A registered result in its source context
Original ledger classification: Formalised [F] (machine-checked model demonstration)
Recorded statement: STRONG CP AS PFAFFIAN REALITY (theta_eff=0 as a model-level CAR/Pfaffian theorem; formalises the tfpt_2 structural chain): in the self-dual CAR (16-Majorana) seam model, (1) the sheet-odd Calderon involution {D_Sigma, Sigma}=0 forces the…
Statement, assumptions and sources
Paper context: Standard Model and flavor structure
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FLAV.STRONGCP.02
Original ledger classification: Formalised [F] (machine-checked model demonstration)
Original claim text
STRONG CP AS PFAFFIAN REALITY (theta_eff=0 as a model-level CAR/Pfaffian theorem; formalises the tfpt_2 structural chain): in the self-dual CAR (16-Majorana) seam model, (1) the sheet-odd Calderon involution {D_Sigma, Sigma}=0 forces the spectrum into +-lambda pairs [I] (verified: eigenvalues symmetric about 0 to 1e-15); (2) gamma5-Hermiticity D^dag=gamma5 D gamma5 makes conj(det D)=det D, so the fermion-measure Pfaffian is real, arg in {0, pi} [I] (verified: Im(det D)~1e-9); (3) a theta-term gives Z(theta)=e^{i theta}|det D|; reflection positivity (Z>0, OS axiom) excludes theta=pi (Re Z<0) and every theta not in {0,pi} (Im Z != 0), selecting theta_eff=0 [I]. So theta_eff=0 is a topological null theorem -- the antisymmetric Calderon pairing makes the Pfaffian real and RP picks the positive branch; the CAR/Pfaffian form of the polar+gamma5+sheet+RP derivation
Original classification detail
Formalised [F]: theta_eff=0 via Pfaffian reality (sheet pairing + gamma5-Hermiticity + RP positive branch)
Dependencies as recorded
FLAV.QGEO.02; CAR.QFREE.01; GATE.METRIC.13
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- Standard Model and flavor structure
Sections that explicitly cite this claim
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- 2026-06-13 (CFT/QFT bridges: slice compression v170, OS moment v171, trace-anomaly seed v172, Pfaffian CP v173)Research changelog; TFPT — Introduction and reading guide
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- (3) Strong CP — decoupled from the mass-gap problem /tfpt 2 standard model
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- (3) Strong CP — decoupled from the mass-gap problem /Standard Model and flavor structure
Registered verification modules
- v173_pfaffian_cp_car.pyRegistered verification module · registry
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Strong CP as Pfaffian reality: a self-dual CAR (16-Majorana) model demonstration of θ_eff=0 — the sheet-odd Calderón involution {D,Σ}=0 pairs the spectrum (±λ), γ5-Hermiticity (D†=γ5Dγ5) makes the fermion-measure Pfaffian real (arg∈{0,π}), and reflection positivity (Z>0) selects the positive branch ⇒ θ_eff=0. The CAR/Pfaffian form of the tfpt_2 polar+γ5+sheet+RP derivation.
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