TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/neutral_moebius_source_20261029/P1-KERNEL-TYPES.txt
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Inclusive original lines: 1-73
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | RECOVERED ORIGINAL KERNEL TYPES AND THE CORRECT NEXT SOURCE TEST
000002 | 29 October 2026. Source clarification, not a new GNS theorem.
000003 | 
000004 | 1. Thin P1
000005 | documents/tfpt_1_architecture_e8/sections/001-source.tex:67-80 declares the
000006 | oriented seam, primitive RP boundary kernel, unit winding and c3=1/(8pi).
000007 | It does not specify that kernel's argument space, word products or insertions.
000008 | The older snapshot has the same wording. This passage alone licenses neither
000009 | an assertion that the kernel is only a two-point function nor an assertion
000010 | that it already gives all field histories.
000011 | 
000012 | 2. Geometric boundary datum
000013 | documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/
000014 | sections/001-section-primitive-core-and-carrier-interface-handoff.tex:65-110
000015 | defines (A_+,H_+,D_+,J,Gamma,B_Sigma), the collar D_+=gamma_n(partial_n+B),
000016 | and a Calderon projector on the Cauchy-data Hilbert space. This is an operator
000017 | and domain package. J is not thereby an OS word reflection. At319-343 the
000018 | field-insertion algebra is introduced separately and the physical net is
000019 | defined by A AND A* reducing restriction, not arbitrary compression P A P.
000020 | 
000021 | documents/archive--paper-latex--tfpt-42/sections/
000022 | 027-subsection-primitive-completion-from-the-boundary-kernel.tex:3-20
000023 | names a further spectral package the boundary primitive kernel. Its explicit
000024 | definition says no vacuum datum belongs to that package.
000025 | 
000026 | 3. Full operational seed
000027 | documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/
000028 | sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex:
000029 | 103-144 defines Seedop=(A_loc,tau_t,Theta,omega,[u],D_coll), including the
000030 | local Euclidean source algebra, time, reflection and RP clustering state.
000031 | For actual full positive-time words F,G, its reflected functional is already
000032 |     K(F,G)=omega((Theta F)G).
000033 | With the appropriate existing OS semigroup/domain bounds, this can be
000034 | reconstructed without a second independently chosen Berezin/CAR law.
000035 | The paper's proof architecture alone does not prove all those analytic bounds.
000036 | 
000037 | The functor in that passage is Seedop -> SBord_adm: operational source to
000038 | geometric boundary data. No inverse or state-preserving section of that
000039 | functor is supplied by its displayed definition/proof architecture.
000040 | 
000041 | 4. Reuse the already present repair
000042 | experiments/theory-contracts/primitive-seam-operator-reconstruction-20261025/
000043 | OS-SOURCE-REPAIR.txt:181-260 states the actual full-word RP and time bounds,
000044 | and the sufficient unital graded word map iota preserving full reflected
000045 | moments, reflection and positive time. It induces an OS isometry onto the
000046 | cyclic source image; no global equivalence of entire source theories is
000047 | necessary. Connected logZ derivatives must first be converted to full moments
000048 | of Z/Z[0]. This repair already exists and is reused, not counted as new.
000049 | 
000050 | The Clifford/Kac-Moody checks in the selected original architecture sections
000051 | are calculations inside the supplied Fock/critical-fermion source. They do
000052 | not retrospectively define the arguments of thin P1. Conversely, if the full
000053 | operational source is the starting assumption, a new physical quantization
000054 | need not be derived merely to reconstruct that already supplied source.
000055 | 
000056 | 5. Concrete next comparison
000057 | First locate the actual proposed images of neutral bilinear words F,G on
000058 | BOTH original boundary faces and calculate
000059 |     omega_original((Theta iota(F))iota(G)).
000060 | It must agree with the same boundary word, including products, all cross
000061 | terms, charge, subtraction, real support and time. A free Wick value inserted
000062 | as input is not this comparison. A finite successful sample is necessary,
000063 | not sufficient for equality of the full reflected functional.
000064 | 
000065 | The newly proved current-net Moebius standard pair in PROOF.txt supplies its
000066 | vacuum-side operators and modular geometry constructively. It does not fill
000067 | the original word value or identify original Theta by itself. The elliptic
000068 | Gibbs state must retain its own source identity.
000069 | 
000070 | Priority correction: pursue this original local full-functional image first.
000071 | The actual field-Hessian/Berezin action remains one possible route to obtain
000072 | it; it is not a universal extra requirement when the full source is already
000073 | part of the operational Seedop input.