# U1 — training size matters, and a depth/length decline remains

On the frozen artificial cross-document chains, increasing training from256 to2048 improves depth16 centered cosine by0.07094 (paired conditional95% interval[0.06973,0.07218]). At matchedN2048, all-slot centered cosine falls from0.6631 atdepth2 to0.1341 atdepth16. Comparing only the same first2 target slots still gives a depth16−depth2 change of−0.30291 [−0.30668,−0.29901]. These are fixed-cohort ridge results, not a general information-capacity limit. Depth jointly changes token length and content count, and artificial concatenations differ from natural paragraphs.

| Depth | Ridge raw cosine | Ridge centered cosine | Mean raw cosine | Ridge retrieval@128 | Direct-chain retrieval@128 | Shuffled-ridge retrieval@128 |
|---:|---:|---:|---:|---:|---:|---:|
| 2 | 0.6999 | 0.6631 | 0.3141 | 0.9990 | 0.9927 | 0.0078 |
| 4 | 0.5516 | 0.4778 | 0.3138 | 0.9744 | 0.9263 | 0.0107 |
| 8 | 0.4092 | 0.2841 | 0.3137 | 0.5664 | 0.6571 | 0.0087 |
| 16 | 0.3414 | 0.1341 | 0.3142 | 0.0295 | 0.2891 | 0.0084 |

The depth16 mean baseline raw cosine is92% as large as ridge raw cosine. A raw-cosine floor therefore includes substantial anisotropic baseline similarity. Mean-predictor centered cosine is intentionally undefined; all learned/direct centered endpoints are defined. All four registered prediction events occurred, with probabilities/Brier scores retained.

The primary retrieval task draws distractors from other chains. It therefore tests constituent identification against unrelated alternatives and does not require distinguishing positions inside the same chain. Direct-chain vectors outperform ridge on raw retrieval atdepth8/16 despite poorer reconstruction cosine. This is evidence that metric/estimator choice matters: weak ridge retrieval cannot be equated with absence of encoded information. A separately frozen posthoc diagnostic will add same-chain distractors and centered retrieval.

Every slot was scored. Atdepth16/N2048 centered cosine decreases from0.404/0.317 atslots1/2 toward approximately0.01 at the last slots. This is a position-sensitive association under the current model/data/budget, not proof of irreversible loss. Per-slot rows and predictions remain available. All actual input lengths passed the no-truncation gate: maximum322 tokens against model limit514. Real-target oracle retrieval is1.0 for every condition.

Data:57344 unique source documents and exact sentence strings,3584 master chains with2048train/512calibration/1024test. Bootstrap resamples test master chains only, conditional on this training/calibration/source allocation. No source-document leakage was found in the independent allocation check. The historical natural depth16 reconstruction instead has only3 test documents and overlapping windows; its aggregate curve is not interchangeable with U1.

Code/protocol/data hashes were frozen at02:15:26 UTC after independent review. The algebra recovery/shuffled-label and oracle fixtures passed. Saved predictions arefloat64, matching the metric computation. Full reconstruction inputs, token counts, candidate IDs, preprocessing, alpha choices and per-item measurements are retained. Independent result audit reproduced all32 cells, per-slot metrics/R2 and calibration alpha selections from retained arrays (reviews/U1_AGGREGATE_INDEPENDENT_CHECK.json); it did not rerun full forwards or the bootstrap. The original results are not modified by follow-up analyses.