TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_origin_derivation_20261029/PROOF.txt
Original file SHA-256: db1151d97d3901948564a4dbc8da10a6bd794c60c6b3b2bd096b6db9f9e3111b
Inclusive original lines: 1-143
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.

000001 | Original-source derivation search, not a supplied-moment recovery
000002 | 2026-10-29. Continuation of the existing elliptic/Moebius source contract.
000003 | 
000004 | STATUS: source-reviewed next derivation target and scoped rejected bridge.
000005 | No original P1 field action or full TFPT proof is claimed.
000006 | 
000007 | [OMITTED: non-scientific conversation or execution metadata]
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000013 | 
000014 | The immediate target is an actual source identity on the ORIGINAL field space.
000015 | It must derive the response family internally. The complete common-parent goal
000016 | still includes T1-T8, not just a free boundary model or an E8 field hull.
000017 | 
000018 | 2. Original definitions and the first missing typed arrow
000019 | 
000020 | boundary_kernel_source/001:65-110 supplies the linear geometric Dirac collar,
000021 | its domain and Cauchy/Calderon data. At302-316 it declares a relative spectral
000022 | trace profile plus eta phase. At319-343 the physical local net is a reducing
000023 | restriction under A AND A*, not arbitrary compression P A P.
000024 | 
000025 | boundary_kernel_source/002:103-143 starts from an operational seed already
000026 | containing the local net,time,reflection and state. It constructs boundary data
000027 | from that seed. It does not prove an inverse source construction. RP and
000028 | clustering in that definition do not state faithfulness of the global state.
000029 | 
000030 | qft_source/005:144-160 defines Schwinger derivatives of an introduced Z_rel.
000031 | qft_source/007:115-145 uses the ACTUAL field Hessian
000032 |   G_(k,phi)=(S_adm^(2)[phi]+R_k)^(-1)
000033 | and retains all higher derivatives as interaction vertices. Therefore a geometric
000034 | D_+ is not automatically the physical odd field Hessian or its inverse covariance.
000035 | 
000036 | First target: identify the original odd fields,local source map and action so
000037 | that K_phi=delta^2 S_adm/(delta barpsi delta psi) is a proved equality on their
000038 | actual domain. For an actually free complex action, the corresponding source law
000039 | would be
000040 |   (K_phi partial^L_bar_eta - eta) Z_phi=0,
000041 | with the adjoint law, normalization and original boundary/reflection data.
000042 | For interacting actions retain the derivative operators of the ACTUAL vertices.
000043 | The SD hierarchy alone can admit multiple solutions; the selected integration
000044 | law,positivity,boundary/state conditions and an appropriate existence/uniqueness
000045 | or observational-equivalence theorem must also be supplied.
000046 | 
000047 | This is the fermionic construction route. A direct original neutral local OS
000048 | source identity remains a valid alternative; neutral response does not require
000049 | every charged spinor as an observable or a full local E8 extension.
000050 | These are targets, not extra assumed physical axioms. Inner fluctuations,
000051 | canonical CAR quantization and BV BFV supply strong follow-on constructions
000052 | once their represented field/action data are present. They do not automatically
000053 | create the missing physical field identification from a bosonic spectral trace.
000054 | 
000055 | 3. Actual independent candidate generation and the first decisive test
000056 | 
000057 | [OMITTED: non-scientific conversation or execution metadata]
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000062 | 
000063 | The actual full Fock source has energies which are sums of n+alpha and
000064 | n+1-alpha, n>=0, alpha=1/4 or3/4. The empty state has energy0 and the least
000065 | positive spectral point is gap=1/4. This is the existing full-source result,
000066 | not a claim inferred from a finite cutoff.
000067 | 
000068 | If V_t U(s) V_t^*=U(exp(-2pi t)s) for ALL s, with U(s)=exp(isH), strong
000069 | continuity and Stone uniqueness imply
000070 |   V_t H V_t^*=exp(-2pi t) H.
000071 | Choose t=log2/(2pi), so the right side is H/2. Unitary conjugation preserves
000072 | the spectrum and its least positive point. H/2 instead has least positive
000073 | point1/8. Equivalently, the required scale invariance would put gap/2 into a
000074 | spectrum whose least positive point is gap. This is impossible.
000075 | 
000076 | GapObstruction.lean proves that elementary spectral-set implication via the
000077 | automated tactic grind. Its kernel audit lists only propext,Classical.choice,
000078 | Quot.sound. No sorry or new axiom is used. Stone,spectral theory and the original
000079 | P1 source are NOT formalized by that small Lean file; their connections are
000080 | the written mathematical argument above and the existing source spectrum.
000081 | 
000082 | This excludes the SAME gapped H as the nontrivial Borchers translation P.
000083 | It does not exclude a different gapless parabolic generator,proper local
000084 | standard inclusions or HSMI constructions generally. In the alternative
000085 | K=H/8 source convention the minimum is1/32, with the same obstruction.
000086 | Single parameter values or discrete quarter periods do not prove an all-parameter
000087 | group law. The old v438/SeamStandardPair route remains conditional on its
000088 | actual continuum standard pair; its finite ladder is not identified with H.
000089 | 
000090 | 4. Other candidate checks and older results reused
000091 | 
000092 | [OMITTED: non-scientific conversation or execution metadata]
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000101 | 
000102 | The source audit of v259 confirms an ALREADY ANNOTATED gap: it sets f=exp(-u)
000103 | and correctly computes its moments. Its decisive modular-to-cutoff identification
000104 | is registered by check(...,True). KMS normalization for its own modular flow
000105 | does not by itself identify that generator with a spectral cutoff operator.
000106 | Both exp(-u) and exp(-2u) are mathematical positive Laplace profiles; their
000107 | integral/f(0) ratios1 and1/2 only illustrate the extra profile dependence.
000108 | We do not assert two complete P1 models satisfying every original condition.
000109 | The exact conditional moments and the original ledger remain unchanged.
000110 | The existing graph dossier PS.SPECACT.02 already flags this missing derivation;
000111 | this is manual confirmation, not a newly discovered independent theorem.
000112 | 
000113 | [OMITTED: non-scientific conversation or execution metadata]
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000123 | 
000124 | 5. What a complete discovery search has to do
000125 | 
000126 | The generator may propose field maps,source actions,identities or proof lemmas.
000127 | Every proposed arrow is checked at its first consequential identification.
000128 | The source identity must be derived from original inputs. Candidate moments,
000129 | Wick values,chosen states or a target coupling cannot certify its provenance.
000130 | A completed original-source certificate needs the actual local field/action
000131 | map,normalized joint functional,admissible restriction,charges/P2,phases and
000132 | eight-arc support with actual time/reflection; continuum claims need their own
000133 | uniform/analytic proof. A full TFPT claim additionally needs the same common
000134 | parent satisfying T1-T8. A finite response fit does not supply these statements.
000135 | 
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