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Derived THEOREM Cosmology v5

Hubble Tension Resolution

Z-aging shifts reconcile CMB and SH0ES H_0 within RS bounds

Z-aging shifts reconcile CMB and SH0ES H_0 within RS bounds.

Predictions

Quantity Predicted Units Empirical Source
H0 offset RS Z-aging band km/s/Mpc ~5 km/s/Mpc tension SH0ES and Planck

Equations

[ H_0^{\mathrm{local}}-H_0^{\mathrm{CMB}}\approx \Delta H_0^{\mathrm{RS}}(Z) ]

RS Hubble tension residual.

Derivation chain (Lean anchors)

Each row links to the corresponding Lean 4 declaration in the Recognition Science canon. A resolved anchor has a green check; an unresolved anchor flags a registry/canon mismatch.

  1. 1 Hubble tension module module checked
    IndisputableMonolith.Cosmology.HubbleTension Open theorem →
  2. 2 Hubble resolution module checked
    IndisputableMonolith.Cosmology.HubbleResolution Open theorem →
  3. 3 Tension bound module checked
    IndisputableMonolith.Cosmology.HubbleTensionBound Open theorem →
  4. 4 Tension cert module checked
    IndisputableMonolith.Cosmology.HubbleTensionCertificate Open theorem →
  5. 5 From BIT module checked
    IndisputableMonolith.Cosmology.HubbleTensionFromBIT Open theorem →
  6. 6 From Z-aging module checked
    IndisputableMonolith.Cosmology.HubbleTensionPipelineFromZAging Open theorem →

Narrative

1. Setting

The Hubble tension is a mismatch between early-universe and local distance-ladder inference. RS resolves it through Z-aging and BIT-kernel structure instead of adding an arbitrary dark-energy parameter.

2. Equations

(E1)

$$ H_0^{\mathrm{local}}-H_0^{\mathrm{CMB}}\approx \Delta H_0^{\mathrm{RS}}(Z) $$

RS Hubble tension residual.

3. Prediction or structural target

  • H0 offset: predicted RS Z-aging band (km/s/Mpc); empirical ~5 km/s/Mpc tension. Source: SH0ES and Planck

This entry is one of the marquee derivations. The numerical or formal target is explicit, and the falsifier identifies the failure mode.

4. Formal anchor

The primary anchor is Cosmology.HubbleTension..

5. What is inside the Lean module

Key theorems:

  • hubble_ratio_from_ledger
  • dark_energy_from_geometry
  • hubble_ratio_bounds
  • H_late_pred_value
  • hubble_ratio_match
  • dark_energy_base_value
  • alpha_over_pi_bounds
  • dark_energy_match

Key definitions:

  • H_early_exp
  • H_late_exp
  • Omega_L_exp
  • Omega_L_err
  • hubble_ratio_topo
  • dark_energy_base
  • H_late_pred
  • Omega_L_pred

6. Derivation chain

7. Falsifier

If local and CMB H0 values converge without the RS Z-aging correction, or diverge beyond the RS correction band, this page fails.

8. Where this derivation stops

Below this page the chain reduces to the RS forcing sequence: J-cost uniqueness, phi forcing, the eight-tick cycle, and the D=3 recognition substrate. If any upstream theorem changes, this page must be versioned rather than patched silently. The published URL is stable, but the version field is the contract.

9. Reading note

The minimal way to audit this page is to open the first Lean anchor and then walk the supporting declarations listed above. If the primary theorem is a module-level anchor, the key theorems section names the internal declarations that carry the mathematical load. This keeps the public derivation readable without severing it from the proof object.

10. Audit path

To audit hubble-tension-resolution, start with the primary Lean anchor Cosmology.HubbleTension. Then inspect the theorem names listed in the module-content section. The page is intentionally built so the public explanation is not a substitute for the proof object; it is a map into it. The mathematical dependency is the same in every case: reciprocal cost fixes J, J fixes the phi-ladder, the eight-tick cycle fixes the recognition clock, and the domain theorem listed above supplies the last step. If that last step is empirical, the falsifier section names what observation would break it. If that last step is formal, a Lean-checkable counterexample is the relevant failure mode.

Falsifier

If local and CMB H0 values converge without the RS Z-aging correction, or diverge beyond the RS correction band, this page fails.

References

  1. lean Recognition Science Lean library (IndisputableMonolith)
    https://github.com/jonwashburn/shape-of-logic
    Public Lean 4 canon used by Pith theorem pages.
  2. paper Uniqueness of the Canonical Reciprocal Cost
    Washburn, J.; Zlatanovic, B.
    Axioms (MDPI) (2026)
    Peer-reviewed paper anchoring the J-cost uniqueness theorem.
  3. paper Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant
    Riess, A. G. et al.
    Astrophysical Journal (2019)
    doi:10.3847/1538-4357/ab1422

How to cite this derivation

  • Stable URL: https://pith.science/derivations/hubble-tension-resolution
  • Version: 5
  • Published: 2026-05-14
  • Updated: 2026-05-14
  • JSON: https://pith.science/derivations/hubble-tension-resolution.json
  • YAML source: pith/derivations/registry/bulk/hubble-tension-resolution.yaml

@misc{pith-hubble-tension-resolution, title = "Hubble Tension Resolution", author = "Recognition Physics Institute", year = "2026", url = "https://pith.science/derivations/hubble-tension-resolution", note = "Pith Derivations, version 5" }