hubbleTensionCert
This definition assembles the Z-aging Hubble tension certificate by instantiating the HubbleTensionCert structure with the phi^5 identity, numerical bounds on phi^5, the five-channel count, and the empirical band containment. Cosmologists studying the late/early H_0 discrepancy via recognition-field aging would cite it as the A5 closure for the predicted ratio interval containing 1.083. The construction is a direct record instantiation that wires in the upstream lemmas for each field without additional reasoning.
claimLet $r_H$ be the late-to-early Hubble ratio and let $Z$-aging channels be the five configuration dimensions (matter density, radiation density, dark energy, curvature, scalar perturbation). The certificate asserts the identity $phi^5 = 5 phi + 3$, the bounds $11.05 < phi^5 < 11.11$, that the $Z$-aging channel type has cardinality 5, and that the predicted band for $r_H$ contains the empirical central value 1.083.
background
Recognition Science models the Hubble tension as the cumulative effect of $Z$-complexity aging of the recognition field across cosmic time. The module introduces five $Z$-aging channels, each tied to a rung of the phi-ladder, and gives the amplitude formula $r_H = 1 + (1/phi^5) c$ where $phi^5 = 5 phi + 3$ is the Fibonacci identity and $c$ is an amplitude normaliser. The local setting is the A5 precision closure that places the RS prediction inside the empirical SH0ES/Planck interval.
proof idea
This is a definition that constructs the HubbleTensionCert record by direct field assignment: phi5_fibonacci receives the theorem phi5_eq, phi5_lower receives phi5_gt, phi5_upper receives phi5_lt, five_channels receives zAgingChannel_count, and band_contains receives hubbleBand_contains_empirical. No tactics or further lemmas are applied beyond these assignments.
why it matters in Recognition Science
The declaration supplies the Z-aging instance of the Hubble tension certificate that is consumed by the general HubbleTensionCert definitions in the HubbleTensionBound and HubbleTensionFromBIT modules. It closes the A5 claim in the module documentation by verifying that the predicted ratio band contains the empirical value 1.083. In the framework it links the five-channel correction to the phi-ladder mass formula and the eight-tick octave structure.
scope and limits
- Does not derive the five-channel count from the spatial dimension D=3.
- Does not compute the amplitude normaliser c from first principles.
- Does not address the full set of cosmological evolution equations.
- Does not supply error bars or statistical uncertainties on the phi^5 bounds.
formal statement (Lean)
74noncomputable def hubbleTensionCert : HubbleTensionCert where
75 phi5_fibonacci := phi5_eq
proof body
Definition body.
76 phi5_lower := phi5_gt
77 phi5_upper := phi5_lt
78 five_channels := zAgingChannel_count
79 band_contains := hubbleBand_contains_empirical
80
81end IndisputableMonolith.Cosmology.HubbleTensionPipelineFromZAging