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Explain the Lean theorem `match_rsbridge_rung_neutrinos` 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.

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Explanation of the theorem match_rsbridge_rung_neutrinos

(1) In plain English, the declaration states that the rung values produced by compute_rung for the three neutrino generations (nu1, nu2, nu3) are identical to the legacy values returned by RSBridge.rung.

(2) In Recognition Science this matters because it verifies that the new rung constructor preserves the prior mapping for neutrinos (which use baseline 0 due to Z=0 and a distinct +8 generation step for the second generation, per the docstring). This maintains internal consistency of the mass/rung framework across legacy and updated code paths.

(3) The formal statement is the conjunction

compute_rung (.fermion .nu1) = RSBridge.rung .nu1 ∧
compute_rung (.fermion .nu2) = RSBridge.rung .nu2 ∧
compute_rung (.fermion .nu3) = RSBridge.rung .nu3

proved by ⟨rfl, rfl, rfl⟩. In Lean this means each equality holds definitionally by reflexivity; no further rewriting or computation is required.

(4) Visible dependencies in the supplied source are the imported compute_rung (from Motif) and RSBridge.rung (from RSBridge.Anchor), together with the master theorem match_rsbridge_rung that proves the same claim for an arbitrary Fermion by exhaustive case analysis. The neutrino case is one of several specialized matching theorems (e.g., the charged-lepton and quark variants) that feed into the master result.

(5) The declaration does not prove the numerical rung values themselves, the underlying mass-scaling formula, any physical predictions, the SDGT rung variants (which differ for quarks), or empirical comparisons. It only certifies syntactic matching for neutrinos.

cited recognition theorems

outside recognition

Aspects Recognition does not yet address:

  • Definition of compute_rung (in Motif module, not supplied)
  • Definition of RSBridge.rung (in RSBridge.Anchor module, not supplied)
  • Any mass-scaling theorem or phi-power formula
  • Empirical predictions, falsifiers, or PDG comparisons for neutrino masses

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.