Physical Emergence of Riemann Zeros in Dissipative Chaotic Circuits

The Hilbert-Polya conjecture motivates the search for physical operators whose spectra encode Riemann zeta zeros. Here we investigate whether SPICE-simulated non-autonomous chaotic circuits — with realistic component models including multiplier imperfection, op-amp bandwidth limitation, and saturation nonlinearity — exhibit spectral signatures consistent with the first nontrivial Riemann zeros. We employ two complementary extraction methods: Markov eigenphase analysis (6 zeros matched with MAE = 0.54) and a binning-free Hankel Dynamic Mode Decomposition that directly approximates Koopman operator eigenvalues (11 modes matched with MAE = 1.09), overcoming the discretization bottleneck by 3.7x. The eigenphase alignment procedure uses the first zero t1 for single-point scaling and a supervised start-index selection based on the known t1/t2 ratio; subsequent zeros (t3-t11) serve as independent validation. Ratio-based comparison against null baselines (uniform, random, GUE) is consistent with zeta-specific structure under the present protocol, with the SPICE circuit achieving ratio MAE = 0.18 versus 12.67 for uniform spacing. Hardware designs for discrete-component (~80 CNY) and FPGA (Zynq-7020, ~800 CNY) implementations are provided. Preliminary FPGA deployment yields 4 matched zeros (MAE = 1.01) from oscilloscope data, demonstrating feasibility of the simulation-to-hardware pipeline. We emphasise that this spectral correspondence does not constitute a proof or realisation of the Hilbert-Polya conjecture, but provides empirical evidence motivating further investigation of the connection between dissipative chaotic dynamics and the Riemann spectrum.