pith. sign in
module module high

IndisputableMonolith.Cosmology.HubbleTension

show as:
view Lean formalization →

The Cosmology.HubbleTension module assembles the Hubble ratio of 13/12 from ledger geometry, alpha derivation, and CKM structure. Cosmologists resolving the early-versus-late H_0 discrepancy would cite it as the RS-native bridge between constants and expansion parameters. The module organizes sibling definitions for H_early_exp, H_late_exp, hubble_ratio_topo and related bounds into a single coherent object.

claimThe ratio satisfies $H_mathrm{late}/H_mathrm{early}=13/12$, obtained from topological ledger expressions and the fine-structure constant derived via Gauss-Bonnet on the cubic lattice.

background

Recognition Science sets the fundamental time quantum at τ₀ = 1 tick. Upstream modules supply the alpha derivation from vertex deficits of Q₃ and the CKM mixing angles from ledger geometry. The present module operates inside the cosmology domain, introducing expressions for early and late Hubble parameters together with dark-energy and ratio bounds that rest on the phi-ladder and eight-tick octave.

proof idea

This is a definition module, no proofs. It imports the four supporting modules and declares the family of expressions H_early_exp, H_late_exp, Omega_L_exp, hubble_ratio_topo, dark_energy_base, hubble_ratio_from_ledger and hubble_ratio_bounds.

why it matters in Recognition Science

The module supplies the central ratio that feeds the HubbleTensionCertificate, which registers T-001 as the complete resolution of the Hubble tension. It closes the chain from the alpha derivation and CKM geometry into an observable cosmological prediction.

scope and limits

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (4)

Lean names referenced from this declaration's body.

declarations in this module (18)