A registered result in its source context

Original ledger classification: PMNS closed modulo the keystone [E]/[C]/[O] (CP-phase origin = the tau=omega CM phase v405; angles [E]; J=-0.0297 derived; absolute scale = one seesaw ratio = v_geo; zero free flavor dials beyond v_geo). Resolves v270's open phase + scale

Recorded statement: The PMNS dynamics closed modulo the tau=omega keystone (2026-06-24): the CP-phase ORIGIN is the family CM point (v405) and the absolute scale is one v_geo-class unit, so PMNS has zero free flavor dials beyond v_geo. Resolves the two [O]'s…

Statement, assumptions and sources

Paper context: Standard Model and flavor structure

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FLAV.PMNS.CLOSE.01

Original claim text

The PMNS dynamics closed modulo the tau=omega keystone (2026-06-24): the CP-phase ORIGIN is the family CM point (v405) and the absolute scale is one v_geo-class unit, so PMNS has zero free flavor dials beyond v_geo. Resolves the two [O]'s v270 left open (the assembled phase + the open scale). [E] the three angles sin^2 th12=1/3-phi0/2 (v9), th23=45 (v9), sin^2 th13=phi0 e^{-5/6} (v268) assemble to one exactly-unitary U_PMNS (v270). [C] CP-PHASE ORIGIN: delta_PMNS=4pi/3 is the tau=omega hexagonal CM phase (v405/v220/v233), arg zeta6=pi/3, mu6=mu3 x mu2 -- so under SEAM.EQUIV.02 the phase has an operator home, upgrading v270's [O] assembled input to a keystone consequence. [C] J_PMNS=s12 c12 s23 c23 s13 c13^2 sin(delta)=-0.0297, a derived CP strength (no free phase once delta is the keystone value), matching NuFIT ~ -0.026. [E] the absolute scale = one seesaw ratio m3=(y_nu v_EW)^2/M_R (v272) -- one v_geo-class UV input the No-Unit theorem (v153) forbids deriving, NOT a flavor gap. [C] net: PMNS = three angles[E] + delta[tau=omega keystone] + J[derived] + absolute scale[one v_geo unit]; zero free flavor dials. [O] residual: the seesaw operator realisation (M_R not a clean Mbar power, v272/v184) + the normal-ordering Sigma m_nu floor 0.0586 eV kill test (v272).

Original classification detail

[E] the three angles + the scale-reduction to one seesaw ratio; [C] the CP-phase origin via the tau=omega keystone (upgrades v270's [O] to a keystone consequence) + the derived J=-0.0297 + the net closure (zero free flavor dials beyond v_geo); [O] the seesaw operator realisation / v_geo-class scale (v272/v184) + the NO floor kill test. A closure-accounting building on v405; no new number.

Dependencies as recorded

SEAM.EQUIV.02; FLAV.PMNS.03; FLAV.NUSCALE.01; v405; v270; v272; v9; v268; v153

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Location recorded in the ledger

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Standard Model and flavor structure
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Sections that explicitly cite this claim

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2026-06-24 (The [formula in source] dual keystone + the flavor residuals it homes: v405– v407)Research changelog; TFPT — Introduction and reading guide
Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog

Navigation through a shared verification script

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The unique attractor: a gapped transport selects ONE fixed pointorigin theory
The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
Neutrinostfpt 2 standard model
NeutrinosStandard Model and flavor structure
The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
The unique attractor: a gapped transport selects ONE fixed pointOrigin Theory

Registered verification modules

v406_pmns_phase_origin.pyRegistered verification module · neutrinos
Read the description recorded in the module registry
FLAV.PMNS.CLOSE.01: the PMNS dynamics closed modulo the tau=omega keystone (v405) -- the CP-phase ORIGIN is the family CM point and the absolute scale is one v_geo-class unit, so PMNS has zero free flavor dials beyond v_geo. [E] the three angles (sin^2 th12=1/3-phi0/2, th23=1/2, sin^2 th13=phi0 e^{-5/6}; v9/v268) assemble to a unitary U_PMNS (v270). [C] CP-phase origin: delta_PMNS=4pi/3 is the tau=omega CM phase (v405), upgrading v270's [O] assembled input to a keystone consequence. [C] J_PMNS=-0.0297 derived. [E] absolute scale = one seesaw ratio = v_geo-class UV input (v272/v153), not a flavor gap. [C] net: PMNS = angles+delta[keystone]+J+scale[v_geo], zero free flavor dials. [O] residual = the seesaw operator realisation (M_R not a clean Mbar power, v272/v184; one-parameter carrier-normalised candidate v481) + the NO Sigma m_nu floor kill test.

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