Vol3 Section 259 · P-COSMO-Λ-1 through P-COSMO-Λ-5

Λ = π/((3⁷)³⁶ × 36×5) — No Free Parameters

Λ_UFOT ≈ 1.017×10⁻¹²² Planck units. 36 = 2²×3² tier crossings. 180 = 36×5 self-reference. The degree bridge embeds the tier count.

Λ_UFOT
1.017×10⁻¹²²
same order as Planck 2018
·
36 Crossings
2²×3² = 6²
4 spacetime dims × 3² each
·
Propositions
5
P-COSMO-Λ-1 to P-COSMO-Λ-5
The Derivation

Λ from the {2,3,5,π} lattice alone

The cosmological constant emerges from 36 dimensional tier crossings at the atomic factor 3⁷=2187, scaled by the degree bridge 180/π=36×5/π. The self-reference: 36 appears twice — as crossing count and embedded in 180.

P-COSMO-Λ-1
Λ = π / (180 × (3⁷)³⁶) ≈ 1.017 × 10⁻¹²²
= π/(2²×3²⁵⁴×5) | 36 = 4 spacetime dims × 3² | 180 = 36×5 (self-reference)
Observed Λ ≈ 2.888×10⁻¹²² — same order of magnitude
Registered Propositions

Key Results

P-COSMO-Λ-1

Λ = π/(180×(3⁷)³⁶) ≈ 1.017×10⁻¹²². No free parameters.

P-COSMO-Λ-2

36 = 2²×3² = (4 spacetime dims) × (3² atomic crossings each).

P-COSMO-Λ-3

Self-reference: 180 = 36×5. The tier count 36 is embedded in the degree bridge. Λ emerges when the dimensional tier count reaches the value already in the angular conversion.

P-COSMO-Λ-4

Canonical form: Λ = π/((3⁷)³⁶×36×5). Exact {2,3,5,π} identity. No free parameters. Λ is a geometric identity of the prime lattice.

Cross-references: Vol3 Section 259 | Section 260 (degree domain) | Section 257 (tier structure)