Masses Channel Distinction Channel Distinction Boundary

The boundary without the model

A channel in this framework is a way a particle can couple to a force, such as charge or color. The distinction is the basic unit of information: a two-sided axis, like presence or absence, or up or down. The question is how many such axes each channel carries. The framework's model chooses two, but the theorem channelDistinction_boundary proves that this choice is not a free parameter. It shows that using one axis per channel, or three, would produce different predictions for the electron's mass-related behavior.

Specifically, the theorem states that for any integer value Z, the predicted value for a lepton with a deformed total of minus one, zero, or one differs from the prediction at zero. This is a formal, machine-checked result in the framework's library of formal theorems. It does not say which alternative is correct; it only proves that they are observably distinct. The choice of two axes per channel, called the canonical model, is a definitional choice, not a theorem. The theorem establishes the boundary of the model: if you change the number of axes, you change the physics.

The proof relies on a precedent from the framework's own coherence exponent, which counts three spatial, one temporal, and one balance axis, totaling five. Counting the two-sided balance as two axes would give six, breaking the established count. This precedent supports the idea that the unit of a degree of freedom is the axis, not the side. The boundary theorem then applies this logic to the channel structure, showing that the model's specific choice of two axes per channel is testable.

In plain terms, the declaration establishes a testable consequence of the framework's internal model. It does not claim that the two-axis model is the only possible one, nor does it prove that any particular alternative is wrong. It simply proves that the alternatives are not equivalent. This is a significant result because it means the framework's choice of two axes per channel is not arbitrary; it is a commitment that can be checked against measurement.

/-- **THEOREM (alternative axis counts are observably distinct).** One axis
per channel (coefficient 1) and three axes per channel (coefficient 3) both
meet every banked clause of the table, and both change observable
predictions. -/
theorem channelDistinction_boundary (Z : ℤ) :
    predictAt .Lepton (deformedTotal (-1) Fermion.e) Z
      ≠ predictAt .Lepton (deformedTotal 0 Fermion.e) Z
    ∧ predictAt .Lepton (deformedTotal 1 Fermion.e) Z
      ≠ predictAt .Lepton (deformedTotal 0 Fermion.e) Z :=
  ⟨baseRule_predictions_differ (-1) (by norm_num) Z,
    baseRule_predictions_differ 1 (by norm_num) Z⟩

What this page does not claim

The theorem does not prove that the two-axis model is the correct one. The theorem does not claim that alternative axis counts are physically realized. The theorem does not derive the value of any particle mass.

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)

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.

Derived articles

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