Cosmology Wmass Anomaly Structure W Mass Anomaly Resolved

The resolution claim

The W boson is one of the carriers of the weak nuclear force, and its mass has been a source of tension in particle physics. In 2022, the CDF collaboration at Fermilab measured the W mass as 80,433.5 ± 9.4 MeV, a value about 7σ above the Standard Model prediction of 80,357 ± 6 MeV derived from global electroweak fits. A later ATLAS measurement in 2024 gave 80,367 ± 16 MeV, consistent with the Standard Model but also within 2σ of the CDF value. The question is whether the CDF result points to new physics or to an experimental systematic error.

In the Recognition Science framework, the W mass is not a free parameter. The framework models the electroweak scale as a rung on a φ-ladder, a discrete hierarchy of masses related by powers of the golden ratio φ ≈ 1.618. The declaration w_mass_anomaly_resolved packages this modeling into a single machine-checked theorem. It asserts the existence of four numbers: an RS prediction for the W mass in the interval 80,400 to 80,450 MeV, the Standard Model prediction of 80,357 MeV, the CDF measurement of 80,433.5 MeV, and the ATLAS measurement of 80,367 MeV. The theorem also records that the anomaly is explained, in the sense that a value around 80,420 MeV lies between the Standard Model and CDF values.

The framework's prediction of about 80,420 MeV sits 1.4σ from the CDF value and 3.3σ from the ATLAS value. That statistical comparison is also part of the formalized statement. The interpretation offered is that the true W mass is intermediate between the Standard Model and CDF values, with CDF carrying a small positive offset and ATLAS a small negative offset. The resolution is therefore not an appeal to new particles or exotic physics; it is a claim that the φ-ladder electroweak scale is the correct physical value.

What the declaration does not claim is just as important. The theorem does not prove that the CDF anomaly is real; it assumes the anomaly as a premise and packages a resolution within the framework's structure. It does not establish that the φ-ladder prediction is correct, only that a number in the stated interval exists. The comparison to measurements is an empirical check, not a derivation from first principles. The declaration also does not claim that the Standard Model is wrong; it treats the SM prediction as one input among several. The framework's claim is narrower: given its own scale structure, the W mass should be near 80,420 MeV, and the anomaly is a reflection of that structure rather than evidence for new physics.

theorem w_mass_anomaly_resolved : WMassAnomalyResolution :=
  ⟨⟨80420, by norm_num, by norm_num⟩,
   ⟨80357, rfl⟩,
   ⟨80433.5, rfl⟩,
   ⟨80367, rfl⟩,
   trivial⟩

/-- **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

/-- **T-005 φ-Ladder Position**: The W boson mass position on the
    RS mass hierarchy (φ-ladder).
    
    The W mass is related to other electroweak-scale masses through
    φ-scaling relationships. -/
theorem w_mass_phi_ladder_position :
    ∃ (r_W : ℤ),
      r_W > 12 ∧ r_W < 18 := by
  -- W boson sits at approximately rung 15 of the φ-ladder
  -- This places it between the Z boson and top quark
  use 15
  constructor
  · norm_num
  · norm_num

What this page does not claim

The CDF anomaly is real and not an experimental artifact. The φ-ladder prediction for the W mass is correct. The Standard Model is wrong or incomplete. The framework derives the W mass from first principles without any input from measured values.

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.

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