IndisputableMonolith.Physics.LeptonGenerations.Defs
This module supplies the core numerical definitions and step functions for extending the electron mass to the muon and tau in the lepton generation ladder. Physicists deriving Standard Model masses from cubic ledger geometry would cite these constants when building T10 results. The module is purely definitional, importing anchors from ElectronMass.Defs, MassTopology, and RSBridge.Anchor without theorems or proofs.
claimDefines the muon mass $m_μ$ (MeV), tau mass $m_τ$ (MeV), generation steps step_{eμ} and step_{μτ}, predicted residues, and predicted masses on the topological ladder extending from the electron.
background
The module sits in the T9–T10 chain of Recognition Science, where lepton masses arise from the geometry of the cubic ledger Q₃ rather than free parameters. Upstream, ElectronMass.Defs isolates the electron mass definitions to break import cycles, while MassTopology supplies the refined ledger fraction δ = 2W + (W + E_total)/(4 E_passive) + α² + E_total α³. RSBridge.Anchor provides the Z-map and gap function F(Z) = ln(1 + Z/φ)/ln(φ) that indexes fermion species, and PhiSupport fixes φ² = φ + 1 together with the RS time quantum τ₀ = 1 tick from Constants.
proof idea
This is a definition module, no proofs. It directly declares the mass values, step functions, residues, and predicted masses by referencing the imported geometric constants and the electron mass anchor.
why it matters in Recognition Science
The definitions feed the parent T10 LeptonGenerations module, which states the mass of a lepton in generation n via the topological ladder, and the Necessity module that seeks to replace two axioms with proven inequalities. They close the definitional gap between the T9 electron mass and the full lepton spectrum, enabling the forced derivation of m_μ and m_τ from earlier geometric results.
scope and limits
- Does not prove any mass values or step relations.
- Does not derive the generation ladder theorems.
- Does not address quarks or neutrinos.
- Does not perform experimental fits beyond CODATA references.