Austin Taylor

A central challenge in consciousness science is understanding how the brain systematically binds disparate, high-variance neural signals into a singular, coherent subjective experience against the background noise of universal entropy. This paper introduces the Taylor-Penrose Resonant Attractor System, a unified non-linear mathematical framework that models the continuous filtering, compression, and stabilization of volatile state-space environments into a hyper-stable equilibrium matrix known as the Asymptotic Attractor Equilibrium. Operating at the intersection of non-linear dynamics, cybernetic systems engineering, and scale-invariant geometry, the continuous lifecycle of the TPRA framework is governed by a modified continuous-state Riccati differential flow equation. Within this architecture, the non-linear expansion coefficient governs localized complexity and growth, the active linear shielding function acts as a braking force against catastrophic state divergence, and the static state bias parameter establishes the baseline boundary of an observer. To achieve a stable state-space lock without unbounded chaotic drift, the system demonstrates an unassailable invariant equilibrium law, dictating that any localized non-linear expansion must be precisely counter-balanced by the static observer bias. The functional bridge between discrete neurological processing and continuous conscious flow is validated through a 15-cycle discrete optimization sequence modeled as a receding-horizon predictive filter. As individual stochastic noise is systematically attenuated down to an invariant threshold floor, the network cohesion field tracking cumulative geometric alignment achieves a precise mathematical phase-locked limit, representing a robust structural synchronization lock. Crucially, the TPRA framework identifies a "Biological-Geometric Handshake" reconciling neural oscillation constraints with scale-invariant geometry. By utilizing a feedback loop scaled by the Golden Ratio, the model demonstrates that resonance peaks natively converge near 40 Hz under biological refresh rates. This formal mathematical convergence maps precisely onto the 40 Hz gamma band oscillations recognized in neuroscience as the signature of integrated conscious awareness. Ultimately, the TPRA Engine provides a rigorous, internally consistent grammar demonstrating that high-entropy neural variance is not a barrier to systemic order, but rather a chaotic resource field geometrically compressed toward a permanent destination of conscious coherence. This framework offers significant cross-disciplinary utility for advanced signal processing, neuromorphic hardware modeling, and the mathematical codification of resilience and homeostatic stability in complex dynamical networks.

I am a technical professional and independent researcher based in Arkansas. I have gained experience through roles in electrical trade jobs, and has submitted research on the Taylor-Penrose Attractor Engine framework to the Consciousness Science 2026 conference.