arXiv:2610.26966v1 Announce Type: new Abstract: We consider nonlinear ill-posed operator equations $F(x)=y$ in a Hilbert space, where $F$ is monotone with a Lipschitz continuous Fr\'echet derivative that is self-adjoint near the solution $x^\dg$ (a locally \emph{potential} operator), and only noisy data $y^\delta$ with unknown noise norm $\delta:=\|y-y^\delta\|$ is available. For the nonstationary iterated Lavrentiev regularization \[ x_{k+1}^\delta=x_k^\delta-\bigl(F'(x_k^\delta)+\alpha_kI\bigr)^{-1}\bigl(F(x_k^\delta)-y^\delta+\alpha_k(x_k^\delta-x_0)\bigr), \] all classical stopping rules require $\delta$. We analyze a \emph{noise-level-free} parameter-choice rule of retrospective type, selecting a minimizer $k_*$ of $\theta(k,y^\delta)=\|F(x_k^\delta)-y^\delta\|^2/\alpha_k^2$ over a finite computed window. Under a standard noise condition (necessary in view of the Bakushinskii veto) the rule is well defined and $\alpha_{k_*}^2\ge c\,\delta/\|x_0-x^\dg\|$. If moreover $x_0-x^\dg\in\R(F'(x^\dg))$ and $k_*\ge1$, we prove $\|x_{k_*}^\delta-x^\dg\|=O(\sqrt{\delta_*}+\sqrt{\delta})$ with the computable $\delta_*=\|F(x_{k_*}^\delta)-y^\delta\|$ satisfying $\kappa\delta\le\delta_*\le C\sqrt\delta$, yielding the baseline rate $O(\delta^{1/4})$ along admissible growing-horizon families, and $O(\sqrt\delta)$ whenever $\delta_*=O(\delta)$; no range-invariance or tangential cone conditions are imposed. Rates under H\"older source conditions with $p\ge1$ (including saturation) follow; the case $p<1$, the removal of the self-adjointness assumption, and a full oracle inequality are identified as open problems.