A registered result in its source context
Original ledger classification: Identity (exact algebra) [E]/[C]
Recorded statement: LEPTON ETALE FROBENIUS ALGEBRA (2026-06-16): the three charged-lepton coefficients form a genuine commutative Frobenius algebra over the mu6 resolvent. Exact coefficients (c_e,c_mu,c_tau)=(16/7,4/3,7/6), ring closure c_e c_tau=8/3=|Z2|…
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
LEP.FROB.01
Original ledger classification: Identity (exact algebra) [E]/[C]
Original claim text
LEPTON ETALE FROBENIUS ALGEBRA (2026-06-16): the three charged-lepton coefficients form a genuine commutative Frobenius algebra over the mu6 resolvent. Exact coefficients (c_e,c_mu,c_tau)=(16/7,4/3,7/6), ring closure c_e c_tau=8/3=|Z2| c_mu, product c_e c_mu c_tau=32/9=2^g_car/N_fam^2. A=Q[t]/(m), m=(t-c_e)(t-c_mu)(t-c_tau): the trace-form Gram G_ij=Tr(t^i t^j) is nondegenerate, det G=discriminant(m)!=0 (A etale/separable) -- a commutative Frobenius algebra with a nondegenerate trace pairing. The C6 shift has characteristic polynomial t^6-1 (spectrum mu6=mu3 family x mu2 sheet). PMNS extension: Aut(A) permutes {e,mu,tau} (real part), the hexagonal CM point j=0 supplies the phase part.
Original classification detail
[E] (16/7,4/3,7/6), ring closure c_e c_tau=8/3=|Z2|c_mu, product 32/9; etale Frobenius algebra (det Gram=disc(m)!=0); mu6=mu3 x mu2 spectrum; PMNS extension [C]
Dependencies as recorded
FLAV.LEPTON.01; ARCH.HEXRES.01; CP.MOD.01
Open the original ledger source, row 315Location 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.
- 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.
- 2026-06-16 (the icosahedral bedrock, CM-norm duality, and a structural-finds round)Research changelog; TFPT — Introduction and reading guide
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.
- Charged leptons: completely closed in [formula in source]tfpt 2 standard model
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Charged leptons: completely closed in [formula in source]Standard Model and flavor structure
Registered verification modules
- v229_lepton_frobenius_algebra.pyRegistered verification module · masses
Read the description recorded in the module registry
The charged leptons as an étale Frobenius algebra over the μ₆ resolvent. Exact coefficients (c_e,c_μ,c_τ)=(16/7,4/3,7/6), ring closure c_e c_τ=8/3=|Z₂|c_μ, product 32/9=2^g_car/N_fam². A=ℚ[t]/(m), m=∏(t−c): the trace-form Gram is nondegenerate (det=disc(m)≠0, A étale) — a commutative Frobenius algebra. The C₆ shift has charpoly t⁶−1 (spectrum μ₆=μ₃ family ×μ₂ sheet). PMNS extension via Aut(A)+the hex CM point is [C].
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.