# Bregman meets Lévy: Stochastic mirror descent with heavy-tailed noise

**Paper:** *Bregman meets Lévy: Stochastic mirror descent with heavy-tailed noise in continuous and discrete time*

**ORID:** `69IOkVkTQX`  
**Paper source:** [arXiv:2606.03769v1](https://arxiv.org/abs/2606.03769)  
**Source definitions:** LMF (Eq. LMF), SDA (Eq. SDA), Theorems 1, 3, 4, 5, Corollary 1, and the weak Itô theorem in the v1 TeX source.

## Verdict index

| anchored claim | verdict | measured quantity |
|---:|---|---|
| 1 | **VERIFIED** | LMF time-averaged objective gap over horizons and p |
| 2 | **VERIFIED** | LMF stationary last-iterate squared distance over eta and p |
| 3 | **VERIFIED** | LMF first-passage time over δ and p |
| 4 | **VERIFIED** | SDA and LMF time-averaged objective gaps over T and p |
| 5 | **VERIFIED** | SDA iterations until ensemble MSE reaches ε |
| 6 | **VERIFIED** | Pathwise weak-Itô inequality margin with and without correction |

The six claim pages are the only claim pages in this bundle. Every numerical
table is produced by the lane-authored `reproduce.py` run with scalar streaming
updates and fixed seed lists reported on the corresponding page.