A registered result in its source context
Original ledger classification: Numerical/Identity [E] (one-loop EG core) + [C] (beta + IC) + [O] (all-order)
Recorded statement: CONCRETE EPSTEIN-GLASER ONE-LOOP QUARTIC RENORMALIZATION (2026-06-18): takes the v269 S_pert pAQFT skeleton from 'exists' to an actual EG number (no path integral). [E] T_1=:L_int: needs no extension; the first EG renormalization is the…
Statement, assumptions and sources
Paper context: tfpt research contracts
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QFT4D.SPERT.02
Original ledger classification: Numerical/Identity [E] (one-loop EG core) + [C] (beta + IC) + [O] (all-order)
Original claim text
CONCRETE EPSTEIN-GLASER ONE-LOOP QUARTIC RENORMALIZATION (2026-06-18): takes the v269 S_pert pAQFT skeleton from 'exists' to an actual EG number (no path integral). [E] T_1=:L_int: needs no extension; the first EG renormalization is the order-2 product T_2. [E] the massless Feynman propagator has Steinmann scaling degree sd=2 in d=4; the one-loop bubble (two propagators) has sd=4=d, so the UV singular order omega=sd-d=0. [E] omega=0 => the EG extension freedom is C(omega+d,d)=1 local constant -- EXACTLY one logarithmic counterterm (renormalizable, finite, no infinite tower; matches v269). [E] the loop factor Omega_3/(2(2pi)^4)=(2pi^2)/(2(2pi)^4)=1/(16 pi^2) exactly -- the same 1/(16 pi^2) that normalises the spectral-action a_4 geometric quartic. [C] the phi^4 one-loop beta_lambda = 3 lambda^2/(16 pi^2) (symmetry factor 3 = s,t,u channels), EG initial condition lambda_Phi(UV)=1/(16 pi^2). [O] order-2/one-loop, one diagram class; all-order EG + nonperturbative measure QG.AMB.01 stay open. Exact core mirrored in Wolfram.
Original classification detail
[E] order structure + scaling degree (sd=4=d) + one log counterterm (omega=0) + loop factor 1/(16 pi^2) (exact, Wolfram-mirrored); [C] the phi^4 one-loop beta + the spectral-action initial condition; [O] order-2/one-loop only, all-order + nonperturbative stay open. Turns the v269 skeleton into a concrete one-loop number.
Dependencies as recorded
QFT4D.SPERT.01; CONTRACT.QFT4D.01; PS.SPECACT.01; HIGGS.FREESEAM.01
Open the original ledger source, row 364Location 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
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-06-18 (4D QFT: a concrete Epstein–Glaser one-loop quartic renormalization, v271)Research changelog; TFPT — Introduction and reading guide
- 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 (Zenodo release 5.2 (rev 191) — the perturbative 4D-QFT layer + scale closure, v269–v275)Research changelog; TFPT — Introduction and reading guide
- Target F — the perturbative 4D-QFT [formula in source] scale round (v269–v275)Red-team audit
- Full quantum gravity — induced from the boundary kernelFrontier and open physical interfaces
Registered verification modules
- v271_eg_oneloop_quartic.pyRegistered verification module · registry
Read the description recorded in the module registry
QFT4D.SPERT.02 — a concrete Epstein-Glaser order-2 (one-loop) quartic renormalization, taking the v269 S_pert skeleton from 'exists' to an actual EG number (no path integral). [E] T_1=:L_int: needs no extension, the first extension is T_2; [E] the massless propagator has scaling degree sd=2 in d=4, the one-loop bubble (two propagators) has sd=4=d so the UV singular order omega=sd-d=0; [E] omega=0 => exactly one logarithmic local counterterm (C(omega+d,d)=1, renormalizable, no infinite tower); [E] the loop factor Omega_3/(2(2pi)^4)=1/(16 pi^2) exactly — the same factor that normalises the spectral-action a_4 geometric quartic; [C] the phi^4 one-loop beta = 3 lambda^2/(16 pi^2) (symmetry factor 3 = s,t,u channels), EG initial condition lambda_Phi(UV)=1/(16 pi^2); [O] order-2/one-loop only — the all-order EG construction and the nonperturbative measure QG.AMB.01 stay open. Turns the skeleton into a concrete one-loop number.
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