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Explain the Lean theorem `match_boson_Z` 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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The declaration match_boson_Z is the statement theorem match_boson_Z : compute_rung .Z = 1 := by rfl.

(1) In plain English it asserts that the rung constructor applied to the Z boson returns the integer 1; the proof is immediate by reflexivity, i.e., the equality holds by definition of compute_rung.

(2) In Recognition Science the theorem verifies that the boson sector of the particle table is reproduced exactly by the rung assignment (W, Z and H all receive rung 1). This is part of the larger matching of the legacy RSBridge.rung table and the SDGT variant; see the surrounding theorems that establish the same for leptons, quarks and neutrinos.

(3) The formal statement is read as: the function compute_rung (imported from the Motif submodule) maps the Z constructor to 1, with the := by rfl tactic confirming the equality is definitional.

(4) Visible dependencies in the supplied source are the identical reflexivity proofs for the other bosons (match_boson_W, match_boson_H) and the SDGT counterparts (sdgt_boson_Z, sdgt_boson_W, sdgt_boson_H). The module also contains the master matching theorem match_rsbridge_rung that covers all fermions and the SDGT agreement theorems for bosons.

(5) The declaration does not prove any physical mass value, any derivation of the rung from the J-cost functional equation, or any link to the actual Z-boson mass; it is solely a table-matching verification. The definition of compute_rung itself and the Motif module that supplies it are not present in the supplied slice.

outside recognition

Aspects Recognition does not yet address:

  • definition of compute_rung
  • physical derivation of boson masses from rungs
  • connection to J-cost or phi scaling for masses
  • any theorem outside the RungConstructor.Proofs module

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.