Fractalyx Vault: Cryptographic Primitives Unified by the Fractal-Stochastic Model (MFSU) with FractalShield Deniable Encryption

This paper presents Fractalyx Vault v1.0, a complete symmetric cryptographic system derived from the Unified Fractal-Stochastic Model (MFSU): ∂ψ/∂t = −δF(−Δ)^(β/2)ψ + γ|ψ|²ψ + ση(x,t). All cryptographic primitives — a memory-hard key derivation function (8 MB scratchpad), a dual-layer stream cipher (fractal field + SHA3-256 whitening), a Merkle-Damgård fractal hash, and a TOTP 2FA module — emerge from the same physical equation with parameters δF=0.921, β=1.079, H=0.541. The centerpiece innovation is FractalShield: an oracle-free, multi-layer deniable encryption scheme where attacker cost escalates geometrically (3.5× / 7.5× / 15.5× per protection level) and all layers are statistically indistinguishable. Empirical validation includes chi-square uniformity tests (p=0.49), Pearson autocorrelation < 0.003, and avalanche effect 49–51% for all primitives. The reference implementation is open-source (Apache 2.0) and distributed as a Python package with CLI and Streamlit web interface.