Masses Channel Distinction Couples To Charge True Iff

What the charge predicate decides

In the Recognition Science framework, the declaration couplesToCharge_true_iff establishes a precise equivalence: a particle couples to the charge channel exactly when its charge value is not zero. The theorem states that for any fermion, the Boolean predicate couplesToCharge returns true if and only if the charge value is nonzero. This is a formal, machine-checked result in the framework's library of theorems.

The declaration is part of a larger structure about how particles couple to different gauge channels. The framework models each channel as carrying two distinction axes: presence and orientation. For the charge channel, this means a nonzero charge is exactly a charge with a sign, either positive or negative. The theorem charged_has_sign follows directly: if a particle couples to charge, then its charge value is either greater than zero or less than zero.

This result does not claim that the framework derives the actual values of electric charges. It does not say what the magnitude of any charge is, nor does it identify which particles couple to charge. The theorem only establishes the logical equivalence between the coupling predicate and the nonzero condition. The framework's model of channel distinctions is a definitional choice, not a derived consequence.

/-- The charge predicate decides nonzero charge. -/
theorem couplesToCharge_true_iff (f : Fermion) :
    couplesToCharge f = true ↔ tildeQ f ≠ 0 := by
  unfold couplesToCharge
  by_cases h : tildeQ f = 0 <;> simp [h]

/-- The charge predicate decides nonzero charge. -/
theorem couplesToCharge_true_iff (f : Fermion) :
    couplesToCharge f = true ↔ tildeQ f ≠ 0 := by
  unfold couplesToCharge
  by_cases h : tildeQ f = 0 <;> simp [h]

/-- Every species coupled to the charge channel has a definite sign. -/
theorem charged_has_sign (f : Fermion) (h : couplesToCharge f = true) :
    0 < tildeQ f ∨ tildeQ f < 0 :=
  ((charge_channel_two_distinctions (tildeQ f)).mp
    ((couplesToCharge_true_iff f).mp h)).symm

What this page does not claim

The framework derives the numerical values of electric charges. The theorem identifies which specific particles couple to charge. The channel distinction model is a derived consequence rather than a definitional choice.

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/Masses/ChannelDistinction.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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