Lattice-Loll: Phase-Uncorrelated Sub-Machine Behavior in Resonance Graph Core Processors, Observable in FPGA In-System Logic Analyzer Captures

We introduce lattice-loll as the name for the phase-uncorrelated, free-running behavior of synchronous sub-machines within a Resonance Graph Core (RGC) processor. Individual internal phases drift relative to one another, yet the collective output remains externally coherent and correctly framed. This phenomenon is directly observable at gate-level resolution in Vivado In-System Logic Analyzer (ILA) captures of an operating 115200-baud UART transmitter on a Digilent Arty A7-100T FPGA running the Etymos 49-core gold bitstream (v4.12). Nine ILA captures taken on 12 May 2026 document the staggered transitions of the baud-rate counter carry-chain stages and data shift register, while the external TX line shows only clean, properly framed bytes. The term distinguishes the framing of this behavior (phase-uncorrelated sub-machines producing coherent system-level output) from the well-known engineering fact of carry-chain timing offsets in synchronous digital design. Lattice-loll is hypothesized to be the small-scale signature of the partial non-computability claimed for Tav topology in the Tau Universe framework: multiple sub-systems running at their own internal phases, with the externally observable output remaining deterministic yet fundamentally inaccessible in full internal detail. A clear falsification condition is stated: if scaling the RGC to hundreds or thousands of cores causes the phase-uncorrelated behavior to statistically average out to synchronous-equivalent operation, the scaling hypothesis fails. Conversely, persistence (or amplification) of lattice-loll at larger scales would strengthen the analogy to the framework-level halting-problem embeddings. This work provides the first empirical documentation of lattice-loll in a live RGC processor and supplies a precise, testable link between observed FPGA behavior and the broader Tau Universe claims of partially non-computable resonance graphs.