Pith. sign in

Explain the Lean theorem `match_boson_H` 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

Plain English statement

The theorem match_boson_H states that the rung constructor assigns rung value 1 to the Higgs boson.

Relevance to Recognition Science

RS derives particle masses from a discrete rung ladder scaled by powers of phi. This theorem confirms that H (along with W and Z) sits at rung 1, the base of the boson sector, which is required for the subsequent mass formula yardstick * phi^(rung - 8 + gap(Z)) to place the electroweak bosons at the observed scale.

Reading the formal statement

 theorem match_boson_H : compute_rung .H = 1 := by rfl

compute_rung is applied to the constructor .H; the equation asserts equality to the literal 1. The proof by rfl means the equality holds definitionally (no computation or external lemmas required).

Visible dependencies and certificates

The declaration sits in the same module as the sibling boson theorems match_boson_W and match_boson_Z, the SDGT counterparts sdgt_boson_H, sdgt_boson_W and sdgt_boson_Z, and the fermion matching theorems such as match_lepton_e. The module imports IndisputableMonolith.Masses.RungConstructor.Motif (source of compute_rung) and IndisputableMonolith.RSBridge.Anchor (legacy rung values). No sorry appears in any of these matching theorems.

What this declaration does not prove

It only certifies the integer rung assignment for H. It does not contain the definition of compute_rung, the phi-power mass scaling formula, the gap(Z) correction, or any comparison to experimental PDG masses. Those steps reside in other modules (Anchor, ConstantDerivations) outside the supplied slice.

outside recognition

Aspects Recognition does not yet address:

  • Definition of compute_rung (imported from Motif, not expanded in slice)
  • Phi-power mass scaling formula and gap(Z) term
  • Empirical mass comparison or PDG validation

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.