Determinism vs. Amplification: Computation by Admissibility, Exact Singular Decomposition, and Non-Invertible Topological Reconnection

This work introduces "Computation by Admissibility" as a deterministic, physical alternative to quantum computing's reliance on combinatorial state exploration and randomness amplification. Rather than expending massive overhead to maintain fragile superpositions and perform active error correction, this framework establishes rigid topological and geometric boundary conditions where the desired solution emerges as the only admissible physical state. The computational substrate is grounded in three-dimensional solenoidal vortex dynamics. Convective vortex stretching accelerates system trajectories toward localized reconnection events, where anomalous inviscid dissipation acts as an irreversible thermodynamic trapdoor, permanently expelling environmental perturbations. In the Deterministic Spectral Manifold (DSM-861) processor architecture, stability is enforced through a dual-layer mechanism: out-of-plane noise is instantaneously annihilated by geometric boundary projection, while in-plane fluctuations are exponentially suppressed by a massive discrete spectral gap. Computation is thus transformed from probabilistic exploration into autonomous physical relaxation down a Lyapunov free-energy landscape, achieving hardware-level fault tolerance without algorithmic overhead or quantum randomness.