Skip to main content

A registered result in its source context

Original ledger classification: Numerical (NCG inner fluctuations) [E]/[C]

Recorded statement: INNER FLUCTUATIONS Omega^1_D -> SM HIGGS DOUBLET (no 126, no junk) + sigma (2026-06-17): closes the open obligation v250 #5 (Higgs content, NOT 126), the NO-JUNK obligation, and fixes the sigma quantum numbers (v250 #4 rep-theory half).…

Statement, assumptions and sources

Paper context: 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

PS.NCG.FLUCT.01

Original ledger classification: Numerical (NCG inner fluctuations) [E]/[C]

Original claim text

INNER FLUCTUATIONS Omega^1_D -> SM HIGGS DOUBLET (no 126, no junk) + sigma (2026-06-17): closes the open obligation v250 #5 (Higgs content, NOT 126), the NO-JUNK obligation, and fixes the sigma quantum numbers (v250 #4 rep-theory half). Inner fluctuation D -> D + A + eps' J A J^-1 with A = sum pi(a)[D_F,pi(b)] in Omega^1_D = span{pi(a)[D_F,pi(b)]}. Because D_F is purely chirality-odd (Yukawa L<->R + Majorana), every 1-form is odd, so the FINITE fluctuations are SCALARS (gauge bosons come from the continuum [D_M,a]). (1) [E] Omega^1_{D_F} purely chirality-odd, gauge part 0. (2) [E] NO JUNK / NO 126: for the SM algebra C(+)H(+)M_3 every 1-form has support exactly inside the Higgs-doublet pattern (chirality-odd, colour-diagonal, no quark<->lepton mixing) = the single SM Higgs doublet (1,2)_{1/2}; no colour/weak triplet, no (10,1,3)/126-type scalar (0 junk entries, machine-checked). (3) [E] sigma NEEDS BEYOND FIRST ORDER: with the SM algebra the sigma (nu_R nu_R^c Majorana) direction is NOT generated by Omega^1_D (consistent with first order HOLDING, v252) but with the Pati-Salam algebra it IS generated -- sigma is precisely the Chamseddine-Connes-van Suijlekom beyond-first-order scalar (v251/v252). (4) [E] sigma quantum numbers: SM singlet (1,1,0) with B-L=2 (nu_R has B-L=-1, so sigma*(nu_R nu_R) is gauge invariant only for B-L(sigma)=+2), giving the nu_R Majorana mass and breaking B-L (the PS (4,1,2)->SM step). (5) [C] sigma=scalaron: sigma is a real SM-singlet scalar at the B-L/PS scale, consistent in quantum numbers and scale with the R+R^2 scalaron (M_PS=kappa M_s, v249/v253); the gravitational coupling proper remains [C]/[O].

Original classification detail

[E] finite fluctuations = SM Higgs doublet (no junk/no 126) + sigma beyond first order + sigma B-L=2 singlet; [C] sigma=scalaron; closes v250 #5 + no-junk obligation + sigma QN

Dependencies as recorded

PS.DIRAC.02; PS.DIRAC.01

Open the original ledger source, row 340

Location 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.

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.

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.

Registered verification modules

  • v254_inner_fluctuations.pyRegistered verification module · registry
    Read the description recorded in the module registry

    PS.NCG.FLUCT.01 — the inner fluctuations Ω¹_D(A_F) of the finite Dirac operator computed explicitly (reuses the v252 triple); closes v250 #5 (Higgs content, not 126) + the no-junk obligation + the σ quantum numbers. [E] Ω¹_{D_F} purely chirality-odd → finite fluctuations are scalars; [E] no junk / no 126: SM-algebra 1-forms sit exactly in the Higgs-doublet pattern (the single (1,2)_{1/2}); [E] σ (ν_R Majorana) direction absent for the SM algebra but present for Pati-Salam — σ is the CCvS beyond-first-order scalar; [E] σ is an SM singlet (1,1,0) with B-L=2; [C] σ=scalaron consistency.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries