Cosmology Baryon Higher Order Correction Factor Lt One

The correction factor

The baryon asymmetry of the universe is the observed excess of matter over antimatter. In the standard cosmological model, the Planck 2018 CMB measurement gives this asymmetry as (6.104 ± 0.058) × 10⁻¹⁰. The Recognition Science framework's leading-order prediction is φ⁻⁴⁴ ≈ 6.376 × 10⁻¹⁰, which overshoots the measured value by about 4.5 percent.

To address this gap, the framework proposes a first-order correction based on an eight-tick cycle, a discrete unit of recognition events. The correction factor is defined as 1 − φ⁻⁸, where φ is the golden ratio. The proved theorem correction_factor_lt_one establishes that this factor is strictly less than 1, meaning the correction reduces the leading prediction. The corrected value is φ⁻⁴⁴ × (1 − φ⁻⁸) ≈ 6.28 × 10⁻¹⁰, which roughly halves the gap to the CMB value.

In Recognition Science, this is a formal result in a machine-checked library of theorems. The theorem itself only proves the inequality: the correction factor is positive and less than 1. It does not prove that the correction is correct, that the mechanism is physical, or that the corrected value matches any measurement. Those are separate claims with different epistemic status.

The physical mechanism behind the correction, the eight-tick washout during the electroweak phase transition, is a HYPOTHESIS with a named falsifier. If precision measurements establish the baryon asymmetry outside [6.0, 6.5] × 10⁻¹⁰ at more than 3σ, the corrected prediction is falsified. The theorem correction_factor_lt_one remains true regardless of any measurement, because it is a statement about the arithmetic of the defined quantities.

/-- The correction factor is less than 1 (since δ > 0). -/
theorem correction_factor_lt_one : correction_factor < 1 := by
  unfold correction_factor
  linarith [delta_pos]

/-- The first-order correction factor: 1 − φ⁻⁸. -/
noncomputable def correction_factor : ℝ := 1 - delta_washout

/-- The first-order corrected baryon asymmetry. -/
noncomputable def eta_B_corrected : ℝ :=
  eta_B_phi_scale * correction_factor

What this page does not claim

The theorem does not prove the correction mechanism is physically real. The theorem does not prove the corrected value matches any measurement. The theorem does not establish the value of the baryon asymmetry itself.

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

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