A registered result in its source context
Original ledger classification: Numerical [N]/[C]/[O] (candidate relation; informal pi phi0 table heuristic superseded as comparator)
Recorded statement: SPLITTING RATIO = LEPTONIC JARLSKOG (2026-07-02, v468): the neutrino mass-squared splitting ratio equals the Jarlskog invariant of the FROZEN PMNS matrix -- dm21^2/dm31^2 = |J_PMNS| = 0.029 653 vs NuFIT 6.0 NO measured 0.029 805 +- 0.000 792…
Statement, assumptions and sources
Paper context: Standard Model and flavor structure
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FLAV.DM2RATIO.01
Original ledger classification: Numerical [N]/[C]/[O] (candidate relation; informal pi phi0 table heuristic superseded as comparator)
Original claim text
SPLITTING RATIO = LEPTONIC JARLSKOG (2026-07-02, v468): the neutrino mass-squared splitting ratio equals the Jarlskog invariant of the FROZEN PMNS matrix -- dm21^2/dm31^2 = |J_PMNS| = 0.029653 vs NuFIT 6.0 NO measured 0.029805 +- 0.000792 -> -0.19 sigma; equivalently m2/m3 = sqrt|J| = 0.17220 vs 0.17264(229). A parameter-free CANDIDATE relation for a ratio the compiler does not otherwise predict: |J| is the canonical derived CP invariant of the already-frozen matrix (angles v9/v268 + delta = 4pi/3, assembled v270; zero dials). It SUPERSEDES the informal tfpt_2 table heuristic m2/m3 ~ pi phi0 = 0.16704 (a '~' entry, never frozen), which is now at -2.44 sigma vs NuFIT 6.0. Spectrum consistency: with r = |J| the NO floor Sigma m_nu = m3(1+sqrt|J|) = 0.0588 eV reproduces the documented 0.0586 eV (v272); the absolute scale stays the ONE seesaw ratio (no absolute number added). HONEST: post-hoc; as a free formula the window density is ~1.2e-2 (unremarkable alone) -- the content is structural (canonical invariant, zero dials); NO mechanism (the mu-tau texture gives theta13 = 0 at leading order and cannot carry this relation) -- [O] until an M_nu-level derivation exists. Pre-registered kill: JUNO shrinks the r-window ~4x; a stable offset from 0.029653 at >3 sigma kills the relation; the v467 pattern would shift |J| to 0.028849 (-1.21 sigma today), so the two candidates cross-discriminate at JUNO precision.
Original classification detail
Open [O] candidate relation (post-hoc, parameter-free): dm21^2/dm31^2 = |J_PMNS(frozen)| at -0.19 sigma (the informal pi phi0 heuristic, -2.44 sigma, is retyped to this comparator); NO floor Sigma m_nu consistent; JUNO decides; needs an M_nu-level derivation
Dependencies as recorded
FLAV.PMNS.03; FLAV.TH13.01; FLAV.NUSCALE.01; FLAV.THIRDGEN.PATTERN.01
Open the original ledger source, row 529Location recorded in the ledger
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- Standard Model and flavor structure
Sections that explicitly cite this claim
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- 2026-07-02 ( v467/ v468 — two named post-hoc \ flavor candidates, record unchanged: the three [formula in source] mixing tensions as one third-generation [formula in source] pattern, and the splitting ratio [formula in source] )Research changelog; TFPT — Introduction and reading guide
- Neutrinostfpt 2 standard model
- NeutrinosStandard Model and flavor structure
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Front matter / supportFrontier and open physical interfaces
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.
- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- 2026-07-03 ( v472 — the determinant line over the [formula in source] -twist moduli of the collar model carries curvature [formula in source] the inflow level: the v470 bridge lemma exhibited at the finite/model level; ALPHA.QUILLEN.EXACT.01 stays . Plus: bird's-eye rounds — electron-sector/Cabibbo whitespot probes, Calder\'on UV-universality, parameter-free flat-budget closure (sandbox); the flat-budget closure enters the evidence scorecard)Research changelog; TFPT — Introduction and reading guide
- 2026-07-14 ( v479– v481 — the bird's-eye ``overlooked tools'' round: R3's graph [formula in source] geometry bridge discharged to Kronheimer 1989; the four [formula in source] marks realised as the exactly solvable four-interval multilocal modular geometry with [formula in source] manifest; and the absolute [formula in source] -scale collapsed to a one-parameter, PS-window-bracketed candidate under the carrier normalisation [formula in source] — no gate closes, no marker moves)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v468_dm2_ratio_jarlskog.pyRegistered verification module · neutrinos
Read the description recorded in the module registry
FLAV.DM2RATIO.01: Δm²₂₁/Δm²₃₁ = |J_PMNS(frozen)| = 0.029653 vs measured 0.029805(792) → −0.19σ — a parameter-free candidate relation for the (previously unpredicted) splitting ratio; the informal m₂/m₃ ~ πφ₀ heuristic is now −2.44σ and retyped; NO floor Σm_ν = 0.0588 eV consistent; post-hoc [O], JUNO decides
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