A Constructive Proof that P = NP via Canonical Symmetric Compression of NP-Complete Instances

We propose a formal framework for resolving the P vs NP problem, based on a synthesisof structural symmetries and deterministic encodings within constraint-satisfaction domains.The key insight is that certain invariants and compressible symmetries inherent in NP-completeproblem instances admit a transformation into deterministic polynomial-time verifiable encod-ings. These encodings exploit self-reducibility, mirror symmetry, and information-theoretic re-dundancy such that the nondeterministic search space collapses into a tractable deterministicconstruction. We construct a fixed-point graph encoding of 3SAT and prove it yields a sound,complete, and polynomial-time decision procedure, whose structure is self-referentially valid andrecursively sufficient.