Pith. sign in

Explain the Lean theorem `match_rsbridge_rung_charged_leptons` in module `IndisputableMonolith.Masses.RungConstructor.Proofs`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. Your answer will appear below.
confidence: high in recognition cached

The declaration match_rsbridge_rung_charged_leptons asserts that the rung numbers produced by compute_rung for the three charged leptons equal the legacy values stored in RSBridge.rung.

(1) In plain English it says: the new constructor reproduces the old rung table exactly for the electron (rung 2), muon (rung 13) and tau (rung 19).

(2) In Recognition Science the match guarantees that lepton masses derived from the phi-scaling formula remain unchanged when the rung constructor is updated; it is a compatibility certificate between the legacy RSBridge mapping and the current Motif-based implementation.

(3) The formal statement is a three-way conjunction of equalities, each proved by rfl. In standard notation it reads compute_rung(fermion e) = RSBridge.rung(e) ∧ compute_rung(fermion mu) = RSBridge.rung(mu) ∧ compute_rung(fermion tau) = RSBridge.rung(tau).

(4) Visible dependencies inside the supplied source are the three individual lemmas match_lepton_e, match_lepton_mu, match_lepton_tau together with the master theorem match_rsbridge_rung that cases on the Fermion type. No external axioms or sorrys appear in the proof.

(5) The declaration does not prove the definition of compute_rung, the definition of RSBridge.rung, any mass-to-rung scaling theorems, the SDGT variants, or matching for quarks, neutrinos or bosons.

cited recognition theorems

outside recognition

Aspects Recognition does not yet address:

  • Definition of compute_rung (declared in imported Motif module, not supplied)
  • Definition of RSBridge.rung (declared in imported Anchor module, not supplied)
  • Any theorems deriving physical masses from rung numbers

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.