# Deterministic Case I squared-residual rate

## Author claim mapped

For the stated Case I schedule, the paper gives an `O(1/k^2)` last-iterate bound on `||G(x_k)||^2`.

## Scope and source route

- Assumptions: `G` is monotone and `L`-Lipschitz.
- Update: `eq:goma_triangle`.
- Schedule: `beta_k = 2/(k+6)` and `eta_*` in `(0, 1/(2 sqrt(3)L))`.
- Statement: `thm:main`; displayed bound: `eq:simple_bound`.
- Appendix route: `appx:thm:main`, with `lemma:potential_eta` at `appx:lemma1`.
- Evidence tier: source/theorem crosswalk only.

## Pin

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