Sovereign Mathematics - The Paul Phillips Compendium
1. Interactive 4D-to-3D Golden Ratio (Φ) 600-Cell Projection
Quantum Lattices & Holographic Braids
This live visualization computes the 120 vertices of the 4D regular 600-cell dynamically using the Golden Ratio
Φ = (1 + √5)/2. The coordinates are formed by the 16 tesseract vertices, 8 16-cell vertices,
and 96 even permutations of (±Φ, ±1, ±Φ⁻¹, 0).
By dividing this topology into a 5x5 Rook Grid, we partition it into 5 disjoint 24-cells, enabling O(1) projective addressing via PG(2, 𝔽₄). This guarantees drift-less floating-point accuracy across distributed networks.
The Mathematical Anchor:
// 1. Landau's Operator Identity (Tsirelson's Bound)
B² = 4I + [A₀, A₁][B₀, B₁]
8 = 4 + 4 => |B| ≤ 2√2
// 2. Hurwitz Quaternion Doubling
600-Cell → E₈ Lattice (240 roots)
E₈ ≅ { (q₁, q₂) ∈ I×I : q₁ ≡ q₂ mod (1+i) }
// 3. The Monster Anchor (Twin Primes 71, 73)
d = 71² - 1 = 5040 = 7!
Mined directly from the DCoop / Paul Bachler University Proof Package.
2. F100 Logo Asset Preview & Compositor
Select Math Variation
Asset Canvas Context
Active: Golden Ratio Variant