Constants External Anchors Muon Mass Me V Pos

A positive mass

The muon is a heavier cousin of the electron, about 207 times as massive. In the standard model of particle physics, it is a fundamental lepton with a measured mass of 105.6583755 MeV (million electron volts), a value that comes from the CODATA 2022 adjustment of physical constants. The declaration muon_mass_MeV_pos is a formal statement in the Recognition Science framework's machine-checked library of formal theorems: it asserts, and proves, that this number is greater than zero.

The proof is a simple one. The library defines the muon mass as the positive real number 105.6583755. The lemma then uses a routine arithmetic check to verify that this number is indeed positive. In Lean, the proof is a single line: by norm_num [muon_mass_MeV]. The declaration is tagged with @[simp], meaning it is available as a simplification rule for other proofs. Its purpose is not to discover physics but to keep the formal library consistent: any later theorem that needs to divide by the muon mass, or to compare it with another mass, can rely on the fact that it is not zero.

What the lemma does not claim is more important than what it does. It does not derive the muon mass from first principles. The mass value itself is an external anchor, a piece of empirical data that the framework imports from CODATA. The framework's core derivation, which produces constants like the fine-structure constant from a cost function, does not generate particle masses. The muon mass is simply a number that the framework accepts from experiment, and this lemma only guarantees that the number is positive.

The lemma also does not claim that the muon mass is fundamental or that it fits any particular pattern. It does not assert that the muon mass is related to the electron mass by a simple ratio, nor does it imply anything about the origin of mass. It is a small, technical guarantee, the kind of bookkeeping that a formal library needs to stay sound. For a reader, the practical consequence is this: in the Recognition Science framework, the muon mass is available as a well-defined, positive constant that can be used in further proofs without fear of division by zero.

lemma muon_mass_MeV_pos : 0 < muon_mass_MeV := by norm_num [muon_mass_MeV]

/-- **EXTERNAL ANCHOR**: Muon mass (PDG 2024).
    m_μ = 105.6583755(23) MeV/c² -/
@[simp]
noncomputable def muon_mass_MeV : ℝ := 105.6583755

What this page does not claim

The muon mass is derived from the framework's cost function. The muon mass is predicted by any theoretical pattern within the framework. The lemma establishes any physical property of the muon beyond its mass being positive.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Constants/ExternalAnchors.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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