A registered result in its source context
Original ledger classification: Contract [C]/[O] (perturbative skeleton)
Recorded statement: PERTURBATIVE 4D S-MATRIX (S_pert) AS AN EPSTEIN-GLASER / pAQFT SKELETON (2026-06-18): the honest middle layer of the three-layer S-matrix -- S_top (2d DHR braiding monodromy |M|=1, statistics, v243), S_pert (4d EG/BV S-matrix of the Connes…
Statement, assumptions and sources
Paper context: tfpt research contracts
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QFT4D.SPERT.01
Original ledger classification: Contract [C]/[O] (perturbative skeleton)
Original claim text
PERTURBATIVE 4D S-MATRIX (S_pert) AS AN EPSTEIN-GLASER / pAQFT SKELETON (2026-06-18): the honest middle layer of the three-layer S-matrix -- S_top (2d DHR braiding monodromy |M|=1, statistics, v243), S_pert (4d EG/BV S-matrix of the Connes spectral action), S_phys (LSZ on the OS-reconstructed admissible Wightman functions, v240). The spectral-action a_4 interaction is power-counting renormalizable (all operators mass dim <= 4) with a finite counterterm basis (7 marginal + 3 relevant), so by the Epstein-Glaser theorem the perturbative S-matrix S(g)=T exp(i int g L_int) exists order by order (causal factorisation + finite local extension; no path integral, no UV divergences). Gapped admissible sector (Delta=6log(3/2)) gives an IR-safe adiabatic limit. PERTURBATIVE only: the nonperturbative ambient measure QG.AMB.01 stays open; the canonical 4D reading is boundary-only (v265).
Original classification detail
[E] three-layer typing + power-counting renormalizable (dim<=4) + finite counterterm basis (7+3); [C] Epstein-Glaser order-by-order existence (cited theorem applied) + adiabatic/gap link to S_phys; [O] perturbative only -- ambient measure QG.AMB.01 stays open. A contract/skeleton, not a nonperturbative closure.
Dependencies as recorded
CONTRACT.QFT4D.01; DHR.SMATRIX.01; DYN.GNS.01; PS.SPECACT.01; QFT4D.FORK.01
Open the original ledger source, row 362Location recorded in the ledger
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- Research contracts
Sections that explicitly cite this claim
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- Research Contract 1 — [formula in source]tfpt research contracts
- 2026-06-18 (4D QFT: the perturbative S-matrix as an Epstein–Glaser / pAQFT skeleton, v269)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- 2026-06-23 (External-review closure: the two genuine residual targets named — v381 the all-order Epstein–Glaser/BRST contract for [formula in source] , and v382 the Quillen determinant-line variation as a tracked target)Research changelog; TFPT — Introduction and reading guide
- 2026-06-18 (scale + frontier round: [formula in source] -mass scale, EG gauge running, over-determination, QG roadmap, v272– v275)Research changelog; TFPT — Introduction and reading guide
- 2026-06-18 (4D QFT: the [formula in source] LSZ bridge [formula in source] one-loop unitarity, v278)Research changelog; TFPT — Introduction and reading guide
- 2026-06-18 (Zenodo release 5.2 (rev 191) — the perturbative 4D-QFT layer + scale closure, v269–v275)Research changelog; TFPT — Introduction and reading guide
- 2026-06-18 (4D QFT: a concrete Epstein–Glaser one-loop quartic renormalization, v271)Research changelog; TFPT — Introduction and reading guide
- 2026-06-18 (Red Team Target F — adversarial audit of the v269–v275 round, rt_F)Research changelog; TFPT — Introduction and reading guide
- Target F — the perturbative 4D-QFT [formula in source] scale round (v269–v275)Red-team audit
All 9 linked sections
Registered verification modules
- v269_spert_paqft_skeleton.pyRegistered verification module · registry
Read the description recorded in the module registry
QFT4D.SPERT.01 — the perturbative 4D S-matrix (S_pert) as an Epstein-Glaser / pAQFT skeleton: the honest middle layer of the three-layer S-matrix (S_top 2d DHR braiding v243 / S_pert 4d EG of the spectral action / S_phys LSZ on OS Wightman v240), NOT a nonperturbative closure. [E] three distinct layers (the 2d braiding |M|=1 is statistics, not 4d cross-sections); [E] every spectral-action a_4 operator has mass dim <= 4 in 4D (power-counting renormalizable); [E] finite counterterm basis (7 marginal + 3 relevant, no infinite tower); [C] Epstein-Glaser existence -- a renormalizable interaction has an order-by-order S(g)=T exp(i int g L_int) by causal factorisation + finite local extension, no path integral, no UV divergences; [C] adiabatic limit/gap (Delta=6log(3/2)>0) -> S_phys via LSZ; [O] perturbative only, the ambient measure QG.AMB.01 stays open. A contract/skeleton, explicitly perturbative.
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