A registered result in its source context
Original ledger classification: Identity [E] (non-circular setup + reduction) + premise [O] (bounded sub-principal residual)
Recorded statement: ATTACKING omega o rho = omega DIRECTLY ON THE RAW SEAM (work package A, external-review priority 1, 2026-06-14): a further localising reduction, not a closure. (1) SETUP NON-CIRCULAR [E]: rho is the carrier clock = the Coxeter element of…
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
QGEO.STATE.01
Original ledger classification: Identity [E] (non-circular setup + reduction) + premise [O] (bounded sub-principal residual)
Original claim text
ATTACKING omega o rho = omega DIRECTLY ON THE RAW SEAM (work package A, external-review priority 1, 2026-06-14): a further localising reduction, not a closure. (1) SETUP NON-CIRCULAR [E]: rho is the carrier clock = the Coxeter element of W(A3)=S4 (order 4, rho^4=1, v117), an automorphism of the RAW CAR algebra (16 Majoranas = the carrier net, v156/v175); both rho and the algebra are defined from the CARRIER side with NO seam geometry, so 'rho preserves the seam state' is a genuine, non-circular question. (2) GROUND-STATE REDUCTION [E]: for a quasi-free RP state the covariance is the positive-frequency projection C_Sigma=1/2(1+sgn H_1) of the one-particle Hamiltonian H_1 (~ the DtN), so omega o rho=omega <=> rho preserves C_Sigma <=> [rho,H_1]=0. (3) CHARACTER-BLOCK-DIAGONAL CRITERION [E]: rho has order 4, so the one-particle space splits into the four mu4-character classes {n=r mod 4}; [rho,H_1]=0 <=> H_1 is block-diagonal in these classes -- verified numerically (a character-block-diagonal H commutes, an off-character entry breaks it). (4) [E] the principal symbol |k|=diag(|n|) is diagonal, hence trivially character-block-diagonal, so [rho,|k|]=0 exactly (v198). (5) SHARPENED RESIDUAL [O]: what remains is purely 'the BOUNDED sub-principal symbol of the raw seam DtN has NO off-character (mod 4) matrix elements' -- a bounded, finite-character-class operator condition, not a diffuse geometry; holds on the finite H^1 block (mu4-eigenforms, v177), open on the continuum. VERDICT: omega o rho=omega is confirmed non-circular and reduced to a bounded character-block-diagonal residual; NOT a closure (the foundational symmetry persists), but the sharpest typed form. Python-only
Original classification detail
Identity/premise [E]/[O]: omega o rho=omega is non-circular (rho a carrier automorphism, raw CAR algebra) and reduces to [rho,H_1]=0 <=> H_1 is mu4-character-block-diagonal; residual = the bounded sub-principal symbol has no off-character matrix elements; not a closure
Dependencies as recorded
QGEO.MODULAR.01; QGEO.SYM.01; QGEO.DTN.01; v198_modular_commutator_reduction.py; v177_seam_marking_kernel.py
Open the original ledger source, row 272Location 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.
- Research contracts
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.
- 2026-06-14 (work packages A+B: attacking [formula in source] + the variational scan — v199, v200)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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.
- 2026-06-15 (QGEO: the bedrock recast as a falsifiable kill-test)Research changelog; TFPT — Introduction and reading guide
- 2026-06-15 (bedrock: the [formula in source] residual reduced once more — v201)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- 2026-06-24 (The five TOE/QFT closure contracts v398– v402 + a ledger rescope)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- 2026-06-15 (archive integration \#5: six dormant results revived from the old papers)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- 2026-06-25 (The (LTO-RP) reduction of the keystone SEAM.EQUIV.01: v424)Research changelog; TFPT — Introduction and reading guide
All 9 linked sections
Registered verification modules
- v199_seam_state_invariance.pyRegistered verification module · registry
Read the description recorded in the module registry
QGEO.STATE.01 (work package A) — attacking ω∘ρ=ω directly on the raw seam: a further localising reduction, not a closure. [E] setup non-circular (ρ = Coxeter of W(A3)=S4, ρ⁴=1, an automorphism of the raw CAR algebra; both carrier-side, no seam geometry); [E] ground-state reduction ω∘ρ=ω ⟺ [ρ,H₁]=0 (C_Σ=½(1+sgn H₁)); [E] character criterion: [ρ,H₁]=0 ⟺ H₁ block-diagonal in the four μ4-character classes {n=r mod 4} (block-diag commutes, off-character breaks it); principal symbol |k|=diag(|n|) passes automatically. [O] residual: the bounded sub-principal symbol has NO off-character matrix elements — non-circular, sharply typed, holds on H¹ (v177); not a closure.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.