Wepresent the AOVF-Ω(Asymptotic Obstacle via Frustrated Ω-geometry) framework, a complete, modular, and fully auditable proof that P̸ = NP. The result is unconditional: it does not rely on unproven conjectures beyond the PCP Theorem (Dinur, 2007) and classical results in spectral graph theory and communication complexity. The argument is built around a family of computational problems called Ring-on-a-Chain Frustration (RCFn), defined on the product graph Gm,L = Sm ×CL, where Sm is the LPS Ramanujan expander of degree 8 with m = Θ(n2/3) vertices, and CL is a directed cycle of length L = Θ(n1/3). These problems are NP-complete, and our central contribution is proving that no polynomial-size Boolean circuit family can decide them. The proof has seven independent technical pillars. Pillar U1 establishes a superlinear lower bound T1(n) ≥ Ω(n4/3/logn) for any deterministic singletape Turing machine deciding RCFn, via crossing-sequence analysis. Pillar U2proves that all local Markov chains on the RCFn solution space have exponential mixing time 2Ω(n1/3), establishing Local-P ⊊ NP. Pillar U4 provides an unconditional Resolution lower bound 2Ω(n1/3) for Tseitin–RCF refutations via the Ben-Sasson–Wigderson size-width relation. Pillar H1 establishes the central communication-complexity barrier: CC(KWRCFn ) ≥ C0n4/3/log3n with explicit constant C0 = Cinf = 0.01876, derived from the vertex expansion hVS = 0.15007 of LPS-7 via the Expander Mixing Lemma. Pillar H3 proves that the Ramanujan spectral gap is preserved under PCP gadget insertion, with perturbation O(n−1/6) → 0. Pillar H2 amplifies the single-layer bound via the Braverman–Rao direct-sum theorem for information complexity, yielding CC(KWFd ) ≥ Ω(n5/3/logn) for a composed function Fd that is NP-hard. Pillar L3 establishes a robust soundness gap γ ≥ 1/22 for the reduction from NAE-3SAT to RCFn, ruling out approximate solutions. Assembling these pillars via the Karchmer–Wigderson correspondence between communication depth and circuit depth yields a circuit lower bound of 2Ω(n5/3/log2 n) for an NP-complete function, completing the proof. The framework provably avoids the Relativization [3], Natural Proofs [19], and Algebrization [1] barriers; the precise reasons are analyzed in Section 14.