| Compatible-force row estimates | statement | lemma M.1 | arxiv |
| Same-budget comparison | statement | lemma H.3 | arxiv |
| A nonwinner quadratic bank at the random escape endpoint | statement | lemma U.6 | arxiv |
| Simultaneous alignment and refit gains | statement | corollary U.14 | arxiv |
| Four biased profiles | statement | lemma L.1 | arxiv |
| Raw coupled-bank regularity interface | statement | lemma G.3 | arxiv |
| 4XKX6XPGHE | statement | theorem | arxiv |
| Initial normalized-bank obstruction | statement | lemma H.4 | arxiv |
| Uniform field, loss, and AGOP expansions | statement | lemma U.2 | arxiv |
| Unconditional initial headroom and a same-run gain | statement | corollary U.4 | arxiv |
| A one-winner projection bound at general rank | statement | proposition U.12 | arxiv |
| Exact quadratic cancellation in the actual feature bank | statement | lemma U.7 | arxiv |
| Population subspace learning on a loss plateau | statement | theorem 4.1 | arxiv |
| A probability bound for the boundary-width improvement | statement | corollary U.11 | arxiv |
| Rank-one attained refit risk on the plateau | statement | theorem U.8 | arxiv |
| Common-event and headroom rule | statement | lemma D.1 | arxiv |
| Positive balanced H1 entry releases original risk | statement | lemma N.2 | arxiv |
| One-dimensional weighted trace | statement | lemma G.1 | arxiv |
| Joint SwiGLU alignment and refit gains | statement | corollary 5.2 | arxiv |
| An initial-risk statement at the boundary width | statement | proposition U.10 | arxiv |
| Orthogonal-frame floor | statement | proposition A.1 | arxiv |
| The lower-width, fixed-time obstruction | statement | proposition U.9 | arxiv |
| Frame-to-full-AGOP comparison | statement | lemma K.1 | arxiv |
| Hermite correlation | statement | lemma H.2 | arxiv |
| Expansion, tracking, and escape facts | statement | lemma U.5 | arxiv |
| Escape and the unique first winner | statement | lemma U.1 | arxiv |
| Simultaneous actual AGOP acquisition during a high-loss window | statement | theorem F.1 | arxiv |
| Initial population spectral rank and simplicity | statement | lemma H.1 | arxiv |
| Comparable mixture signals | statement | theorem E.1 | arxiv |
| Tracking up to a fixed comparator time | statement | lemma U.3 | arxiv |
| Full-teacher kink regularity | statement | lemma N.1 | arxiv |
| SwiGLU plateau and leading AGOP alignment | statement | theorem 5.1 | arxiv |
| Dimension-free $H^1$ kink regularity | statement | lemma G.2 | arxiv |
| Complete-prefix entry to same-step release | statement | corollary N.3 | arxiv |
