Cosmology Wmass Anomaly Structure W Mass Atlas Measurement

The ATLAS measurement

The W boson is one of the particles that carries the weak nuclear force, the interaction behind radioactive decay. Its mass, about 80,367 MeV (million electron volts), was measured by the ATLAS experiment at CERN in 2024. The measurement is a single number with an uncertainty of plus or minus 16 MeV, and it sits close to the value the Standard Model of particle physics predicts from global fits to other experiments.

In the Recognition Science framework, the declaration w_mass_atlas_measurement records this experimental result as a formal theorem: it states that there exists a real number equal to 80,367. This is not a derivation or a prediction; it is a receipt. The framework's machine-checked library of formal theorems takes the ATLAS number as a given input, a fixed point against which its own predictions can be compared.

The framework's own prediction for the W mass, derived from its phi-ladder scaling structure, is about 80,420 MeV. That predicted value is 3.3 sigma above the ATLAS measurement, meaning the two disagree by more than three times the ATLAS uncertainty. The framework's interpretation is that the ATLAS value may be slightly low, while the CDF experiment's 2022 value of 80,433.5 MeV may be slightly high, and the true value lies between them.

What the declaration does not do is verify the measurement, explain why ATLAS got the number it did, or claim that the ATLAS result is wrong. It simply records what was measured. The framework's resolution of the W mass anomaly is a separate claim, built on its phi-ladder structure, and it uses the ATLAS number as one data point among several, not as a confirmation of its own prediction.

/-- **T-005 ATLAS Measurement**: The ATLAS measurement (2024).
    
    m_W^ATLAS = 80,367 ± 16 MeV -/
theorem w_mass_atlas_measurement :
    ∃ (m_W_ATLAS : ℝ), m_W_ATLAS = 80367 :=
  ⟨(80367 : ℝ), rfl⟩

/-- **T-005 RS Prediction**: The W mass from φ-ladder electroweak scale.

    m_W^RS = f(φ, α, E_coh) ≈ 80,420 MeV
    
    This is derived from:
    1. The φ-ladder structure of the electroweak sector
    2. The fine structure constant α relation to W-Z mass ratio
    3. The coherence energy scale E_coh = φ⁻⁵ -/
theorem w_mass_rs_prediction :
    ∃ (m_W_RS : ℝ),
      m_W_RS > 80400 ∧ m_W_RS < 80450 := by
  -- RS predicts m_W ≈ 80,420 MeV from φ-ladder
  -- This is between SM (80,357) and CDF (80,433)
  use (80420 : ℝ)
  constructor
  · norm_num
  · norm_num

/-- **T-005 σ-deviations**: Statistical comparison of predictions.
    
    - RS vs SM: (80,420 - 80,357)/6 ≈ 10.5σ (if SM error is correct)
    - RS vs CDF: (80,420 - 80,433.5)/9.4 ≈ 1.4σ
    - RS vs ATLAS: (80,420 - 80,367)/16 ≈ 3.3σ
    
    The RS prediction is closest to CDF, but suggests a small
    experimental offset in the CDF measurement. -/
theorem w_mass_sigma_comparison :
    ∃ (sigma_rs_sm sigma_rs_cdf sigma_rs_atlas : ℝ),
      sigma_rs_sm > 10 ∧ sigma_rs_sm < 15 ∧
      sigma_rs_cdf > 1 ∧ sigma_rs_cdf < 2 ∧
      sigma_rs_atlas > 2 ∧ sigma_rs_atlas < 4 := by
  use (80420 - 80357 : ℝ) / 6, (80433.5 - 80420 : ℝ) / 9.4, (80420 - 80367 : ℝ) / 16
  constructor
  · norm_num
  constructor
  · norm_num
  constructor
  · norm_num
  constructor
  · norm_num
  constructor
  · norm_num
  · norm_num

What this page does not claim

The declaration does not verify the ATLAS measurement's accuracy. The declaration does not claim the ATLAS value is incorrect. The declaration does not derive the ATLAS number from the phi-ladder.

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/Cosmology/WMassAnomalyStructure.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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