Symplectic Cohomological Characterization of Entanglement-Assisted Nucleotide Error Syndromes: Algebraic Stability Bounds for Quantum Information Persistence in Anomalous Biological Substrates

Mathematical Applications of Science Fiction We present a rigorous topological framework for quantifying the persistence of quantum information withinbiological nucleotide sequences, modeled as symplectic manifolds under the influence of non-Hermitianmetabolic Hamiltonians. By constructing a filtered Floer-Novikov cohomology theory for the entanglement-assisted error syndromes, we derive algebraic stability bounds that characterize the resilience of geneticinformation against decoherence in anomalous substrates. We introduce the Nucleotide-Maslov Index andprove that the rank of the symplectic cohomology groups SH∗(N, Eent) provides a lower bound on the numberof stable error-correcting configurations. Furthermore, we establish an isomorphism between the quantumcohomology of the nucleotide phase space and the local entanglement syndrome algebra, generalizing theArnold Conjecture to the context of biological quantum error correction. This work bridges the gap betweensymplectic topology, homological algebra, and quantum biology, offering a predictive model for informationpreservation in high-temperature biological environments.