IndisputableMonolith.Cosmology.HubbleTensionCertificate
The HubbleTensionCertificate module certifies that the ratio of late-universe to early-universe Hubble constants equals exactly 13/12. Cosmologists studying the tension between CMB and local measurements would cite this exact prediction. The module assembles the result by importing the cosmological-constant derivation and the ledger-geometry formalization of the tension, then exposing the ratio through its sibling declarations.
claimThe Hubble ratio satisfies $H_0^{late}/H_0^{early}=13/12$, where the two Hubble parameters are obtained from the ledger geometry via the imported derivations of the cosmological constant and the early/late tension.
background
The module sits inside the Recognition Science treatment of cosmology. It imports the C-010 derivation of the cosmological constant from ledger geometry and the T13 formalization that extracts both the Hubble tension and dark-energy density from the same geometry. The upstream HubbleTension module states that observations show a discrepancy between Early Universe ($H_{early} approx 67.4$) and late-universe values; the certificate module supplies the exact ratio that removes the discrepancy inside the framework.
proof idea
This is a certificate module whose argument is carried by its sibling declarations. It imports the two upstream modules and then defines hubble_ratio_exact together with supporting lemmas (hubble_ratio_numerator_origin, hubble_ratio_denominator_origin, hubble_match_precision) that reduce the ratio to 13/12 by algebraic identities inherited from the ledger geometry.
why it matters in Recognition Science
The module supplies the certificate for T-001.1 and thereby feeds the parent results in CosmologicalConstantDerivation and HubbleTension. It shows that the observed tension is a direct prediction of the eight-tick octave and the Recognition Composition Law rather than an anomaly. The result closes one link in the chain from the forcing sequence (T0-T8) to observable cosmology.
scope and limits
- Does not incorporate observational error bars or statistical fitting.
- Does not derive absolute Hubble values, only their exact ratio.
- Does not extend the ledger-geometry assumptions to modified gravity or extra fields.
- Does not perform numerical simulations or direct data comparisons.
depends on (2)
declarations in this module (11)
-
theorem
hubble_ratio_exact -
theorem
hubble_ratio_numerator_origin -
theorem
hubble_ratio_denominator_origin -
theorem
hubble_match_precision -
theorem
dual_metric_structural -
theorem
hubble_tension_is_prediction -
theorem
hubble_and_lambda_connected -
theorem
both_predictions_match -
theorem
H_late_precision_bounds -
theorem
ratio_more_robust_than_absolute -
def
T001_certificate