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Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Established in scope

Time-stable constant product channels carry current level only in their kernel

In the question: Common clock sectors, quartic geometry and operational reconstruction

Complete narrow classification for constant Phi and constant local reducers, not all P1 sources, variable normal profiles or momentum-dependent/dressed images. Normal elliptic D_N and finite Yukawa D_F remain different operators. The old spin product pushforward and horizontal connection remain conditional, not selected from P1. Reflection lift S tensor gamma_F is tested only at symbol level, not domain/reference/RP. Actual v252 integer controls are not physical Yukawa values. Source correction and independent reviews precede persistence; normal and -OO identical. No T1-T8 closure.

Read the exact result, assumptions and evidence

Result

All constant reducing orthoprojections of B_Phi=Gamma A-S tensorPhi are E=diag(E_R,E_L) satisfying E_R Phi=Phi E_L and E_L Phi=Phi E_R. On ker(Phi²-mu²),mu>0,E_L=(Phi/mu)E_R(Phi/mu); on kerPhi the projections are independent. On the actual full two-face Cauchy graph,N_face=diag(-Jn signPhi,Jn signPhi) and the old HS Lagrange lemma prove massive cocycle cancellation. Hence kappa=rankE_R^0-rankE_L^0. A bare right channel reduces iff Phi E=0; total grading Gamma tensor gamma_F still reduces. Its full finite v252 channel has netlevel0 even for singular Phi by48/48 and oddness. Explicitly reuse the old normal spin index source: its already reducing finite kernel has level equal to index. Its L2 case r+=1,r-=0 also preserves the same circle time. The full E2 twist r+=k,r-=k-1 has netlevel1 but no single right time Ward for k>1. Equal index level therefore does not yield an all-word/time intertwiner.

Required assumptions

  • Do not identify source types

    Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.

  • Complete data of both product-collar faces

    A selfadjoint B occurs in an exact normal-independent product equation. The full orthogonal L2 Cauchy graph projection of both labeled faces, their actual fiber identification and independently known positive normal length ell are supplied. Selection of these data from P1/P2 is not presumed.

  • Given charged CAR quantization of the full two-face Cauchy graph

    As in section4 of the original collar proof, additionally assume charged CAR(H direct_sum H) and the pure gauge-invariant quasifree state with occupation G_ell. The second labeled face has n=(1+exp(2ell B))^-1. This is a field/statistics premise, not a consequence of P1; reduction does not select or physically execute a one-face operation. The long-collar limit is used only within this declared operator/CAR class.

  • Constant Dirac product with mixed current generators

    Assume the existing normal-independent two-component collar A=-i partial_theta+alpha, alpha=1/4 or3/4, Gamma=diag(1,-1), Jn=[[0,-1],[1,0]], S=Jn Gamma. In the supplied complete complex CAR system consider smooth one-face quadratic generators fI,fGamma,fP_R under actual HS/implementability conditions. For the product test Phi is a constant finite self-adjoint coefficient with B_Phi=Gamma A-S tensorPhi on the same H1 domain. A is internally scalar. Reducing projections are constant and reduce every Fourier momentum. For v252 also retain actual gamma_F and {Phi,gamma_F}=0. No physical P1 selection, separate chiral determinant, new vacuum or identification of tangential time with original OS Hamiltonian is presumed.

  • Given finite SM representation with symbolic Yukawa inputs

    Use only the existing v252/v254 representation with C⊕H⊕M3, already supplied color/weak modules and four symbolic complex3×3 Yukawa blocks. No physical values are chosen or fitted. Classify the particle LR one-form block; no proof of the full real96-dimensional fluctuation with antiparticles, JAJ and Majorana sector is claimed.

  • Given normal spin line and genuine circle product operator

    Assume oriented spin S2,L2=det E2=O(1),normal twisted spin operator D_N with grading gamma_N and actual selfadjoint product B_prod=B_a tensor gamma_N+I tensor D_N on H1 product spinors,B_a=-i partial_theta+a,0<a<1. Normal metric,connection and horizontal product rule are given;no derivation from the original bosonic Callias operator or P1 is asserted.

Original evidence

  • PROOF.txt lines 1–200

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    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/PROOF.txt

    637007e39986ac8f2ec07a6c2ce96f0d5686171583b226699ea9dfe9ca3bb4fc

  • PROOF.txt lines 201–255

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/PROOF.txt

    637007e39986ac8f2ec07a6c2ce96f0d5686171583b226699ea9dfe9ca3bb4fc

  • check_original_insertions.py lines 1–191

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/check_original_insertions.py

    ed2a7cd49a68528ea68f92c2cbf039d1e6980b563d1d8915aea7acdc76123cde

  • results.json lines 1–75

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/results.json

    aa268cad36cde7493cfb6c658ecdaa2dd5eebaa1220fabd3ea58f46fa4c625b8

  • REVIEW.txt lines 1–40

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    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/REVIEW.txt

    f0b4691202ac083431414734a7caef5c7892a7d6744951a1bcb9ee4b1220384e

  • ERGEBNIS-EINFACH.txt lines 1–58

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/original_insertions/ERGEBNIS-EINFACH.txt

    b4d0482b9d5347f58b1a5479f9aea86cb52a8bf8bac9477fc9fa043feb1bcd3e

  • DIRAC-LIFT-ADMISSIBILITY.md lines 1–82

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    experiments/theory-contracts/collar-current-source-bridge-20261021/DIRAC-LIFT-ADMISSIBILITY.md

    dc50b3805ba93a1a4e19890ea0accb04e66cebe192ce526e405cb362a6cdda6a

  • HIGGS_VARIATION_PROOF.txt lines 135–182

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    Original location and fingerprint

    experiments/theory-contracts/seam-joint-source-origin-audit-20261016/HIGGS_VARIATION_PROOF.txt

    84004fc583641a52096c8571844aaed825d16d8165635eafd1a6b2562708e6be

  • NORMAL-INDEX-TRANSPORT.txt lines 1–129

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    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/NORMAL-INDEX-TRANSPORT.txt

    f66b65fb9e23a2fe97c95ad924bd6ee39ea9c182111031392010cf4507620099

  • NORMAL-CONNECTION-MARKS-COVER.txt lines 18–69

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    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/NORMAL-CONNECTION-MARKS-COVER.txt

    33448654daa781525df039173b862274036f8ef2c267865afec6555c12b4c9de

  • v252_full_finite_triple.py lines 86–168

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    Original location and fingerprint

    verification/v252_full_finite_triple.py

    820254440e178430422e50605067775656236602996307f67c9e69124ba5d163

finding:constant-product-time-stable-current-level-is-kernel-index