Skip to main content

A registered result in its source context

Original ledger classification: Numerical (exact rep theory) [E]/[O]

Recorded statement: PATI-SALAM NCG ALGEBRA + EXACT SM MATCHING (2026-06-17): the finite algebra A_F = H_L (+) H_R (+) M_4(C) and its consequences (Reviewer-A Theorem 2). (1) [E] unimodular gauge group SU(2)_L x SU(2)_R x SU(4)_c (ranks 1+1+3=5=rank SO(10),…

Statement, assumptions and sources

Paper context: tfpt anschluss zellen seam 2026-09-14

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.ALGEBRA.01

Original ledger classification: Numerical (exact rep theory) [E]/[O]

Original claim text

PATI-SALAM NCG ALGEBRA + EXACT SM MATCHING (2026-06-17): the finite algebra A_F = H_L (+) H_R (+) M_4(C) and its consequences (Reviewer-A Theorem 2). (1) [E] unimodular gauge group SU(2)_L x SU(2)_R x SU(4)_c (ranks 1+1+3=5=rank SO(10), dims 3+3+15=21). (2) [E] one generation 16 = (4,2,1)+(4bar,1,2) = 8+8. (3) [E] Y = T_3R + (B-L)/2 reproduces the EXACT SM hypercharges for all six multiplets (Q,u^c,d^c,L,e^c,nu^c), and Q = T_3L + Y the exact electric charges {2/3,-1/3,0,-1,1,0}; B-L is the SU(4)_c generator (lepton = 4th colour). (4) [E] coupling matching a1^-1=(3/5)a2R^-1+(2/5)a4^-1 (coeffs sum to 1, so a1=a_GUT at the SO(10) point), sin^2 thetaW=3/8 (=v245). (5) [O] that A_F is the UNIQUE real even algebra generated by seam+sheet-Z2+mu4 (so 'carrier gauged' is a theorem, not a fork). (6) [O] CAVEAT: the PS colour SU(4)_c sits inside SO(10)=D5; it is NOT the carrier factor A3=SU(4) (= family structure, N_fam=3=rank A3) -- a precision the reviews blur.

Original classification detail

[E] A_F -> SU(2)xSU(2)xSU(4) PS group, 16=(4,2,1)+(4bar,1,2), exact hypercharges/charges, matching a1^-1=(3/5)a2R^-1+(2/5)a4^-1, sin^2=3/8; [O] seam-reconstruction + the colour/family distinction

Dependencies as recorded

QFT4D.MATTER.01; PS.E8BRANCH.01

Open the original ledger source, row 334

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

  • v248_ps_algebra.pyRegistered verification module · registry
    Read the description recorded in the module registry

    PS.ALGEBRA.01 — the Pati-Salam NCG algebra A_F = ℍ_L⊕ℍ_R⊕M₄(ℂ) and its exact SM matching. [E] unimodular group SU(2)_L×SU(2)_R×SU(4)_c (ranks 5, dims 21); [E] 16=(4,2,1)+(4̄,1,2)=8+8; [E] Y=T₃R+(B−L)/2 gives the exact SM hypercharges and Q=T₃L+Y the exact charges (B−L = SU(4)_c gen, lepton = 4th colour); [E] matching α1⁻¹=(3/5)α2R⁻¹+(2/5)α4⁻¹, sin²θ_W=3/8. [O] A_F uniquely from seam+sheet+μ4 (carrier gauged as theorem); [O] CAVEAT PS colour SU(4)_c ⊂ SO(10)=D5 is NOT the carrier A3=SU(4) (=family).

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