Cosmology Theta Crit From Dimension Eta B Rung Derived Eq

The derived baryon rung

In the Recognition Science framework, the baryon asymmetry of the universe is represented by a quantity called eta_B, which measures the excess of matter over antimatter. The framework places this quantity on a ladder of powers of the golden ratio phi, where each rung of the ladder is an integer exponent. The declaration eta_B_rung_derived_eq establishes that this rung is exactly minus 44.

The derivation works from the spatial dimension. The framework first proves that space has three dimensions. It then defines a gap number as D squared times D plus two, which at D equals 3 gives 9 times 5, or 45. The baryon rung is defined as 1 minus this gap, so 1 minus 45 equals minus 44. This is not a free choice but a forced consequence of the dimension being three, within the framework's axioms.

The theorem is machine-checked, meaning a computer has verified the steps. It also proves that this derived value matches the older definition of the baryon rung, so the new derivation is consistent with what was previously assumed. The same set of theorems shows that the product of the baryon scale and the consciousness threshold equals phi itself, which the framework calls a duality.

What the declaration does not claim is that the number minus 44 has been measured in any experiment. It is a structural result inside the framework, not an empirical prediction. The framework does not claim that the baryon asymmetry of the actual universe is exactly phi to the minus 44; that would be a separate empirical question. The theorem only establishes the internal consistency of the framework's ladder.

theorem eta_B_rung_derived_eq : eta_B_rung_derived = -44 := by
  unfold eta_B_rung_derived A
  norm_num [gap_at_D3]

theorem eta_B_rung_derived_eq : eta_B_rung_derived = -44 := by
  unfold eta_B_rung_derived A
  norm_num [gap_at_D3]

/-- Bridge: the derived rung matches the existing definition. -/
theorem eta_B_rung_derived_matches_old :
    eta_B_rung_derived = BaryonAsymmetryExact.eta_B_rung := by
  rw [eta_B_rung_derived_eq]
  rfl

What this page does not claim

The number minus 44 is not a measured value from any experiment. The framework does not claim the actual baryon asymmetry of the universe equals phi to the minus 44. The declaration does not prove that D equals 3; it relies on that as a prior theorem.

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/ThetaCritFromDimension.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.

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