Skip to main content

A registered result in its source context

Original ledger classification: Readout [C] (CP strength); [O] phase origin + absolute scale

Recorded statement: COMPLETE COMPLEX PMNS MATRIX + LEPTONIC JARLSKOG J_PMNS (CP STRENGTH) (2026-06-18): the four TFPT channels (sin^2 th12 = 1/3 - phi0/2 v9/v263, sin^2 th23 = 1/2 v9/v263, sin^2 th13 = phi0 e^{-5/6} v16/v268, delta = 4 pi/3 = 240 deg…

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.PMNS.03

Original ledger classification: Readout [C] (CP strength); [O] phase origin + absolute scale

Original claim text

COMPLETE COMPLEX PMNS MATRIX + LEPTONIC JARLSKOG J_PMNS (CP STRENGTH) (2026-06-18): the four TFPT channels (sin^2 th12 = 1/3 - phi0/2 v9/v263, sin^2 th23 = 1/2 v9/v263, sin^2 th13 = phi0 e^{-5/6} v16/v268, delta = 4 pi/3 = 240 deg v231/v233) assemble into one exactly-unitary complex PMNS matrix U = R23 U13(delta) R12, from which the Jarlskog CP strength J_PMNS = Im(U_e1 U_mu2 U*_e2 U*_mu1) = s12 c12 s23 c23 s13 c13^2 sin(delta) = -0.02965 (J_max = 0.03424) is a DERIVED number (the leptonic analogue of the CKM J, v88). Data: J_max vs NuFIT 5.2 J_max 0.0332 (~3%), J vs best fit -0.026 (delta_data ~232 deg within ~1 sigma), the negative CP-violating sign reproduced. Closes the CP-STRENGTH readout; delta itself is the mu6/triality phase (assembled, not from M_nu/D_F) and the absolute neutrino-mass scale (Sigma m_nu, M_R) stays open.

Original classification detail

[E] the three angle channels + the exact unitary assembly; [C] the derived Jarlskog CP strength + its NuFIT confrontation; [O] the phase's operator origin (delta = mu6/triality, not M_nu) + the absolute scale. A PMNS assembly + CP-strength readout, not a full operator closure.

Dependencies as recorded

FLAV.TH12.01; FLAV.PMNS.02; FLAV.TH13.01; CP.MU6.01; CP.TRIALITY.01

Open the original ledger source, row 363

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 11 linked sections

Registered verification modules

  • v270_pmns_jarlskog_assembly.pyRegistered verification module · neutrinos
    Read the description recorded in the module registry

    FLAV.PMNS.03 — the complete complex PMNS matrix + the leptonic Jarlskog J_PMNS (the CP strength), assembled from the four TFPT channels (sin²θ₁₂=1/3-φ₀/2, sin²θ₂₃=1/2, sin²θ₁₃=φ₀e^{-5/6}, δ=240°=4π/3) into one unitary object. [E] the three angle channels; [E] U=R23·U13(δ)·R12 is exactly unitary; [C] J_PMNS=Im(U_e1 U_mu2 U*_e2 U*_mu1)=-0.02965 (formula and full matrix agree), J_max=0.03424 — a DERIVED CP strength, the leptonic analogue of the CKM J (v88); [C] data: J_max vs NuFIT 0.0332 (~3%), J vs best fit -0.026, negative sign reproduced; [O] δ is the μ6/triality phase (assembled input, NOT from M_ν/D_F) and the absolute ν-mass scale (Σm_ν, M_R) stays open. Assembles PMNS + CP strength; does not derive δ from D_F nor fix the scale.

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