Theorem: Model 1 record

For every fixed $\lambda \ne 0$, some fixed $\tau >0$ and $\theta =\pi /2$ give

The limiting contrast is positive. At $\lambda =0$, the two record laws agree exactly for every $\epsilon ,\tau ,\theta$.

Proof. Apply Lemma lem:contrast with $d=\left|\lambda \right|d_1$. The edge error is at most $\frac{1}{2}[{\mathcal{E}}_{\epsilon }({\nu }_0;\tau )+{\mathcal{E}}_{\epsilon }({\nu }_1;\tau )]$. At $\lambda =0$, the generator acts only on the common scalar factor.