Skip to main content

A registered result in its source context

Original ledger classification: Lattice [E] (parity census double-determined + exact 16-fold-way arithmetic + TEE fence) + [C] (KLM condensation step cited) + [O] (continuum; SEAM.EQUIV.01 unchanged)

Recorded statement: THE SPIN-STRUCTURE PARITY CENSUS: mu_pre = 4 WITNESSED ON THE LATTICE (2026-07-20; ground-state witness round, companion of SEAM.CCC.01/v489): the T^2 ground-state fermion parity of the v367 p+ip seam lattice model, resolved per spin…

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

SEAM.MU.01

Original ledger classification: Lattice [E] (parity census double-determined + exact 16-fold-way arithmetic + TEE fence) + [C] (KLM condensation step cited) + [O] (continuum; SEAM.EQUIV.01 unchanged)

Original claim text

THE SPIN-STRUCTURE PARITY CENSUS: mu_pre = 4 WITNESSED ON THE LATTICE (2026-07-20; ground-state witness round, companion of SEAM.CCC.01/v489): the T^2 ground-state fermion parity of the v367 p+ip seam lattice model, resolved per spin structure (boundary-condition sector AA, AP, PA, PP) and determined TWICE -- (a) the Read-Green TRIM product parity(s) = prod_{k* in TRIM(s)} sign(dz(k*)) and (b) the real-space Majorana Pfaffian sign via Schur decomposition (parities relative to the trivial M=3 phase so the Pf convention drops out). The number of even sectors = the gauged (fermion-parity-gauged) torus GSD = the total quantum dimension mu of the gauged theory. [E] REAL-SPACE = BLOCH SANITY: the twisted real-space BdG spectrum equals the Bloch bands per sector to 9e-15. [E] PER-LAYER CENSUS: (AA, AP, PA, PP) = (+,+,+,-), TRIM product == Pfaffian in every sector -- 3 even sectors, the nu = 1 Ising signature (gauged #anyons = 3). [E] 16 LAYERS => mu_pre = 4: parity_16(s) = parity_1(s)^16 = + in ALL FOUR sectors => gauged torus GSD = 4 = mu(SO(16)_1) = |det Cartan(D8)| -- the lattice ground-state witness that the carrier sits in the SO(16)_1 class BEFORE the mu4 condensation (v378 step 1). [E] 16-FOLD-WAY BRIDGE: Kitaev's theta_v = exp(2 pi i nu/16) with the MEASURED nu = 2 c_- = 16 (v489) gives theta_v = 1 EXACTLY (sympy) -- the gauged vortex is a boson, condensable; rivals nu = 1, 2, 8 give theta_v != 1 (not holomorphically condensable). [E] NON-DISCRIMINATOR FENCE (honest): the fermionic Kitaev-Preskill TEE is identically zero -- gamma_f = 0.000001 (M=1, topological) AND 0.000000 (M=3, trivial) -- an invertible fermionic phase has no TEE, so gamma_f does NOT discriminate (E8)_1 vs SO(16)_1 (both exist only after gauging); computed and recorded so it is never mistaken for a discriminator. [C] THE KLM CONDENSATION STEP stays cited: mu_post = mu_pre/|L|^2 = 4/2^2 = 1 (holomorphic, (E8)_1; v378/KLM CMP 219 (2001)); the condensed model is interacting, NOT free-fermion computable -- the numerics pin only the premise package {c_- = 8 (v489), mu_pre = 4, theta_v = 1}. [O] the continuum scaling limit (MMST, v336) stays [O]; SEAM.EQUIV.01 is NOT closed. No gate closes, no marker moves.

Original classification detail

Lattice witness [E]/[C]/[O]: parity census (+,+,+,-) per layer, all-even for 16 layers => gauged torus GSD = 4 = mu(SO(16)_1) = mu_pre; theta_v = 1 exactly at nu = 2 c_- = 16 (rivals excluded); TEE fence gamma_f = 0 for both phases (no discriminator); KLM 4 -> 1 stays [C]; SEAM.EQUIV.01 stays [O]

Dependencies as recorded

SEAM.EQUIV.01; SEAM.CCC.01; SEAM.S3.LATTICE.01; SEAM.S3.MODULAR.01; v336; v351; v367; v378; v489

Open the original ledger source, row 552

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

  • v490_seam_parity_census.pyRegistered verification module · core
    Read the description recorded in the module registry

    SEAM.MU.01: the T^2 spin-structure fermion-parity census for the v367 seam lattice model -- the lattice ground-state witness of 'mu_pre = 4 before condensation' (step 1 of the v378 KLM chain) + the 16-fold-way bridge theta_v = 1 with the measured nu = 2 c_- = 16 (v489). Parity per sector (AA, AP, PA, PP) determined twice: Read-Green TRIM product AND real-space Majorana Pfaffian (Schur), relative to the trivial phase. [E] sanity: twisted real-space spectra == Bloch bands to 9e-15. [E] per-layer census (+,+,+,-), TRIM == Pfaffian in every sector (3 even sectors = Ising nu = 1). [E] 16 layers: parity^16 = + in ALL 4 sectors => gauged torus GSD = 4 = mu(SO(16)_1) = |det Cartan(D8)|. [E] theta_v = exp(2 pi i nu/16) = 1 exactly at nu = 16; rivals nu = 1, 2, 8 excluded. [E] fence: fermionic Kitaev-Preskill TEE = 0 for BOTH M=1 and M=3 -- does NOT discriminate (E8)_1 vs SO(16)_1. [C] KLM step 4 -> 4/2^2 = 1 cited (interacting, not free-fermion computable); numerics pin only {c_- = 8, mu_pre = 4, theta_v = 1}. [O] continuum limit (MMST v336); SEAM.EQUIV.01 stays [O]. Python (numpy + scipy + sympy).

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