Masses Mass Genesis T10 Channel Block Window Pricing Wall Electroweak Neutral Re

The counting obstruction

In the Recognition Science account, a ledger (a discrete record of events) pays for physical quantities by counting events. The declaration electroweak_neutral_requiredEventWeight_eq_phi47_div_four examines one specific proposed payment scheme: a summing account that would need to pay a certain window energy from coherence quanta. The scheme defines a required event weight, a number that would have to count events. On the neutral Electroweak seed, that number equals phi^47 / 4.

The number phi^47 / 4 is irrational. A separate theorem proves that no natural number equals phi^47 / 4. Since a count of events must be a natural number, the required weight cannot be a count. This is the counting obstruction: the proposed payment scheme cannot work because it demands a number of events that cannot exist.

The declaration does not claim that the Electroweak sector is impossible, nor that any measured mass is wrong. It targets one specific accounting scheme, the one that would pay a window from coherence quanta. Other payment schemes remain open. The declaration also does not claim that the window energy itself is problematic; the window energy phi^42 / 4 is well-defined and exceeds one. The obstruction is only that this particular way of paying for it would require an impossible count.

/-- On the neutral Electroweak seed the required weight is `phi^47/4`. -/
theorem electroweak_neutral_requiredEventWeight_eq_phi47_div_four :
    requiredChannelBlockEventWeight Anchor.Sector.Electroweak 0 0 =
      phi ^ (47 : ℕ) / 4 := by
  unfold requiredChannelBlockEventWeight
  rw [Anchor.B_pow_Electroweak_eq, YardstickPremiseFreeCert.r0_ew_certified_eq_55,
    MassLaw.gap_zero_neutral]
  have h2 : (2 : ℝ) ^ ((1 : ℤ) - 3) = (1 : ℝ) / 4 := by
    norm_num
  rw [h2]
  have hexp : ((55 : ℤ) : ℝ) + ((0 : ℤ) : ℝ) - 8 + (0 : ℝ) = (47 : ℝ) := by
    norm_num
  rw [hexp]
  -- `phi ^ (47 : ℝ)` is the real power; reduce to Nat power.
  have h47 : (47 : ℝ) = (↑(47 : ℕ) : ℝ) := by norm_cast
  rw [h47, ← Real.rpow_natCast]
  ring

/-- Full irrationality: `phi^47/4` is never a natural number. -/
theorem phi47_div_four_ne_nat (N : ℕ) :
    phi ^ (47 : ℕ) / 4 ≠ (N : ℝ) := by
  intro heq
  have h4 : (4 : ℝ) ≠ 0 := by norm_num
  have hpow : phi ^ (47 : ℕ) = (4 : ℝ) * N := by
    field_simp [h4] at heq
    linarith
  have hcast : (4 : ℝ) * N = ((4 * N : ℕ) : ℝ) := by
    push_cast; ring
  rw [hcast] at hpow
  exact phi_pow_ne_nat 47 (by norm_num) (4 * N) hpow

/-- The required Electroweak event weight is not a natural number. -/
theorem electroweak_neutral_requiredEventWeight_not_nat (N : ℕ) :
    requiredChannelBlockEventWeight Anchor.Sector.Electroweak 0 0 ≠
      (N : ℝ) := by
  rw [electroweak_neutral_requiredEventWeight_eq_phi47_div_four]
  exact phi47_div_four_ne_nat N

What this page does not claim

The declaration does not claim that the Electroweak sector is impossible. The declaration does not claim that the window energy phi^42 / 4 is undefined or problematic. The declaration does not claim that all payment schemes for the window energy fail, only this specific summing account.

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/T10ChannelBlockWindowPricingWall.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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