Resonance Graph Core (RGC) Architecture: An Asynchronous Hardware Embodiment of the Tav Manifold with Sevenfold S1 Topology for High-Dimensional Manifold Mapping and Resonance-Based Attractor Computing

We present the Resonance Graph Core (RGC), an asynchronous, clockless digital hardware architecture that physically embodies the Tav Manifold — a sevenfold S¹ topological model derived from the Tau Universe cosmological framework. The core comprises seven processing elements arranged in a closed circular topology with 360°/7 phase quantization enforced by gate-delay-based asynchronous handshakes. Computation proceeds via a self-propagating wavefront that settles into a stable lattice-loll global attractor. The design is hierarchically recursive (7 → 49 → 294 → wafer-scale), accepts a 174-bit input vector, and produces a 99-bit topological projection upon convergence. A 294-core FPGA embodiment (Xilinx Artix-7) has been reduced to practice and simulated in Vivado, confirming the predicted 142857-mode heartbeat and emergent phase-locking behavior. The architecture is protected by U.S. Provisional Patent Application No. 64/060,172 (Confirmation No. 9854), filed May 7, 2026. This work unifies concepts from Pharis Williams' Dynamic Theory, Tav topology, and modern asynchronous computing, offering a concrete hardware substrate for high-dimensional manifold mapping, optimization, and resonance-based attractor computing.