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Explain the Lean theorem `match_boson_W` 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 theorem match_boson_W asserts that the rung constructor assigns the value 1 to the W boson.

(1) In plain English: it states that compute_rung applied to the W boson yields exactly 1.

(2) In Recognition Science: this verifies that the rung constructor reproduces the boson table entries (W, Z, H all at rung 1), confirming consistency with the legacy RSBridge mapping for the gauge and Higgs sector.

(3) How to read the formal statement: theorem match_boson_W : compute_rung .W = 1 := by rfl declares a named theorem whose type is the equality compute_rung .W = 1; the proof by rfl means the equality is immediate by reflexivity (i.e., direct unfolding or definitional computation).

(4) Visible dependencies or certificates: the declaration sits among sibling theorems match_boson_Z, match_boson_H, sdgt_boson_W and the master match_rsbridge_rung; the module imports IndisputableMonolith.Masses.Anchor, IndisputableMonolith.RSBridge.Anchor and IndisputableMonolith.Masses.RungConstructor.Motif.

(5) What this declaration does not prove: it supplies no derivation of the rung value itself, no mass formula, no physical interpretation of rung 1, and no link to constants such as phi-powers; the definition of compute_rung and any underlying motif logic reside outside this slice.

cited recognition theorems

  • Proofs.match_boson_W The target theorem whose plain-English meaning, RS role, and formal reading are requested.
  • Proofs.match_boson_Z Sibling boson matching theorem showing the pattern for the full gauge/Higgs sector.
  • Proofs.match_boson_H Sibling boson matching theorem completing the boson table verification.
  • Proofs.sdgt_boson_W SDGT variant of the same boson rung, illustrating the distinction between legacy and sector-dependent generation torsion.
  • Proofs.match_rsbridge_rung Master theorem that the constructor reproduces all legacy RSBridge rung values, of which match_boson_W is a special case.

outside recognition

Aspects Recognition does not yet address:

  • Definition of compute_rung (resides in Motif module, not supplied in this slice)
  • Physical derivation or justification of why bosons receive rung 1
  • Mapping from rung values to actual masses via phi-powers or yardstick scaling
  • Any connection to the forcing chain, J-cost, or Alexander duality modules

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.