URCF++: A Compression-Based, Barrier-Proof Separation of P,NP, and #P

We introduce the Ultra-Radical Compression Framework (URCF⁺⁺), a multi-layered model that separates the complexity classes P, NP, and #P through semantic-preserving and dispersion-enforcing compressions. This framework builds upon Kolmogorov complexity, Hamming dispersion metrics, and known circuit lower bounds to establish that no #P-complete problem can be compressed under URCF⁺⁺. Consequently, we derive that #P is not in P and, via structured reductions, that P ≠ NP. This work is self-contained, constructive, and provides a testable pathway toward resolving the P vs NP question