lepton_torsion_verified
plain-language theorem explainer
The theorem certifies that lepton rungs at 2, 13 and 19 satisfy the torsion stability certificate under the Recognition Science ledger. Researchers deriving muon and tau masses from geometric forcing would cite it to replace free parameters with forced values from the cubic ledger. The proof is a direct term construction that applies reflexivity to the rung equalities, simplification on the rung definition for modular residues, and the uniqueness lemma for ladder stability.
Claim. The lepton torsion certificate holds: rung assignments satisfy rung(electron) = 2, rung(muon) = 13, rung(tau) = 19; residues modulo 8 are pairwise distinct; and the ladder {2, 13, 19} is stable.
background
Module T10 proves the lepton ladder is forced from the electron structural mass (T9) together with step functions drawn from cube geometry, the fine-structure constant, and the golden ratio. LeptonTorsionCert is the structure that packages three properties: forced rung values, distinct residues modulo 8, and stability of the specific ladder. The rung map itself is supplied by the RSBridge definition that assigns integer tiers to each lepton species.
proof idea
The term proof constructs the certificate explicitly. Reflexivity discharges the forced rung equalities. Two simp calls using the rung definition verify the distinct residues modulo 8. The stability field is filled by applying the uniqueness lemma lepton_rungs_unique at the concrete values 2, 13, 19 and discharging the resulting equalities by reflexivity.
why it matters
This result closes the T10 necessity step for lepton generations, confirming that the muon and tau arise uniquely from the electron mass via the phi-ladder and cubic ledger symmetries already derived in earlier modules. It feeds the broader claim that all fermion masses are determined by the eight-tick octave and J-cost minimization. No downstream uses are recorded yet, but the certificate directly supports replacement of the original lepton axioms with proven statements.
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