Masses Mass Genesis T10 Yardstick Premise Free Cert Cell Reach Derived Ne Channe

Two different reach counts

The W boson is a carrier of the weak force, the interaction responsible for radioactive decay. In the Recognition Science framework, every force carrier is assigned two numbers. The first, called the cell reach, counts how many broad families of matter particles, quarks and leptons, the carrier touches. The second, the channel reach, counts how many specific particle types, such as the up quark or the electron, it touches. The theorem cellReach_derived_ne_channelReach_derived proves that for the W boson these two numbers are not equal: the cell reach is 3 and the channel reach is 2.

This distinction matters because the framework derives the mass scale of particles from a yardstick, a number built from these reach counts. A rival reading of the same structure would price three cells at two channels each, producing a yardstick of 57. The theorem rules out that reading by showing the two counts cannot be conflated: the cell reach and the channel reach are genuinely different quantities. The correct yardstick, computed from the derived reaches alone, is 55, and the theorem is part of a larger certificate that establishes this value without relying on any pre-set constant.

In Recognition Science, the theorem is one step in a chain that forces the electroweak yardstick to be 55, which in turn fixes a mass exponent of 42. The theorem itself does not claim that the W boson has any particular mass, nor that the framework's mass predictions match experiment. It only establishes the inequality between the two reach counts, a structural fact about the derived coupling. The value 55 and the exponent 42 are separate theorems in the same certificate, each with its own proof.

/-- **THEOREM (the cell reading is not the channel reading, derived
form).** -/
theorem cellReach_derived_ne_channelReach_derived :
    cellReach derivedWCouples ≠ channelReach derivedWCouples := by
  rw [cellReach_derived_w, channelReach_derived_w]
  norm_num

What this page does not claim

The theorem does not claim that the W boson's mass is measured to be any particular value. The theorem does not claim that the framework's mass predictions agree with any experimental data. The theorem does not claim that the cell reach and channel reach are different for any other force carrier.

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/MassGenesis/T10YardstickPremiseFreeCert.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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