Masses Mass Genesis T10 Boson Channel Reach Ew Charged Only Reading Ne Ew Yardst

The charged-only reading

The electroweak sector of the standard model is the part of physics that governs two of the four fundamental forces: the weak force, which drives radioactive decay, and electromagnetism. Its gauge carriers are the W boson, the Z boson, and the photon. In the Recognition Science framework, a ledger (a discrete record of which particles couple to which forces) assigns each carrier a channel reach: a count of how many distinct force channels it resolves. The W and Z bosons each resolve both the charge channel and the colour channel, giving them a channel reach of 2. The photon resolves only colour, giving it 1, and the gluon resolves neither, giving it 0.

The declaration ewChargedOnly_reading_ne_ew_yardstick tests a specific reading of the electroweak sector: that only fermions which couple to charge should count when measuring the sector's reach. Under this reading, the W boson's reach is 3, not 2, because it couples to all fermion species (quarks, charged leptons, and neutrinos) rather than just to those that carry electric charge. The declaration establishes that this charged-only reading does not equal the framework's electroweak yardstick, which is set by the W boson's channel reach of 2. It is a formal, machine-checked statement that a particular interpretive choice fails to match the framework's own measure.

What the declaration does not claim is broader. It does not say the charged-only reading is physically wrong in the standard model; it only says the reading does not reproduce the framework's internal yardstick. It does not derive any particle mass or coupling constant. It does not claim that the W boson's reach of 3 is a physically meaningful quantity outside the framework's ledger. The declaration is a precise negative result inside a specific formal system, not a statement about the physical world beyond it.

/-- **THEOREM (the electroweak reach is `2`).** -/
theorem channelReach_wBoson : channelReach (GaugeCarrier.couples .wBoson) = 2 := by
  unfold channelReach
  rw [if_pos wBoson_resolvesCharge, if_pos wBoson_resolvesColor]
  norm_num

/-- **THEOREM (the Z reach is `2`).** -/
theorem channelReach_zBoson : channelReach (GaugeCarrier.couples .zBoson) = 2 := by
  unfold channelReach
  rw [if_pos zBoson_resolvesCharge, if_pos zBoson_resolvesColor]
  norm_num

/-- **THEOREM (the photon reach is `1`).** -/
theorem channelReach_photon : channelReach (GaugeCarrier.couples .photon) = 1 := by
  unfold channelReach
  rw [if_neg photon_not_resolvesCharge, if_pos photon_resolvesColor]
  norm_num

/-- **THEOREM (the gluon reach is `0`).** Its coupled set is a single
channel cell: it resolves no channel distinction. -/
theorem channelReach_gluon : channelReach (GaugeCarrier.couples .gluon) = 0 := by
  unfold channelReach
  rw [if_neg gluon_not_resolvesCharge, if_neg gluon_not_resolvesColor]
  norm_num

/-- **THEOREM (the cell reading is not the channel-class reading).** The
offset prices the two channel CLASSES (the banked distinctions), not the
three inhabited cells: the nesting makes three cells out of two classes,
and the two-distinction bound plus the banked-yardstick test exclude the
cell reading. -/
theorem cell_reach_ne_channel_reach_ew :
    cellReach (GaugeCarrier.couples .wBoson) ≠ channelReach (GaugeCarrier.couples .wBoson) := by
  rw [cellReach_wBoson, channelReach_wBoson]
  norm_num

What this page does not claim

The charged-only reading is physically incorrect in the standard model. The declaration derives any particle mass or coupling constant. The W boson's reach of 3 is a physically meaningful quantity outside the framework's ledger.

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/T10BosonChannelReach.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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