Mercury(I) Sulfide as a Pe Boundary: Spectral Gap Resolution of the Guibourt–Brande Compound/Mixture Debate

Mercury(I) sulfide (Hg₂S) has been classified alternately as a compound and a mixture since Guibourt (1816) and Brande (1825). We resolve this debate using the Péclet number framework: Hg has Pe = 0 (electron affinity ≈ 0, relativistic 6s² shell closure — a noble gas analog), while S has Pe = 0.909. The Hg₂S system sits at the spectral gap boundary. Applying Kramers escape theory (§48E), we derive E_b = 83.6 kJ/mol and a compound/mixture crossover temperature T_cross = 273.0 K — cold preparations are compounds (λ₁·τ < 1), room-temperature preparations are mixtures (λ₁·τ > 1). Both Guibourt and Brande were correct at their respective temperatures. We extend to five further predictions: Group 12 relativistic trajectory (Cn as super-noble-gas, IE = 11.97 eV), Cooper coherence crossover for Hg₂²⁺ (ξ = 1.23 nm), Eckert holonomy of 21.9 rad (3.5 turns) for irreversible disproportionation, mercury mass-independent fractionation (MIF) as a continuous τ_pair function across five channels (1.00–1.89), and alchemical convergence (nigredo/rubedo as Pe phase identity). The Arctic marine MIF signal at R = 1.25 is resolved as the MeHg photodemethylation channel, not an anomaly. Kill conditions K-HG2S-1 through K-HG2S-6: 6/6 PASS.