Q_effective_calibrated
plain-language theorem explainer
Q_effective_calibrated supplies the numerical value of the effective recognition strain at σ₈ scales by subtracting the ratio of weak-lensing to CMB measurements from unity. Cosmologists testing the σ₈ tension in Recognition Science models would cite this calibrated quantity when comparing predicted suppression to DES and KiDS data. The definition is a direct arithmetic reduction on the two fixed observational constants.
Claim. The effective recognition strain at the σ₈ scale is defined by $Q_ {eff} := 1 - σ_{8,WL}/σ_{8,CMB}$, where $σ_{8,CMB} = 0.811$ from Planck 2018 and $σ_{8,WL} = 0.76$ from combined weak-lensing surveys.
background
Recognition Science resolves the σ₈ tension by introducing cumulative recognition strain Q from eight-tick cycles that suppresses structure growth below the coupling scale λ₈. The module states that σ₈^{RS} = σ₈^{CMB} · (1 - Q/Q_max), with the observed suppression arising from the geometric dilution factor at k ≈ 0.2 h/Mpc. The upstream constants fix the inputs: sigma8_cmb := 0.811 and sigma8_wl := 0.76.
proof idea
The definition is a one-line arithmetic expression that subtracts the ratio of the two supplied σ₈ constants from one. No lemmas are invoked beyond direct reference to sigma8_cmb and sigma8_wl.
why it matters
This value feeds the predicted_ratio definition and the Q_effective_bounds theorem, which confirm that the Recognition Science model matches the observed 5% suppression to within 2σ. It instantiates the eight-tick octave (T7) and the φ^{-5} strain scale at the σ₈ rung, closing the gap between CMB predictions and late-time weak-lensing measurements.
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