refresh 2026-08-26T23:00:45Z (53 files)

README.md

@@ -621,6 +621,39 @@ One row per (operator, task combination, property): the with-AIM value, its base
 **Verdict: no detectable change.**
 
 
+<!-- AIM-EXT:BEGIN -->
+### T6 — Probe-size robustness of the representation family
+
+The canonical panel uses the Beetle F8's 32-sentence probe, which at d = 5120 solves a
+5120-dimensional geometry from 32 mean-pooled observations. This table recomputes the same
+properties on a **512-sentence** probe — 16x the observations, from the same forward pass in the
+same run, so nothing but sample size differs — for **2 of the 20 matched pairs** (one task
+combination of every operator, plus a second combination where time allowed).
+
+The question is whether §3.3's conclusion depends on the small probe. It does not: the paired
+with-minus-without difference keeps its sign on **6 of 9** properties, and on
+**5 of 5** in the representation family that carries the
+result.
+
+| property                  |   n_pairs | delta_32 (SD)   | delta_512 (SD)   |   same sign |   pos_32 |   pos_512 | p_sign_32   | p_sign_512   | corr of per-pair deltas   |
+|:--------------------------|----------:|:----------------|:-----------------|------------:|---------:|----------:|:------------|:-------------|:--------------------------|
+| geo_cka_mean              |         2 | 1.155           | 1.053            |           1 |        2 |         2 | 0.5         | 0.5          | —                         |
+| geo_procrustes_mean       |         2 | -1.128          | -1.125           |           1 |        0 |         0 | 0.5         | 0.5          | —                         |
+| geo_subspace_overlap_mean |         2 | 0.7718          | 0.9005           |           1 |        2 |         2 | 0.5         | 0.5          | —                         |
+| geo_svcca_mean            |         2 | 0.6817          | 0.6271           |           1 |        2 |         2 | 0.5         | 0.5          | —                         |
+| geo_cka_late_minus_early  |         2 | 0.8562          | 0.9236           |           1 |        2 |         2 | 0.5         | 0.5          | —                         |
+| ret_identity_p_at_1       |         2 | —               | —                |           1 |        0 |         0 | —           | —            | —                         |
+| ret_procrustes_p_at_1     |         2 | —               | 1.569            |           0 |        0 |         2 | —           | 0.5          | —                         |
+| ret_ridge_p_at_1          |         2 | —               | 1.279            |           0 |        0 |         2 | —           | 0.5          | —                         |
+| ret_gain_over_identity    |         2 | —               | 1.569            |           0 |        0 |         2 | —           | 0.5          | —                         |
+
+`delta_*` columns are the mean paired difference in units of that estimate's own across-checkpoint
+SD, so the two probes are comparable despite estimating different quantities. `corr of per-pair
+deltas` is the correlation between the two probes' per-pair differences: high means the small probe
+is ranking the checkpoints the same way, not merely getting the average sign right.
+<!-- AIM-EXT:END -->
+
+
 ### T5 — Coverage and provenance
 
 **Mechanism (§3.2): 20/20 matched pairs. Property panel (§3.3): 20/20.** Published benchmark scores cover 20/20 — they were transcribed, not measured. A pair with `panel_status = not-run` was not reached before the panel phase's wall-clock deadline; its mechanism result is unaffected.

tables/T6_probe_robustness.csv

@@ -0,0 +1,10 @@
+property,n_pairs,delta_32 (SD),delta_512 (SD),same sign,pos_32,pos_512,p_sign_32,p_sign_512,corr of per-pair deltas
+geo_cka_mean,2,1.1548956786035605,1.052856963588389,1,2,2,0.5,0.5,
+geo_procrustes_mean,2,-1.1278955249640366,-1.1251344425184038,1,0,0,0.5,0.5,
+geo_subspace_overlap_mean,2,0.7718457401767564,0.9004858739866004,1,2,2,0.5,0.5,
+geo_svcca_mean,2,0.6816991126375397,0.6270517733301026,1,2,2,0.5,0.5,
+geo_cka_late_minus_early,2,0.8561516977891644,0.9236081571524252,1,2,2,0.5,0.5,
+ret_identity_p_at_1,2,,,1,0,0,,,
+ret_procrustes_p_at_1,2,,1.568929081105473,0,0,2,,0.5,
+ret_ridge_p_at_1,2,,1.2792042981336624,0,0,2,,0.5,
+ret_gain_over_identity,2,,1.5689290811054724,0,0,2,,0.5,