A registered result in its source context
Original ledger classification: Numerical [N]/[C]/[O] (candidate pattern; record of v84 untouched)
Recorded statement: THIRD-GENERATION LADDER-BASE PATTERN (2026-07-02, v467): the suite's THREE ~2 sigma mixing tensions (sin^2 theta13 +2.0 sigma, sin^2 theta23 +1.8 sigma, V_cb +1.8 sigma; v307) are ONE common ~ -phi0 suppression -- quantified and…
Statement, assumptions and sources
Paper context: Standard Model and flavor structure
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FLAV.THIRDGEN.PATTERN.01
Original ledger classification: Numerical [N]/[C]/[O] (candidate pattern; record of v84 untouched)
Original claim text
THIRD-GENERATION LADDER-BASE PATTERN (2026-07-02, v467): the suite's THREE ~2 sigma mixing tensions (sin^2 theta13 +2.0 sigma, sin^2 theta23 +1.8 sigma, V_cb +1.8 sigma; v307) are ONE common ~ -phi0 suppression -- quantified and pre-registered as a CANDIDATE, the frozen record (v84/REG.FREEZE.01) is NOT changed. In existing vocabulary the pattern is parameter-free: the seed enters third-generation mixings through the LADDER BASE lambda_C^2 = phi0(1-phi0) (the Yukawa mass-ladder base, tfpt_2) instead of bare phi0, and the 2-3 texture carries the same -phi0/2 shift as theta12: sin^2 theta13 = lambda_C^2 e^{-5/6} = 0.021880 (+2.00 -> -0.12 sigma), sin^2 theta23 = (1-phi0)/2 <=> cos 2theta23 = phi0 = 0.473414 (+1.76 -> +0.20), V_cb = lambda_C^2/(1+lambda_C) = 0.041119 (+1.79 -> +0.01). Scope checks that make it a rule not a fit: V_ub = lambda_C^3/3 has no bare phi0, stays untouched and consistent (-0.23); the 1-2 channels must stay undressed and do (theta12 -0.02, lambda_C -0.25; dressing lambda_C would give -24 sigma). Weighted common deviation of the three affected channels -5.36% +- 1.67% (3.2 sigma non-zero, -0.03 sigma from -phi0); joint chi^2 over the four third-gen observables 10.4 -> 0.11 with ZERO new parameters; Daya Bay alone already prefers the pattern (Delta chi^2 = 4.3). HONEST: post-hoc (5/16 equally-simple dressings fix the two PMNS tensions; (1-phi0)/(1-c3)/resolvent degenerate <1.4%); suppression size phi0 = 5.32% sits INSIDE the seam-gapped correction band (2/3)^6 = 8.78% (v393) but NO seam-transport derivation exists (Bernoulli-variance reading lambda_Y^2 = Var[Bernoulli(phi0)] is an exact identity but only an interpretation). Pre-registered kills: theta13 stable at 0.0231 kills the pattern; at ~0.0219 (sigma_rel<1%) kills the record's bare-phi0 reading; exclusive |Vcb| ~0.0395 kills both; JUNO-era reactors + Belle II decide.
Original classification detail
Open [O] candidate pattern (post-hoc, quantified, pre-registered): three ~2 sigma third-gen mixing tensions = one common -phi0 suppression (3.2 sigma non-zero; ladder-base forms drop joint chi^2 10.4 -> 0.11, zero parameters); frozen record unchanged; needs a seam-transport derivation to become more than a candidate
Dependencies as recorded
FLAV.TH13.PRESSURE.01; REG.FREEZE.01; CORRECTIONS.NUMERIC.01; FLAV.TH13.01; SEED.CROSSVAL.01
Open the original ledger source, row 528Location 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
- Closing the audit gates: is [formula in source] , [formula in source] , [formula in source] derived or imported?Standard Model and flavor structure
- OutcomeRed-team audit
- Closing the audit gates: is [formula in source] , [formula in source] , [formula in source] derived or imported?tfpt 2 standard model
- 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
- v467_thirdgen_mixing_pattern.pyRegistered verification module · neutrinos
Read the description recorded in the module registry
FLAV.THIRDGEN.PATTERN.01: the three ~2σ mixing tensions (θ13, θ23, V_cb) are ONE common −φ₀ suppression (−5.36%±1.67%, 3.2σ non-zero); ladder-base forms λ_C²e^(−5/6) / (1−φ₀)/2 / λ_C²/(1+λ_C) drop the joint χ² 10.4→0.11 with zero parameters; post-hoc candidate [O], record unchanged, JUNO/Belle II decide
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