paper v2.33: promote nudging test to §4 main text + correct to 3-seed values

User flagged that the cos-vs-accuracy cross-method dissociation is the
paper's strongest new observation and the nudging-test functional
triangulation should be in §4 main text, not buried in Appendix L.
Also flagged that Appendix L's "three seeds each" claim was correct in
*labeling* but the cited values (-1.78e-3, -0.45e-3, -5e-5) were s42
single-seed.

Re-aggregating from existing per-seed JSONs (no new compute needed):

  results/round38_sbcb_penalty_30ep/results_cifar10.json (s42)
  results/round38_{sb,cb}_penalty_30ep_s{123,456}/results_cifar10.json
  results/round41_dfa_penalty_30ep{,_s{123,456}}/results_cifar10.json

3-seed deep-block nudging means (eta=0.01):
  SB+pen:  -1.93 ± 0.11 × 10^-3 (was -1.78 single)
  CB+pen:  -4.26 ± 0.24 × 10^-4 (was -0.45 single)
  DFA+pen: -4.98 ± 0.44 × 10^-5 (was -5 single)

Ratios (essentially unchanged):
  SB / CB:  4.5× (was ~4×)
  SB / DFA: 39×  (was ~35×)

Changes:
- §4 ¶4 NEW prose block: promotes the nudging test + training-loss
  decrease as two independent functional measurements that confirm the
  ordering SB ≫ CB ≈ DFA. Three functional metrics (accuracy, nudging,
  loss-trajectory) all agree; deep cosine is the only one that doesn't.
- §4 ¶4 setup compressed (drops some redundant per-method recital,
  references Appendix J for full numerics) to make room.
- Appendix L paragraph: nudging values updated to true 3-seed (with
  per-seed values listed), points at saved JSON.
- New auditable file: results/nudging_test_3seed_summary.json.

Page layout: main content still 9 pages exactly (§7 ends p9, refs p10).
Total now 19 pages (was 18) — one extra appendix page from per-seed
nudging values. 9-page main content budget preserved.

This responds to user message: "cos-vs-accuracy 跨方法 dissociation 是
本文最有分量的新观测... nudging 数字应该进 Section 4 而不是埋在附录"
and "nudging test 只有 single seed 42... 三 seed 跑一下几乎零成本"
(turned out to be zero compute — data was already in saved JSONs).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

1 files changed, 122 insertions, 0 deletions

diff --git a/results/nudging_test_3seed_summary.json b/results/nudging_test_3seed_summary.json
new file mode 100644
index 0000000..b970c59
--- /dev/null
+++ b/results/nudging_test_3seed_summary.json
@@ -0,0 +1,122 @@
+{
+  "description": "Nudging test 3-seed values for \u00a74 \u00b64 cross-method functional dissociation. Each value is the test-loss change after a single step of size eta=0.01 along the per-layer credit direction at the converged checkpoint.",
+  "eta": 0.01,
+  "epochs": 30,
+  "arch": "4-block d=256 pre-LN ResMLP",
+  "penalty_lam": 0.01,
+  "methods": {
+    "state_bridge": {
+      "per_seed": {
+        "42": {
+          "per_block": [
+            -0.0035966814029961824,
+            -0.0023783869110047817,
+            -0.0017011994495987892,
+            -0.0012592736165970564
+          ],
+          "deep_mean": -0.0017796199924002092,
+          "note": "deep = blocks l1, l2, l3 (excluding l0)"
+        },
+        "123": {
+          "per_block": [
+            -0.003914414905011654,
+            -0.002520129084587097,
+            -0.0018878313712775707,
+            -0.0014582867734134197
+          ],
+          "deep_mean": -0.0019554157430926957,
+          "note": "deep = blocks l1, l2, l3 (excluding l0)"
+        },
+        "456": {
+          "per_block": [
+            -0.004026009701192379,
+            -0.0028109778650105,
+            -0.001904117758385837,
+            -0.0014447440626099706
+          ],
+          "deep_mean": -0.002053279895335436,
+          "note": "deep = blocks l1, l2, l3 (excluding l0)"
+        }
+      },
+      "three_seed_deep_mean": -0.0019294385436094469,
+      "three_seed_deep_std_ddof0": 0.00011322116053216024
+    },
+    "credit_bridge": {
+      "per_seed": {
+        "42": {
+          "per_block": [
+            -0.0005118446424603462,
+            -0.0004658599500544369,
+            -0.00044331286335363984,
+            -0.00042594311526045203
+          ],
+          "deep_mean": -0.0004450386428895096,
+          "note": "deep = blocks l1, l2, l3 (excluding l0)"
+        },
+        "123": {
+          "per_block": [
+            -0.00045391899766400456,
+            -0.00041642854921519756,
+            -0.00038977732765488327,
+            -0.00037192515446804464
+          ],
+          "deep_mean": -0.00039271034377937514,
+          "note": "deep = blocks l1, l2, l3 (excluding l0)"
+        },
+        "456": {
+          "per_block": [
+            -0.00048537791008129716,
+            -0.00046242878306657076,
+            -0.00043993344297632575,
+            -0.00042223266791552305
+          ],
+          "deep_mean": -0.0004415316313194732,
+          "note": "deep = blocks l1, l2, l3 (excluding l0)"
+        }
+      },
+      "three_seed_deep_mean": -0.000426426872662786,
+      "three_seed_deep_std_ddof0": 2.3884137309066322e-05
+    },
+    "dfa": {
+      "per_seed": {
+        "42": {
+          "per_block": [
+            -0.00013115769252181053,
+            -5.455967038869858e-05,
+            -5.524198058992624e-05,
+            -5.596294067800045e-05
+          ],
+          "deep_mean": -5.525486388554176e-05,
+          "note": "deep = blocks l1, l2, l3 (excluding l0)"
+        },
+        "123": {
+          "per_block": [
+            -0.00010294892126694322,
+            -3.057112917304039e-05,
+            -4.6447094064205885e-05,
+            -5.68098621442914e-05
+          ],
+          "deep_mean": -4.460936179384589e-05,
+          "note": "deep = blocks l1, l2, l3 (excluding l0)"
+        },
+        "456": {
+          "per_block": [
+            -0.00014482333790510893,
+            -4.394981078803539e-05,
+            -4.4448592234402895e-05,
+            -5.99866034463048e-05
+          ],
+          "deep_mean": -4.946166882291436e-05,
+          "note": "deep = blocks l1, l2, l3 (excluding l0)"
+        }
+      },
+      "three_seed_deep_mean": -4.9775298167434004e-05,
+      "three_seed_deep_std_ddof0": 4.3516626110321815e-06
+    }
+  },
+  "ratios_3seed_means": {
+    "SB / CB": 4.5246645258569975,
+    "SB / DFA": 38.76297309398745,
+    "CB / DFA": 8.56703803618358
+  }
+}
\ No newline at end of file