This pre-registration protocol outlines a maiden out-of-sample test of the continuous variance scaling law on a simulated first-order regulator, with no simulation results yet available.
This pre-registration specifies the maiden out-of-sample test of the GTRS ratio scaling law on a simulated first-order regulator, reversing a previous collapse-threshold framing.
Description: A pre-registration — no simulation has been run at deposit. It specifies the maiden out-of-sample test of the GTRS ratio ρ = τ_σ/τR. The registered claim is a continuous variance scaling law, Var (ẽ) = σq²τ_σ²/ (ρ (ρ+1) ) — monotone, a 3× rise from ρ=2 to ρ=1, with no kink or collapse 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, which was removed. The protocol pre-registers five named failure modes and a power floor, and adjudicates Q1 on the exact moment-ODE ground-truth 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 result is a run-time outcome that does not yet exist. Claim history (collapse threshold → scaling law) is documented in the accompanying Master Registry note. Generative process: synthesis — Claude (Anthropic) ; steelman — Kimi; adversarial — DeepSeek; verification independent numerical confirmation — Benjamin, Harper; HATI² 87. 5/100 — Gemini. Author: John Richard Smith.
John Richard Smith (Sat,) reported a other. Simulated First-Order Regulator was evaluated on Continuous variance scaling law, Var(ẽ) = σ_q²τ_σ²/(ρ(ρ+1)). This pre-registration protocol outlines a maiden out-of-sample test of the continuous variance scaling law on a simulated first-order regulator, with no simulation results yet available.