A registered result in its source context
Original ledger classification: Identity [E] (EG one-loop b_i, exact) + [C] (RG directions) + [O] (all-order)
Recorded statement: EG ONE-LOOP GAUGE SELF-ENERGY -> (b1,b2,b3) = (41/10,-19/6,-7) (2026-06-18): takes v271's quartic mechanism to the gauge sector. [E] the one-loop gauge 2-point function is the order-2 EG product of two currents, scaling degree sd=4=d so…
Statement, assumptions and sources
Paper context: tfpt research contracts
The exact identifier, original classification and full claim are available below.
The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.
Read the exact registered claim and its dependencies
QFT4D.SPERT.03
Original ledger classification: Identity [E] (EG one-loop b_i, exact) + [C] (RG directions) + [O] (all-order)
Original claim text
EG ONE-LOOP GAUGE SELF-ENERGY -> (b1,b2,b3) = (41/10,-19/6,-7) (2026-06-18): takes v271's quartic mechanism to the gauge sector. [E] the one-loop gauge 2-point function is the order-2 EG product of two currents, scaling degree sd=4=d so omega=sd-d=0 -> exactly one local counterterm per gauge coupling (wavefunction/coupling renormalization), the SAME marginal mechanism and loop factor 1/(16 pi^2) as the quartic. [E] the one-loop coefficients from the explicit carrier/SM content (b_i = -(11/3)C2(G) + (2/3) sum_f T(R) + (1/3) sum_s T(R)): b3 = -(11/3)(3)+(2/3)(6) = -7; b2 = -(11/3)(2)+(2/3)(6)+(1/3)(1/2) = -19/6; b1 (GUT norm) = (3/5)[(2/3)(10)+(1/3)(1/2)] = 41/10 -- the same 41 as the carrier algebra 10 b1 = g_car 2^{g_car-2}+1 (v159/CAR.SM.01). [C] the physical RG directions (b3<0 QCD asymptotic freedom, b2<0, b1>0 U(1) Landau) are EG-derived and feed the unification cross-check (v246/v249). [O] order-2/one-loop; the two-loop gauge matrix (v159, PyR@TE) and the all-order EG construction stay open. Exact b_i mirrored in Wolfram.
Original classification detail
[E] the EG gauge self-energy scaling-degree mechanism + the exact one-loop b_i=(41/10,-19/6,-7) from the content (Wolfram-mirrored); [C] the physical RG directions; [O] two-loop + all-order. The gauge analogue of v271's quartic.
Dependencies as recorded
QFT4D.SPERT.02; QFT4D.SPERT.01; EM.BUDGET.02; CAR.SM.01
Open the original ledger source, row 366Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- Research contracts
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- 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
- Research Contract 1 — [formula in source]tfpt research contracts
- 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 (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
- v273_eg_gauge_running.pyRegistered verification module · registry
Read the description recorded in the module registry
QFT4D.SPERT.03 — the gauge sector of the EG one-loop (v271's quartic mechanism applied to the gauge self-energy). [E] the one-loop gauge 2-point has scaling degree sd=4=d so ω=0 → one counterterm per coupling (same marginal mechanism + loop factor 1/(16π²) as v271); [E] the one-loop b_i from the explicit carrier/SM content: b₃=-(11/3)(3)+(2/3)(6)=-7, b₂=-(11/3)(2)+(2/3)(6)+(1/3)(1/2)=-19/6, b₁=(3/5)[(2/3)(10)+(1/3)(1/2)]=41/10 (the same 41 as the carrier algebra, v159/CAR.SM.01); [C] physical RG directions b₃<0 (asymptotic freedom), b₁>0 (U(1) Landau); [O] the two-loop matrix (v159 PyR@TE) + all-order stay open. Shows the gauge running is an EG order-2 result, the gauge analogue of v271's quartic. Exact b_i mirrored in Wolfram.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.