A registered result in its source context
Original ledger classification: Numerical/identity (flavor readout) [E]/[C]/[O]
Recorded statement: REACTOR ANGLE EXPONENT = CARRIER HYPERCHARGE TRACE (2026-06-18): the theta_13 value sin^2 theta_13 = phi0 e^{-5/6} = 0.0231 (v16) has its EXPONENT origin closed exactly -- gamma = tr_E Y^2 = 5/6 over the 5-slot carrier hypercharge…
Statement, assumptions and sources
Paper context: Standard Model and flavor structure
The exact identifier, original classification and full claim are available below.
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FLAV.TH13.01
Original ledger classification: Numerical/identity (flavor readout) [E]/[C]/[O]
Original claim text
REACTOR ANGLE EXPONENT = CARRIER HYPERCHARGE TRACE (2026-06-18): the theta_13 value sin^2 theta_13 = phi0 e^{-5/6} = 0.0231 (v16) has its EXPONENT origin closed exactly -- gamma = tr_E Y^2 = 5/6 over the 5-slot carrier hypercharge Y=diag(-1/3,-1/3,-1/3,1/2,1/2) (anomaly-free roots of 6Y^2-Y-1=0), complement 1/6 the neutrino ratio. theta_13 is confirmed a SEPARATE carrier-trace channel: the mu-tau-breaking eps=3phi0/4 (which gives theta_12) induces only ~1.6e-3 << 0.023, correcting the tempting 'theta_13 from M_nu' route (v263). CP magnitude (delta_PMNS=240 deg, mu6/triality) and absolute nu-mass scale (M_R) remain the open PMNS items.
Original classification detail
[E] gamma=5/6=tr_E Y^2 (exponent origin) + own-channel separation (eps^2 ~ 1.6e-3 != 0.023); [C] value 0.0231 vs ~0.0222; [O] CP magnitude + absolute scale open. Closes the theta_13 exponent origin, not full PMNS dynamics.
Dependencies as recorded
FLAV.TH12.01; FLAV.SOLAR.01; FLAV.PMNS.02; CAR.SM.01
Open the original ledger source, row 361Location recorded in the ledger
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- Standard Model and flavor structure
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.
- 2026-06-18 (PMNS: the reactor-angle exponent closed as the carrier hypercharge trace, v268)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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.
- 2026-06-24 (The [formula in source] dual keystone + the flavor residuals it homes: v405– v407)Research changelog; TFPT — Introduction and reading guide
- 2026-06-25 (No-Ambient-Dependency: no frozen readout is computed from QG.AMB.01: v423)Research changelog; TFPT — Introduction and reading guide
- 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
- OutcomeRed-team audit
- 2026-06-22 (next-steps round: the keystone collapsed to one shared premise (Lean [formula in source] one citable theorem), the [formula in source] solver suite, the cusp weight derived from a minimal rewrite, and the [formula in source] pressure point: FORM.QGEO.BW.01, v325, v326, v327, v328)Research changelog; TFPT — Introduction and reading guide
- Full quantum gravity — induced from the boundary kernelFrontier and open physical interfaces
Registered verification modules
- v268_theta13_carrier_trace.pyRegistered verification module · neutrinos
Read the description recorded in the module registry
FLAV.TH13.01 — the reactor angle theta_13 exponent IS the carrier hypercharge trace. The value sin^2 theta_13 = phi0 e^{-5/6} = 0.0231 was already checked (v16); here the exponent origin is closed exactly: gamma = tr_E Y^2 = 3(1/3)^2+2(1/2)^2 = 5/6 over the 5-slot carrier hypercharge Y=diag(-1/3,-1/3,-1/3,1/2,1/2) (roots of 6Y^2-Y-1=0), complement 1/6 = the neutrino ratio. Own channel: the mu-tau-breaking eps=3phi0/4 (which gives theta_12) induces only ~1.6e-3 << 0.023, so theta_13 is a SEPARATE carrier-trace channel, not the seesaw mu-tau breaking (corrects the tempting 'theta_13 from M_nu' route). [O] CP magnitude + absolute nu scale remain open.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.