module module high

`IndisputableMonolith.Cosmology.CosmologicalConstantDerivation`

The CosmologicalConstantDerivation module encodes the RS prediction for the vacuum energy density parameter as Ω_Λ = 11/16 - α/π. Cosmologists testing ledger geometry against supernova and CMB data would cite it when comparing the D=3 geometric seed to observed acceleration. The module assembles the central definition together with supporting bounds and positivity statements drawn from upstream registry proofs.

claim$\Omega_\Lambda = \frac{11}{16} - \frac{\alpha}{\pi}$

background

The module operates in the cosmology domain and imports the RS time quantum τ₀ = 1 tick from Constants along with calculated proofs from RegistryPredictionsProved. RegistryPredictionsProved supplies rigorous bounds and verifiable numbers for items in the COMPLETE_PROBLEM_REGISTRY.

It centers on definition C-010, which expresses the dark-energy fraction as the difference between the 11/16 geometric seed (from the three-dimensional forcing ledger) and the α/π correction. Sibling declarations establish that the resulting quantity is positive, bounded above, and well-defined.

proof idea

This is a definition module, no proofs. The structure collects the central C-010 definition, then layers supporting statements on positivity, upper bounds, and well-definedness using the imported registry material.

why it matters in Recognition Science

The module supplies the Ω_Λ expression required by the HubbleTensionCertificate for resolving T-001. It fills the C-010 registry slot by linking the D=3 geometric seed to the observed acceleration scale, providing the input that downstream Hubble-tension arguments consume.

scope and limits

Does not derive the numerical value of alpha from the forcing chain.
Does not incorporate quantum corrections to the vacuum energy.
Does not address time evolution of Ω_Λ.
Does not compare the prediction against specific observational datasets.

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