chi2_improvement_significant
plain-language theorem explainer
The chi-squared improvement from the ILG model over standard Lambda-CDM exceeds 10, supplying a quantitative bound on the Hubble tension resolution. Cosmologists comparing early- and late-universe H0 inferences would cite this threshold. The proof is a one-line wrapper that unfolds the precomputed improvement value and verifies the inequality by numerical normalization.
Claim. The improvement in the chi-squared goodness-of-fit statistic under the ILG modification satisfies $13.58 > 10$.
background
The module formalizes the RS/ILG resolution of the Hubble tension, in which the ILG kernel shifts the late-time Hubble constant inference while leaving the early-universe sound horizon unchanged. The quantity delta_chi2_improvement is defined as the concrete real number 13.58 measuring the reduction in fit discrepancy relative to Lambda-CDM. Upstream results supply the explicit value together with the amplitude definitions used in the broader S-matrix and interference contexts that frame the same recognition composition law.
proof idea
The proof is a one-line wrapper that unfolds the definition of the chi-squared improvement and applies norm_num to confirm the numerical inequality 13.58 > 10.
why it matters
This theorem supplies the chi2_good field of the hubble_tension_cert certificate, which records that the tension metric drops from approximately 4 sigma to 1 sigma while the sound horizon remains preserved. It fills the quantitative step in the Hubble-Tension paper asserting that late-time ILG modifications reconcile the measurements without disturbing early-universe physics. The result aligns with the Recognition Science landmarks that the eight-tick octave and phi-ladder structure remain intact under the same forcing chain.
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