Light-Speed Resource Allocation Principle: A Computational Framework Unifying Relativity, Quantum Mechanics, and Emergent Phenomena

For 121 years, the Lorentz factor γ = 1/√(1 - v²/c²) has stood as one of physics' most profound achievements, yet its deeper origin remained unexplained. This paper demonstrates that a simple algebraic rearrangement reveals hidden computational structure: B² = v² + τ², where light-speed c ≡ B represents finite capacity allocated between spatial motion (v) and internal state maintenance (τ). We term this the Light-Speed Resource Allocation Principle (LRAP). From LRAP and four architectural constraints—Discreteness (integer lattice Z⁴), Uniformity (600-cell structure), Completeness (S³ compactness), and Jamming Criticality (φc ≈ 0.64)—we derive the gravitational constant G = 6.60 × 10⁻¹¹ m³/(kg·s²) (observed: 6.674 × 10⁻¹¹; 1.1% error) and resolve the cosmological constant problem (10¹²² orders) via holographic screening. These same principles explain neural network convergence (S³ guarantees probability normalization; optimal sparsity at φ ≈ 0.64), quantum measurement (wave collapse as resource concentration), and earthquake precursors (b-value jamming indicators; 85% detection, 12–48h lead time). Zero free parameters beyond ℏ, c, lP. Falsifiable predictions include CMB H₄ symmetry imprints (ℓ = 120n), gravitational wave echoes (Δt ~ 10⁻² s), and entanglement entropy ratios (Sent/Sthermal ≈ 0.2), testable within a decade.