Topological Analytical Homeostasis: A Unified Geometric Paradigm for Antifragile AI, Zero-Multiplication Hardware, and Quantum Interconnects

We present Topological Analytical Homeostasis (TAH), a unified computational paradigm that replaces statistical brute force with geometric constraints derived from algebraic graph theory. Grounded in the machine-verified Teixido Envelope (τ=−0.5τ=−0.5), we propose a new class of sparse, multiplication-less architectures. This report consolidates validatory benchmarks across four distinct domains: Artificial Intelligence: Achievement of an Antifragile Stability Ratio of 1.1470 on 174,933 solar events, where predictive performance improved under 30% impulse noise. Neuromorphic Hardware: A gate-level audit demonstrating a 52.3x reduction in logic complexity and 37x energy reduction by replacing MAC units with the Teixido-ISA (Tropical Max-Plus Logic). Quantum Computing: A graph-theoretic routing topology that reduces CNOT gate counts by 2.27x and circuit depth by 1.6x for Quantum Volume tasks. Cybersecurity: A Zero-Shot intrusion detection system achieving 97.1% Recall on zero-day DDoS vectors via Topological Contrast. Commercial Licensing:This preprint establishes prior art for the Teixido-Boreal architecture. Proprietary hardware specifications, RTL blueprints (Verilog/VHDL), and commercial licenses for the Teixido-ISA are available.Contact: jvteixido@liberty.edu