# Deterministic Case II squared-residual rate

## Author claim mapped

For the stated Case II 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, with a root `x*` satisfying `G(x*) = 0`.
- Update: `eq:goma_square`.
- Statement conditions: `lemma:potential_gamma`.
- Statement: `thm:main_gamma`; displayed bound: `eq:simple_bound_gamma`.
- Appendix route: `appx:main_gamma`, with `lemma:potential_gamma` at `appx:potential_gamma`.
- 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`.