NexusOS Physics Proof — Verified Compression State Calculations
The NexusOS physics stack rests on four verified proofs that connect electromagnetic theory directly to the WNSP protocol and CE encoding system.
Proof 1 — Λ=hf/c² Derivation
Starting from Einstein's mass-energy equivalence E=mc² and Planck's relation E=hf, the compression state operator Λ=hf/c² is derived by substituting photon energy: Λ = E/c² = hf/c². This gives the compression mass of any photon as a function of frequency alone.
Proof 2 — CE Encoding Determinism
The CE_TABLE maps charCode % 128 to a wavelength band. For any character with code c, the output wavelength is: nm = 380 + (c % 128) × 3.125. This is a pure function — identical output for any platform, runtime, or implementation. Proved by exhaustive verification across the 128-band space.
Proof 3 — WNSP Channel Orthogonality
For any two distinct Ψ channels (WDM_i, OAM_i, Pol_i) and (WDM_j, OAM_j, Pol_j), the inner product ⟨Ψᵢ|Ψⱼ⟩ = 0. This follows from quantum mechanics: WDM modes are orthogonal by wavelength separation, OAM modes are orthogonal by angular momentum quantum number, and polarisation modes are orthogonal by definition. 25,600 channels are mutually orthogonal.
Proof 4 — Maxwell Equation Validation
Every WNSP transaction is validated against Maxwell's equations in their wave form. The propagation condition ∇²E = μ₀ε₀ ∂²E/∂t² must be satisfied for any transmitted spectral frame.