A Deterministic 49-Core Fixed-Point Logistic Lattice: Engineering Characterization of a Reproducible Computational Substrate

We characterize a 49-core synchronous logistic-map lattice (device “Easter Lilly”) implemented in Q1.23 fixed-point arithmetic on a commodity FPGA (Digilent Arty A7-100T, Xilinx Artix-7). Each core k iterates xn+1 = rk xn (1 − xn ) at a fixed control parameter rk = 3.500 + k/96, so the lattice tiles the period-doubling route to chaos, r ∈ [3.5, 4.0], in parallel and exports raw per-core state over sequence-numbered telemetry. Over a continuous 4,000,000-frame cold-start run (158.73 h, ∼ 6.6 days), the device showed zero sequence anomalies (∆n = 49 exactly, 0 of 3,999,951 frames) and reproduced the canonical logistic phenomenology: the bifurcation cascade and its periodic windows, a finite-time Lyapunov exponent climbing to ln 2 ≈ 0.693 at r = 4, invariant densities approaching the arcsine measure, and a symbolic-entropy profile risingtoward ln 2 in the chaotic bands. Two independent cold-starts agree bit-for-bit over their full common prefix (1,209,644 frames, 0 mismatches), and cross-core correlation and transfer-entropy nulls confirm the 49 cores run as independent maps. The principal result is determinism that is intrinsic to the device: the computation is bit-reproducible across runs whose host-side sampling timing differed substantially. We report exact finite-state cycles only for the 16 cores whose telemetry value fully resolves the internal state, and we document that the 24-bit telemetry is a projection of a wider internal accumulator for the remaining 33. The substrate is a reproducible,drift-free computational lattice; this document makes no claim beyond the measured behavior of the hardware. Context: This work belongs to the engineering track of the Tau Universe Framework (TUF2026). It characterizes a reproducible computational substrate for future resonance-graph and τ-imprint experiments. License: CC BY 4.0