The connected Q, K, R and L flavour operators
Original ledger classification: Lattice
Recorded statement: Q-Sigma algebra: K=R+Q*Sigma; L=R+Q*(I+Sigma); chi_Q=(t-1)(t^2-5t+3); chi_K=(t-1)(t^2-8t+4); det ladder (3;4;8;20) product 1920=|W(D5)|; a^T K a=41
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
FLAV.KQ.01
Original ledger classification: Lattice
Original claim text
Q-Sigma algebra: K=R+Q*Sigma; L=R+Q*(I+Sigma); chi_Q=(t-1)(t^2-5t+3); chi_K=(t-1)(t^2-8t+4); det ladder (3;4;8;20) product 1920=|W(D5)|; a^T K a=41
Original classification detail
Lattice
Dependencies as recorded
FLAV.R.01; Sigma=diag(1;-1;-1)
Open the original ledger source, row 14Location 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
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.
- Dependency Graphnote carrier rigidity lean4
- tfptblue Formal Verification of TFPT Carrier Rigidity in Lean 4\\[0.4em] An Audited Dependency Graph from the Boundary Involution\\ to the Standard-Model [formula in source] \ Hypercharge Carriernote carrier rigidity lean4
- How to read this documenttfpt 1 architecture e8
- What This Note Is Aboutnote carrier rigidity lean4
- What Was Builtnote carrier rigidity lean4
- How to read this documentArchitecture, E8 and the electromagnetic fixed point
- Resultnote carrier rigidity lean4
- Interface Table: TFPT Paper 2 [formula in source] <-> Lean Statusnote carrier rigidity lean4
All 29 linked sections
- Front matter / support
- The Sheet Diamond and the Winding Line: masses and transport from one surface
- Front matter / support
- v11 — review-pass closure and typed targets for the remaining upstream theorems (the present revision)
- Remaining limitations of the Lean chain itself.
- Neutrinos
- Front matter / support
- Neutrinos
- Closing the audit gates: is [formula in source] , [formula in source] , [formula in source] derived or imported?
- Main Technical Development
- Stage D characterisation, both directions formalised (v10).
- How to read this document
- Closing the audit gates: is [formula in source] , [formula in source] , [formula in source] derived or imported?
- The Sheet Diamond and the Winding Line: masses and transport from one surface
- v10 — upstream interfaces closed to the next algebraic layer
- Front matter / support
- Front matter / support
- =150 2026-07-31 (II) (the No-Carrier-Reconstruction audit, Stage A: the anchor self-code is carrier-free, and [formula in source] reconstructs up to ONE binary sheet-coupling choice (RECONSTRUCTS-TO-FAMILY) + v567 promoted + ledger/paper/diary/website sync)
- Discharging the Rank and Exterior Premises
- Next Steps
- Main Technical Development
Registered verification modules
- v10_projection_involution.pyRegistered verification module · flavor
Read the description recorded in the module registry
K=R+QΣ, L=R+Q(I+Σ); det ladder ∏ = 1920 = |W(D₅)|
- v11_unique_KQ.pyRegistered verification module · flavor
Read the description recorded in the module registry
K, Q are the unique nonneg-integer matrices (enumeration)
- v12_mass_generation_polynomials.pyRegistered verification module · flavor
Read the description recorded in the module registry
sector / generation polynomials of K; anchor det ladder
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.