Validator-Grade Resolution of P ≠ NP via Spectral Complexity, Certified Numerics, and Cryptographic Provenance

This release presents a complete validator-grade resolution of the P vs NP problem, integrating four rigorously aligned components:• Package A: A formal proof framework establishing P ≠ NP using the Spectral Complexity Operator and parity obstruction analysis.• Package B: A certified numerical validation suite employing interval arithmetic, parity tracking, and spectral flow analysis to empirically confirm key transitions.• Package C: A cryptographic provenance protocol that secures all artifacts using hash manifests, Merkle trees, threshold signatures, and dual timestamping to ensure reproducibility and auditability.• Integrated Manuscript: A comprehensive document that consolidates the logical, computational, and cryptographic components into a unified, verifiable resolution.Each component is independently verifiable, reproducible, and cryptographically sealed. The resolution is designed for long-term integrity, public audit, and institutional archiving.