. Rk is auxiliary. With matched actual bare input and a
000018 | fully evaluated exact endpoint, its shape is not a new physical parameter.
000019 | Sprim, the versioned geometric Gamma_grav, -log Pf, W and Legendre Gamma
000020 | retain their original types. A full fermion integral is only one stage.
000021 | 
000022 | 2. H1: WHAT THE MIXED RESPONSES DO AND DO NOT DETERMINE
000023 | On an actual star-shaped admissible source chart, twice integrating the
000024 | ordinary directional derivative gives the exact reconstruction
000025 |  W[J]=W[0]+W'[0].J+int_0^1(1-s) W''[sJ](J,J) ds.
000026 | For a merely connected chart use compatible local charts/paths. Keep the
000027 | original allowed insertions; do not require every ambient CAR coordinate.
000028 | Odd source directions use their ordered finite Grassmann coefficients.
000029 | The formula needs the actual entire Hessian family, not only W''[0] or a
000030 | few local geometric heat coefficients. Logarithms use a nonzero source
000031 | patch; the original polynomial Z, not a divided expression, crosses zeros.
000032 | 
000033 | Even knowing all CROSS blocks is not the full Hessian. On a genuine local
000034 | product chart of independently admissible source coefficients, zero mixed
000035 | derivatives leave additive functions of each individual source coordinate.
000036 | This is a calculus statement about the chart, not an invented pair of
000037 | complete TFPT sources and not independent dynamics of physical sectors.
000038 | If the full original omega and time are given, their response family is
000039 | already fixed in principle. An unevaluated field representation is not a
000040 | license to choose a new omega or to choose higher 1PI graphs freely.
000041 | 
000042 | Verdict H1: mixed responses supply additional necessary constraints and a
000043 | constructive reconstruction criterion. The supplied a4/current vertices do
000044 | not implement that reconstruction. No uniqueness theorem for the primitive
000045 | whole field density follows from the presently evaluated subset. This does
000046 | not contradict uniqueness of a fully specified original operational source.
000047 |