A Theoretically Grounded Spiking Neural Network Architecture for Real-Time Intracortical Signal Processing: Epistemological Foundations, Mathematical Guarantees, and Falsifiable Predictions for Closed-Loop Brain-Computer Interfaces

Epistemological Position. This work adopts a critical rationalist stance: theoretical claims are formulated as conjectures subject to empirical falsification, with quantitative thresholds specified a priori. Mathematical guarantees are derived from explicitly stated axioms, and all approximations are bounded with error terms. Motivation. Closed-loop brain-computer interfaces (BCIs) require decoding algorithms that simultaneously satisfy: (i) millisecond-scale temporal precision matching cortical dynamics; (ii) adaptation to non-stationary neural statistics over chronic implantation; (iii) calibrated uncertainty estimates enabling risk-aware control; and (iv) energy efficiency compatible with fully implantable hardware. Existing approaches trade biological fidelity for computational tractability, limiting clinical translation. Theoretical Contributions. We introduce a mathematically rigorous framework advancing five dimensions:(i) Biophysical spike generation: Generalized linear model with refractory and coupling terms, proven to satisfy absolute continuity with respect to Poisson measures;(ii) Stochastic neuronal dynamics: Leaky integrate-and-fire model with channel noise, admitting unique strong solutions with exponential moment bounds;(iii) Provably stable plasticity: Weight-dependent STDP rule with Lyapunov-certified convergence under bounded inputs;(iv) Calibrated uncertainty readout: Bayesian inference layer with epistemic/aleatoric decomposition and finite-sample calibration guarantees;(v) Hardware-guided sensitivity: Variance-based global sensitivity analysis with statistical consistency bounds informing neuromorphic co-design. Analytical Results. We establish: (a) information-theoretic upper bounds on decoding capacity; (b) computational complexity lower bounds approaching event-driven optimality; (c) sublinear error scaling with spike count variance (α = 0.62 ± 0.08); and (d) uncertainty-behavior correlation thresholds (r > 0.7) for closed-loop safety. Falsifiable Predictions. Three quantitatively precise, experimentally testable conjectures:[P1] SNN decoding error scales as NRMSE ∝ σ_spikes^α with α ∈ [0.54, 0.70] under controlled spike jitter;[P2] Trial-by-trial predictive variance correlates with behavioral endpoint error: r ∈ [0.67, 0.79], p < 10^-5;[P3] Neuromorphic implementation achieves ≤ 10 μJ per inference versus ≥ 50 μJ for GPU baselines.Empirical contradiction of these intervals necessitates model revision. Validation Approach. All theoretical results are validated through reproducible simulations using high-fidelity synthetic data calibrated to published clinical statistics from BrainGate2 and NeuroTycho consortia. No human or animal subjects were involved in this study. Keywords: spiking neural networks, intracortical brain-computer interfaces, Bayesian inference, uncertainty quantification, global sensitivity analysis, neuromorphic computing, theoretical guarantees, falsifiability, epistemological foundations