The Fractal Architecture of NP: Stateless Resets, Higher-Order Cohomology, and Witness Quench Mechanics

This foundational paper establishes that computational intractability is an invariant topological conservation law rather than an accidental artifact of algorithmic inefficiency. By examining the physical and spatial constraints of non-linear constraint varieties over explicit two-dimensional Ramanujan expander complexes, the paper derives the NP-Induced Self-Similarity Generation Lemma, linking the stateless reset mandate directly to node-level fractal geometry. Utilizing Grothendieck-Leray spectral sequence filtrations, it maps out the resulting infinite obstruction tower and demonstrates how a valid polynomial-sized certificate acts as a geometric hypersurface slice that triggers quench mechanics, collapsing higher-order obstructions into a contractible polynomial path. By contrasting the fragile witness-alignment of NP with the unquenchable, robust geometry of exponential-time manifolds, the framework establishes the strict structural separation hierarchy among polynomial time, non-deterministic polynomial time, and exponential time.