# Finite-k sample-size scaling panel

This is a nested-dataset empirical panel for the repository's fixed `k=3` ResNet. It tests finite-size smoothing and direction-wise recovery, but it cannot estimate the growing-rank exponent of arXiv:2605.14567.

| optimizer | descriptive tail slope | final-n median risk |
|---|---:|---:|
| gd | -0.5362 | 0.25918 |
| muon_a0 | -0.3807 | 0.10382 |
| muon_a1_7_transfer | -0.7789 | 0.069477 |
| muon_a1_3_normalized | -0.5211 | 0.08954 |

The fitted slope uses only the four largest sample sizes and is descriptive. A theorem-facing scaling panel must let the latent rank grow with ambient dimension and reproduce the lifted `D ~ d^q` construction.