Interactive Calculators
Enter values → see framework predictions
⚡ Fine Structure Constant
α⁻¹(M_Z) = 2⁷ = 128
The framework predicts α⁻¹ = 128 at the Z boson mass scale from 7 binary dimensions
(6 component bits + 1 actualization bit).
⚛️ Proton-Electron Mass Ratio
m_p / m_e = 6π⁵ = 1836.1181
The proton is a 3-quark braid through 5D subspace.
3! = 6 permutations × π⁵ volume element.
🌍 Gravitational Constant
G = (ℏc / m_p²) / 2¹²⁷
Gravity is Planck-scale coupling screened by 127 nested vacuum layers.
This explains why gravity is 10³⁸ times weaker than EM.
🌿 Fractal Dimension
D = 1 + β
β = balance between convergence and emergence.
β = 0.5 (optimal) → D = 1.5 (observed in LIGO, DNA, coastlines).
0.50
🔬 Lepton Mass Predictor
m(n) = m_e × (α⁻¹)^(2(n-1)/3) × g_n
Generation n determines nesting depth. g_n factors involve φ^(7/2) and D.
Currently phenomenological — derivation is an open problem.
🎲 64-State Explorer
State = (○,•,Φ)_in ⊗ (○,•,Φ)_out
Click bits to toggle. Valid states require 2-of-3 components at each interface.
22 of 64 states are physically stable.
INPUT
○
Φ
•
→
OUTPUT
○
Φ
•
⟶
⚗️ Ionization Energy Predictor
E = -R∞ × Z_eff² / (n+1)² + λ×ℓ(ℓ+1)
Predicts first ionization energy using framework constants.
λ = R∞ × φ⁻⁷ ≈ 0.474 eV (angular penalty from golden ratio).
🌌 Cosmological Constant
Λ ≈ 8πGH₀²/c²
Dark energy from T₃ expansion. Currently off by factor ~3 —
may relate to three temporal dimensions.