Cosmology Hubble Tension H Late Pred Value

The predicted late Hubble value

The Hubble constant H0 measures how fast the universe is expanding today. Measurements from the early universe, using the cosmic microwave background, give about 67.4 km/s/Mpc. Measurements from the late universe, using nearby distance ladders, give about 73.0 km/s/Mpc. This gap is the Hubble tension.

In Recognition Science, the framework models the ledger, a discrete record of recognition events, as having 12 edges plus one time direction. The ratio of the dynamic ledger to the static ledger is therefore (12+1)/12, which is 13/12 or about 1.0833. The framework's library of formal theorems proves this ratio follows from its geometry.

Multiplying the early-universe measurement by this ratio gives a predicted late-universe value. The theorem H_late_pred_value proves that this prediction lies strictly between 73.01 and 73.02 km/s/Mpc. The framework's library also proves that this prediction is within 0.05 percent of the late-universe measurement of 73.04, a match of about 0.03 percent.

This is a definitional model with a formal check, not a derivation of the Hubble constant from first principles. The early-universe value 67.4 is taken from observation as an input. The framework does not prove that the tension is resolved; it provides a geometric ratio that matches the observed discrepancy.

/-- Predicted late Hubble value. H_late_pred = 67.4 * (13/12) = 73.01666... -/
theorem H_late_pred_value :
    (73.01 : ℝ) < H_late_pred ∧ H_late_pred < (73.02 : ℝ) := by
  simp only [H_late_pred, H_early_exp, hubble_ratio_topo]
  norm_num

/-- The Hubble Ratio matches observation to within 0.05%.

    pred = 67.4 * (13/12) = 73.0166...
    obs  = 73.04
    |pred - obs| / obs = |73.0166 - 73.04| / 73.04 = 0.00032 < 0.0005 ✓

    This is now PROVEN, not axiomatized. -/
theorem hubble_ratio_match :
    abs (H_late_pred - H_late_exp) / H_late_exp < 0.0005 := by
  simp only [H_late_pred, H_late_exp, H_early_exp, hubble_ratio_topo]
  norm_num

/-- The Hubble ratio 13/12 derives from ledger edge count (12) + time dimension (1). -/
theorem hubble_ratio_from_ledger :
    hubble_ratio_topo = (12 + 1) / 12 := by
  simp only [hubble_ratio_topo]
  norm_num

What this page does not claim

The framework does not prove the Hubble tension is resolved, only that a geometric ratio matches the observed discrepancy. The early-universe value 67.4 is an input from observation, not a derived quantity. The match to 73.04 is a numerical check, not a proof that the model is physically correct.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Cosmology/HubbleTension.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: