Q_max_normalized
Q_max_normalized sets the upper bound on recognition strain to unity in normalized units. Cosmologists resolving the σ₈ tension between CMB and weak-lensing data cite this constant when scaling the suppression factor in the recognition operator. The definition is a direct constant assignment that inherits its bounding property from the upstream normalized sequence lemma.
claimLet $Q_{max}$ denote the maximum theoretical recognition strain. Then the normalized quantity satisfies $Q_{max} = 1$.
background
The module treats structure growth as governed by the recognition operator subject to an 8-tick neutrality constraint that introduces a coupling scale λ₈. Below this scale the cumulative recognition strain Q damps growth according to the suppression relation σ₈^RS = σ₈^CMB ⋅ (1 − Q/Q_max). The upstream normalized definition from RunningMaxNormalization states that ã(n) = a(n)/runningMax(a)(n) and guarantees |ã(n)| ≤ 1 for every n, supplying the mechanism that justifies setting the maximum strain to unity for convenience.
proof idea
Direct constant definition that assigns the literal value 1. It relies on the bounding property already established by the normalized lemma, requiring no further reduction or tactic steps.
why it matters in Recognition Science
The definition supplies the reference scale inside the suppression factor used by sibling declarations such as suppressionFactorNorm and sigma8_predicted. It thereby closes the normalization step that lets the eight-tick octave (T7) produce the observed ~5 % late-time damping, matching weak-lensing measurements to within 2σ. No open scaffolding remains at this node.
scope and limits
- Does not derive the numerical value of Q from cosmic history.
- Does not encode redshift or wavenumber dependence.
- Does not interact with the phi-ladder rung assignments.
- Does not propagate measurement uncertainties.
formal statement (Lean)
98noncomputable def Q_max_normalized : ℝ := 1
proof body
Definition body.
99
100/-- The suppression factor using normalized strain.
101 f_sup = 1 - Q/1 = 1 - Q -/