Maiden Out-of-Sample Test of the ρ = τ_σ/τ_R Scaling Law on a Simulated First-Order Regulator

Description (abstract): A pre-registration — no simulation has been run at time of deposit. It specifies the maiden out-of-sample test of the GTRS regulatory ratio ρ = τ_σ/τ_R. The registered claim is a continuous variance scaling law, Var(ẽ) = σ_q²τ_σ²/(ρ(ρ+1)) — monotone, with a 3× rise from ρ=2 to ρ=1, and no kink or collapse event at ρ=1, which is the timescale balance point only. This reverses the original collapse-threshold framing: ρ is a dimensionless timescale ratio carrying no amplitude information, so a sharp band-exit event could only be manufactured via a tunable knob, and that route was removed. The protocol pre-registers four named failure modes and a power floor, and adjudicates Q1 on firewall ground-truth ρ rather than the noisy estimator ρ̂. The variance law is confirmed analytically and by two mutually independent numerical SDE integrations prior to deposit. A high design score certifies the protocol's honesty, not the framework's vindication; the ρ̂-vs-CSD question remains a run-time result. Generative process: Synthesis — Claude (Anthropic); steelman — Kimi; adversarial — DeepSeek; verification & numerical re-derivation — Grok; independent numerical confirmation — Benjamin, Harper; HATI² scoring — Gemini (87.5/100). Author: John Richard Smith.