Skip to main content

A registered result in its source context

Original ledger classification: Identity/Lattice [I]/[L] (the extension theorem exact) + [P] (the seam-side identification)

Recorded statement: SIMPLE-CURRENT EXTENSION THEOREM (the central G_net closing theorem, assembled and stated as Definition+Theorem; external review 2026-06-13): the carrier net A = (D5)_1 (x) (A3)_1 extended by the isotropic mu_4 glue line L = <(1,1)> in…

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

GATE.METRIC.11

Original ledger classification: Identity/Lattice [I]/[L] (the extension theorem exact) + [P] (the seam-side identification)

Original claim text

SIMPLE-CURRENT EXTENSION THEOREM (the central G_net closing theorem, assembled and stated as Definition+Theorem; external review 2026-06-13): the carrier net A = (D5)_1 (x) (A3)_1 extended by the isotropic mu_4 glue line L = <(1,1)> in Disc(D5)(+)Disc(A3) = Z4(+)Z4 is the local simple-current extension B = A |x L with (1) Jones index [B:A] = |L| = 4 = |mu4| (L isotropic: q(k(1,1)) = k^2 in Z, v92/v125; KLM/v89) [I]; (2) central charge c(B) = c(D5)_1 + c(A3)_1 = 5+3 = 8, conformal embedding c_coset = 0 [I]; (3) mu-index mu(B) = mu(A)/|L|^2 = 16/16 = 1 by KLM => B HOLOMORPHIC [I]; (4) a holomorphic c=8 chiral net is the unique even-unimodular rank-8 lattice net => B = (E8)_1 (Minkowski-Siegel, v83; SO(16)_1 mu=4 excluded) [I]/[L]; (5) finite realisation in hand: C[Z4] Longo Q-system index 4 (v125), Z4-graded Frobenius E8 hull on all 6720 root-pair sums (v128/v143), Ramond glue sectors (v148). CONSEQUENCE: G_net is internally CLOSED if the seam-Calderon boundary net is DEFINED as A; it stays ONE external identification ('the RP seam-Calderon net is A') if one derives the boundary net from the seam kernel. Either way this is THE single strict-TOE certification theorem still carrying weight - now a clean simple-current extension statement, not 'find a quantum gravity' [2026-08-05 LXII (v779): finite-level evidence for the identification measured -- the inductive system (Haar isometry tower, commuting index-4 expectation squares, geometric state convergence) is exactly coherent, the finite Haag-duality census gives twisted-duality defect 0 with excess ratio dim B'/dim A' = 4 = the local Watatani index, and the C[Z4] quasi-basis obstruction law 2^-l types the extension as exactly asymptotic at finite level; typed finite evidence, never the continuum theorem. No status move.]

Original classification detail

Identity/Lattice [I]/[L]: (D5)1(x)(A3)1|x<(1,1)> = (E8)1; residue = seam-side identification

Dependencies as recorded

GATE.METRIC.10; GATE.METRIC.09; GATE.METRIC.07; GATE.METRIC.06; v89; v92; v125; v143; v148

Open the original ledger source, row 239

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.

All 37 linked sections

Registered verification modules

  • v154_simple_current_theorem.pyRegistered verification module · registry
    Read the description recorded in the module registry

    Simple-Current Extension Theorem (the central G_net theorem): A = (D5)1(x)(A3)1 extended by the isotropic glue L=<(1,1)> has index |L|=4, c=5+3=8, μ(B)=μ(A)/|L|²=16/16=1 ⇒ holomorphic ⇒ B=(E8)1 (unique even-unimodular rank-8); SO(16)1 excluded; finite realisation in hand (v125/v128/v143/v148); residue = the seam-side identification 'seam net = A'

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