# Stochastic explicit inequality

## Author claim mapped

Under the stochastic statement’s conditions, the stated inequality is:

`E||G(x_N)||^2 <= 1570 L^2 kappa ||x_0 - x*||^2 / sqrt(N+1) + 8 sigma^2 / (kappa sqrt(N+1))`.

## Scope and source route

- Assumptions, update, and schedule: exactly those listed in `thm:last_iter_stoch_rho0`.
- Statement: `thm:last_iter_stoch_rho0` in `example_paper.tex`.
- Appendix route: `appx:last_iter_stoch_rho0` in `appendix.tex`.
- Evidence tier: source/theorem crosswalk only.

## Pin

Use the TeX archive SHA-256 in [`../hash_manifest.json`](../hash_manifest.json), then inspect the named statement and appendix route.