Level Λ Law

The Level Λ Law gives each level's cosmological constant from its own pixel count: the Holographic Pixel Bound read toward the vacuum. The Local Pixel Count at level L is 16 × 2^(2L) pixels, each one bit, and at our level it equals the horizon's capacity S◎ / ln 2 with no Λ in its derivation; since S◎ = 3π / (Λ ℓ_P²), the count fixes Λ. At L = 202 the law gives Λ ℓ_P² = 2.1 × 10⁻¹²² against the measured 2.9 × 10⁻¹²², the same factor of 1.4 the Pixel Bound leaves to the base multiplier and the conversion from nats to bits. Λ in Planck units is also close to one over the square of the universe's age, a coincidence cosmology has long noted, so the law earns its place by deriving its factor, not by the power of two alone. It predicts a far stronger Vacuum Pressure in a shallow universe: Λ ℓ_P² ≈ 1.8 × 10⁻²² at level 36. Formally, Λ · ℓ_P² = 3 · π / (16 · ln(2) · 2^(2 · L)), where Λ [𝕃⁻²] is the cosmological constant of a universe at level L, ℓ_P [𝕃] its Planck length and L [∅] its level: [∅] = [∅]. It connects to Holographic Pixel Bound, Local Pixel Count (Level N), Rupture Rule, Null Vacuum and Vacuum Pressure.

Category: Manuscript

Chapter: Chapter 3

Importance Level: