Skip to main content

A registered result in its source context

Original ledger classification: Identity/Lattice [I]/[L] (exact cohomology action + parity match) + [P] (module identification)

Recorded statement: MOEBIUS D4 REALISATION (R5 at its floor): the FULL dihedral symmetry group of the seam curve <delta: z->iz, iota: z->1/z> = D4 (order 8) acts on H^1(P^1 minus mu4) EXACTLY as the integer model <G, T_A, Sigma>: (1) delta* omega_k = i^k…

Statement, assumptions and sources

Paper context: Standard Model and flavor structure

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

FLAV.QGEO.07

Original ledger classification: Identity/Lattice [I]/[L] (exact cohomology action + parity match) + [P] (module identification)

Original claim text

MOEBIUS D4 REALISATION (R5 at its floor): the FULL dihedral symmetry group of the seam curve <delta: z->iz, iota: z->1/z> = D4 (order 8) acts on H^1(P^1 minus mu4) EXACTLY as the integer model <G, T_A, Sigma>: (1) delta* omega_k = i^k omega_k (v137); (2) iota* swaps omega_1 <-> omega_3 and FIXES omega_2 with +1, det -1, no extra phases - the exponent duality with parity; (3) dihedral relations exact; (4) in the cusp basis T_A IS the iota permutation (fixes the character-2 line with +1, det -1 = glue-swap parity) and Sigma IS the (delta iota) class (-1 on the character-2 line, det +1 = glue-fix parity) - the v98 reflection-class split lands exactly on the geometric classes. STATUS: with spectra (v137), cyclic part (v141) and now the full dihedral action matched, the GATE.QGEO premise reduces to the module identification itself ('generation space = H^1 with its parabolic weights') - no remaining checkable mismatch

Original classification detail

Identity [I]: Moebius D4 = integer D4, parity by parity; premise at its floor

Dependencies as recorded

FLAV.QGEO.06; FLAV.QGEO.05; FLAV.QGEO.04; v97; v98; v137; v141

Open the original ledger source, row 231

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

  • v146_moebius_d4.pyRegistered verification module · registry
    Read the description recorded in the module registry

    Möbius-D4 realisation (R5 floor): ⟨z↦iz, z↦1/z⟩ = D4 acts on H¹(P¹∖μ₄) EXACTLY as the integer model ⟨G,T_A,Σ⟩ — ι swaps χ₁↔χ₃ with +1 on χ₂ (det −1) = T_A; δι = Σ; parities and reflection classes match — the premise reduces to the module identification itself

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