SIP-PREREG-02: Prospective Test of the ρ = τ_σ/τ_R Variance Scaling Law via Direct Timescale Instrumentation (7b-Probe)

Description (deposit abstract)

This is a pre-registered, prospective, falsifiable test of the GTRS variance scaling law

Var(ẽ) = σ_q² τ_σ² / (ρ(ρ+1)),   ρ = τ_σ / τ_R,

whose parameter-free core prediction is the ratio Var(ρ=1)/Var(ρ=2) = 3.0 (with τ_σ held fixed and ρ varied via τ_R). Under this framework ρ=1 is a timescale balance point, not a collapse threshold: the law is smooth and finite through ρ=1.

It is the successor to SIP-PREREG-01 (OSF 10.17605/OSF.IO/Q5HR9), which halted honestly at its negative control when its single-observable (lag-1 autocorrelation) estimator proved structurally unable to recover ρ in the regime τ_σ ≥ τ_R — logged as an anti-portfolio entry. SIP-PREREG-02 is a new, independent registration that (a) replaces the failed estimator with a privileged two-channel probe that instruments τ_σ and τ_R directly, validated by two negative controls (ρ=1 and ρ=2) and a noise-on consistency cross-check, and (b) resolves a calibration defect via factorial isolation. The variance scaling test itself remains the theory test; the probe is an instrumentation-validation step, firewalled from the theory test, which operates on the system response alone.

The deposit fixes the analysis code by SHA-256 prior to any run. The decision rules are pre-committed: the primary hypothesis is confirmed only if the 95% bootstrap confidence interval on the ratio contains 3.0 and excludes a pre-specified set of discriminating alternatives {1.0, 2.0, 2.5, 4.0}; it is falsified if the interval excludes 3.0; otherwise the result is reported as inconclusive. Failure of an instrumentation control or the calibration gate yields an anti-portfolio entry rather than a positive claim.

The freeze rests on internal self-consistency: σ_q² is pinned by a single calibration target (response standard deviation 0.15 at ρ=1), so the ρ=2 standard deviation and the 3.0 ratio are predictions rather than tuned quantities, and both are reproduced analytically, numerically, and by an independent from-scratch reimplementation.

The work was developed through a multi-AI adversarial review pipeline under an independence rule (no contributor evaluates its own work), including steelman, adversarial, independent-verification, and scoring passes; documented limitations are carried forward openly as named debts in the Glassbox tradition, including the central transfer debt — that the privileged probe is not field-deployable and the test establishes the law in simulation while leaving real-data identifiability open.

Generative process: synthesis — Claude (Anthropic); steelman — Kimi; adversarial — DeepSeek; verification & numerical re-derivation — Grok; HATI³ scoring 93/100 — Gemini. Author: John Richard Smith. (The SIP-PREREG-01 record additionally credited independent numerical confirmation to Benjamin and Harper; add them here if they also confirmed 02 — I have not listed contributors who were not part of this study's pipeline.)