HubbleParameterILG
The definition supplies the ILG-corrected Hubble parameter by scaling an early-time input with the locked recognition lag. Cosmologists addressing the Hubble tension would cite this scaling when reconciling CMB-derived values with local measurements. The definition is a direct multiplication that inserts the constant C_lag = phi^{-5} derived from the recognition framework.
claim$H_ {phys} = H_{early} (1 + C_{lag})$ where $C_{lag} = phi^{-5}$ and $phi$ is the self-similar fixed point.
background
The module formalizes Induced Light Gravity corrections to the FRW metric and demonstrates how the recognition lag resolves the Hubble tension. The upstream cLagLock definition supplies the canonical value $C_{lock} = phi^{-5}$. The CPM.LawOfExistence.Constants structure bundles related recognition constants while the various Resolution structures record status of related conjectures.
proof idea
This definition is a one-line wrapper that multiplies the input H_early by (1 + cLagLock) from the Constants module.
why it matters in Recognition Science
This definition is used by the theorem hubble_resolution_converges to demonstrate numerical agreement between scaled CMB and local values. It supplies the explicit ILG correction step inside the cosmology module and connects to the phi-ladder constants where phi^{-5} appears as hbar in native units.
scope and limits
- Does not derive the lag constant from the forcing chain.
- Does not compute numerical Hubble values from first principles.
- Does not address other cosmological parameters such as curvature or dark energy.
Lean usage
let H_late := HubbleParameterILG 67.4formal statement (Lean)
24noncomputable def HubbleParameterILG (H_early : ℝ) : ℝ :=
proof body
Definition body.
25 H_early * (1 + Constants.cLagLock)
26
27/-- **THEOREM: Hubble Tension Resolution**
28 The ILG framework resolves the Hubble Tension by scaling the CMB value
29 (Planck 2018: 67.4 km/s/Mpc) to the local value (SH0ES: ~73.5 km/s/Mpc).
30
31 Prediction: H_late = H_early * (1 + phi^-5)
32 Calculated: 67.4 * (1 + 0.090) = 73.47 -/