module module high

`IndisputableMonolith.Cosmology.CosmologicalConstantDerivation`

This module supplies the RS prediction for the cosmological constant density parameter as Ω_Λ = 11/16 - α/π under definition C-010. Cosmologists addressing dark energy or the Hubble tension would cite it for the geometric derivation from the D=3 ledger. The module assembles the seed term with the fine-structure correction using imported constants and registry predictions.

claimThe Recognition Science prediction for the cosmological constant density parameter is given by $Ω_Λ = 11/16 - α/π$, where 11/16 is the geometric seed from the D=3 ledger and α is the fine-structure constant.

background

Recognition Science derives all physics from the forcing chain T0-T8, with T8 fixing D=3 spatial dimensions and constants such as α^{-1} inside (137.030, 137.039). The module imports the RS time quantum τ₀ = 1 tick from Constants and the calculated proofs for registry predictions from RegistryPredictionsProved. It centers on definition C-010, which states the explicit formula Ω_Λ = 11/16 - α/π with 11/16 = 0.6875 as the geometric seed and α/π ≈ 0.0073 as the correction term.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the Ω_Λ value required by the HubbleTensionCertificate to resolve registry item T-001 on the disagreement between early and late universe H_0 measurements.

scope and limits

Does not derive α from the phi-ladder or J-cost.
Does not incorporate quantum corrections beyond the α/π term.
Does not solve the Friedmann equations or address cosmic evolution.
Does not bound Ω_Λ numerically outside the defining expression.

used by (1)

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

IndisputableMonolith.Cosmology.HubbleTensionCertificate module_import

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Unification.RegistryPredictionsProved module_import

declarations in this module (12)

def Omega_Lambda_RS L85
theorem Omega_Lambda_RS_well_defined L88
theorem Omega_Lambda_lt_upper_bound L93
theorem Omega_Lambda_positive L100
theorem Omega_Lambda_bounds L107
def geometric_seed L121
theorem geometric_seed_pos L124
theorem alpha_over_pi_small L134
theorem Lambda_not_planck_scale L145
theorem Lambda_no_fine_tuning L151
theorem Hubble_from_Omega_Lambda L162
def C010_certificate L183