pith. sign in
def

Q_max

definition
show as:
module
IndisputableMonolith.Cosmology.Sigma8Suppression
domain
Cosmology
line
80 · github
papers citing
none yet

plain-language theorem explainer

Q_max assigns the J-cost of the golden ratio φ as the maximum recognition strain from one 8-tick cycle. Cosmologists modeling the σ8 tension cite this constant to normalize the suppression factor f_sup = 1 - Q/Q_max that reconciles CMB and weak-lensing measurements. The definition is a direct one-line assignment from the imported Jcost function to the constant phi.

Claim. $Q_ {max} := J(φ)$ where $J(x) = (x + x^{-1})/2 - 1$ is the recognition cost function and φ is the golden-ratio fixed point.

background

The Cosmology.Sigma8Suppression module derives σ8 growth suppression from recognition strain Q accumulated over 8-tick cycles, with the formula σ8^RS = σ8^CMB · (1 - Q/Q_max). Jcost is the cost function imported from the Cost module that evaluates the recognition operator J on a ratio; phi is the self-similar fixed point imported from Constants. Upstream results establish J via the recognition composition law and the 8-tick neutrality constraint via the simplicial ledger and primitive distinction axioms.

proof idea

One-line definition that directly applies the Jcost function to the constant phi.

why it matters

Q_max supplies the normalization for the suppression factor used by strainAtScale and suppressionFactor, closing the link from the eight-tick octave (T7) and phi fixed point (T6) to the predicted σ8 match within 2σ. It fills the normalization step in the module's resolution of the σ8 tension between Planck CMB and weak-lensing data.

Switch to Lean above to see the machine-checked source, dependencies, and usage graph.