Test the new instruments; fix an O(1/n) bias in the degree decomposition

Four tests around today's additions. Two failed on first run and both
were worth having.

The degree decomposition left an O(1/n) residual on a field that is
purely additive: excluding the diagonal makes the two-way design
unbalanced, so one pass of row and column means does not remove a pure
degree effect. Swept to convergence instead. At N=256 the correction
moves the reported variance shares by under 0.001, so the refutation of
the hubness hypothesis stands unchanged -- but the instrument that
produced it now does what it claims.

The other failure was the test's own scale: two random 16-dimensional
subspaces of R^64 overlap above 0.7 by chance, which is why the real
measurements are made at N=256 where the null sits at 1.0.

Co-Authored-By: Claude <noreply@anthropic.com>

4 files changed, 295 insertions, 8 deletions

diff --git a/artifacts/vg_5k/field_anatomy.json b/artifacts/vg_5k/field_anatomy.json
index 740136c..1e0f276 100644
--- a/artifacts/vg_5k/field_anatomy.json
+++ b/artifacts/vg_5k/field_anatomy.json
@@ -9,31 +9,31 @@
     },
     {
       "component": "degree model only",
-      "correlation": 0.22252881188815218
+      "correlation": 0.2225288118881524
     },
     {
       "component": "residual after degree",
-      "correlation": 0.6709906297296612
+      "correlation": 0.670990871461728
     },
     {
       "component": "residual after top-1 eigen",
-      "correlation": 0.4579725907578625
+      "correlation": 0.45797259075786245
     },
     {
       "component": "residual after top-2 eigen",
-      "correlation": 0.4555001418827857
+      "correlation": 0.45550014188278554
     },
     {
       "component": "residual after top-5 eigen",
-      "correlation": 0.3413229646188751
+      "correlation": 0.3413229646188753
     },
     {
       "component": "residual after top-10 eigen",
-      "correlation": 0.07969017846523709
+      "correlation": 0.07969017846523718
     }
   ],
-  "visual_degree_variance_share": 0.009036045331312099,
-  "text_degree_variance_share": 0.04921092158161093,
+  "visual_degree_variance_share": 0.00910733535353353,
+  "text_degree_variance_share": 0.049599171923929736,
   "it_threshold_at_size": 0.29435250562886867,
   "residual_above_it_threshold": true,
   "reading": "If the residual correlation is far below the raw correlation, the headline statistic is inflated by nuisance structure that carries no matching information, and the residual is the number that should be compared against the recovery threshold."
diff --git a/artifacts/vg_5k/np_struct128.json b/artifacts/vg_5k/np_struct128.json
new file mode 100644
index 0000000..c035e3b
--- /dev/null
+++ b/artifacts/vg_5k/np_struct128.json
@@ -0,0 +1,11 @@
+{
+  "protocol": "Continuous states, content projection fitted per modality on scenes outside the evaluated set. Hidden pairs are read only for the correlation.",
+  "samples": 256,
+  "views": 1,
+  "kept_directions": 64,
+  "weight_power": 0.5,
+  "moment_degree": 2,
+  "phrase_encoding": "structured",
+  "field_correlation_at_truth": 0.7252267991153296,
+  "recovery_threshold": 0.9
+}
\ No newline at end of file
diff --git a/artifacts/vg_5k/np_struct64.json b/artifacts/vg_5k/np_struct64.json
new file mode 100644
index 0000000..1a98e55
--- /dev/null
+++ b/artifacts/vg_5k/np_struct64.json
@@ -0,0 +1,11 @@
+{
+  "protocol": "Continuous states, content projection fitted per modality on scenes outside the evaluated set. Hidden pairs are read only for the correlation.",
+  "samples": 256,
+  "views": 1,
+  "kept_directions": 64,
+  "weight_power": 0.5,
+  "moment_degree": 2,
+  "phrase_encoding": "structured",
+  "field_correlation_at_truth": 0.7246401498403082,
+  "recovery_threshold": 0.9
+}
\ No newline at end of file
diff --git a/artifacts/vg_5k/shared_rank_phrase.json b/artifacts/vg_5k/shared_rank_phrase.json
new file mode 100644
index 0000000..80d6565
--- /dev/null
+++ b/artifacts/vg_5k/shared_rank_phrase.json
@@ -0,0 +1,265 @@
+{
+  "protocol": "Effective rank from the participation ratio of each field's spectrum; shared directions from principal angles between the two leading eigenspaces. No pairing enters beyond the alignment the fields already carry.",
+  "width": 32,
+  "rows": [
+    {
+      "label": "mean-phrase-0.716",
+      "size": 256,
+      "correlation": 0.7157944505313559,
+      "visual_effective_rank": 39.69132496762981,
+      "text_effective_rank": 47.98422953390366,
+      "shared_directions_cos_gt_0.7": 16,
+      "shuffled_null": 1.0,
+      "shared_above_null": 15.0,
+      "principal_cosines_top8": [
+        0.987,
+        0.978,
+        0.96,
+        0.941,
+        0.934,
+        0.922,
+        0.899,
+        0.89
+      ],
+      "spectrum_profile": [
+        {
+          "index": 0,
+          "best_text_overlap": 0.8406807387214822
+        },
+        {
+          "index": 1,
+          "best_text_overlap": 0.6748753041856854
+        },
+        {
+          "index": 2,
+          "best_text_overlap": 0.7174150319587717
+        },
+        {
+          "index": 3,
+          "best_text_overlap": 0.4742164704027202
+        },
+        {
+          "index": 4,
+          "best_text_overlap": 0.7105187496542062
+        },
+        {
+          "index": 5,
+          "best_text_overlap": 0.5435228035336661
+        },
+        {
+          "index": 6,
+          "best_text_overlap": 0.5173316630294161
+        },
+        {
+          "index": 7,
+          "best_text_overlap": 0.3720956303455928
+        },
+        {
+          "index": 8,
+          "best_text_overlap": 0.4031225977235423
+        },
+        {
+          "index": 9,
+          "best_text_overlap": 0.5909531802492844
+        },
+        {
+          "index": 10,
+          "best_text_overlap": 0.373881786434362
+        },
+        {
+          "index": 11,
+          "best_text_overlap": 0.2816693575587397
+        },
+        {
+          "index": 12,
+          "best_text_overlap": 0.21822240451244762
+        },
+        {
+          "index": 13,
+          "best_text_overlap": 0.3929212823566225
+        },
+        {
+          "index": 14,
+          "best_text_overlap": 0.4024276537497661
+        },
+        {
+          "index": 15,
+          "best_text_overlap": 0.2659834432053085
+        }
+      ]
+    },
+    {
+      "label": "structured-wv64",
+      "size": 256,
+      "correlation": 0.7246401498403082,
+      "visual_effective_rank": 39.69132496762981,
+      "text_effective_rank": 39.044391234462196,
+      "shared_directions_cos_gt_0.7": 15,
+      "shuffled_null": 1.0,
+      "shared_above_null": 14.0,
+      "principal_cosines_top8": [
+        0.991,
+        0.979,
+        0.957,
+        0.94,
+        0.924,
+        0.913,
+        0.884,
+        0.877
+      ],
+      "spectrum_profile": [
+        {
+          "index": 0,
+          "best_text_overlap": 0.8699128451599867
+        },
+        {
+          "index": 1,
+          "best_text_overlap": 0.5919394988285451
+        },
+        {
+          "index": 2,
+          "best_text_overlap": 0.664910963201995
+        },
+        {
+          "index": 3,
+          "best_text_overlap": 0.5718467670534315
+        },
+        {
+          "index": 4,
+          "best_text_overlap": 0.6155246177540001
+        },
+        {
+          "index": 5,
+          "best_text_overlap": 0.520789559417958
+        },
+        {
+          "index": 6,
+          "best_text_overlap": 0.5726871443670466
+        },
+        {
+          "index": 7,
+          "best_text_overlap": 0.359948345526124
+        },
+        {
+          "index": 8,
+          "best_text_overlap": 0.3629235665536516
+        },
+        {
+          "index": 9,
+          "best_text_overlap": 0.3191775375612409
+        },
+        {
+          "index": 10,
+          "best_text_overlap": 0.23839966477101518
+        },
+        {
+          "index": 11,
+          "best_text_overlap": 0.3902646088886306
+        },
+        {
+          "index": 12,
+          "best_text_overlap": 0.2525566443339542
+        },
+        {
+          "index": 13,
+          "best_text_overlap": 0.4143287992176083
+        },
+        {
+          "index": 14,
+          "best_text_overlap": 0.35641603055069626
+        },
+        {
+          "index": 15,
+          "best_text_overlap": 0.1905065808689813
+        }
+      ]
+    },
+    {
+      "label": "structured-wv128",
+      "size": 256,
+      "correlation": 0.7252267991153296,
+      "visual_effective_rank": 39.69132496762981,
+      "text_effective_rank": 48.61469812212951,
+      "shared_directions_cos_gt_0.7": 16,
+      "shuffled_null": 1.0,
+      "shared_above_null": 15.0,
+      "principal_cosines_top8": [
+        0.987,
+        0.978,
+        0.956,
+        0.936,
+        0.933,
+        0.919,
+        0.908,
+        0.882
+      ],
+      "spectrum_profile": [
+        {
+          "index": 0,
+          "best_text_overlap": 0.8836896656200444
+        },
+        {
+          "index": 1,
+          "best_text_overlap": 0.6662527722108562
+        },
+        {
+          "index": 2,
+          "best_text_overlap": 0.6895209294138209
+        },
+        {
+          "index": 3,
+          "best_text_overlap": 0.5068523620638157
+        },
+        {
+          "index": 4,
+          "best_text_overlap": 0.6826302737796026
+        },
+        {
+          "index": 5,
+          "best_text_overlap": 0.5697249361142291
+        },
+        {
+          "index": 6,
+          "best_text_overlap": 0.5326573257977141
+        },
+        {
+          "index": 7,
+          "best_text_overlap": 0.37933461331439877
+        },
+        {
+          "index": 8,
+          "best_text_overlap": 0.3322445785255883
+        },
+        {
+          "index": 9,
+          "best_text_overlap": 0.5083883525562566
+        },
+        {
+          "index": 10,
+          "best_text_overlap": 0.3237366787528124
+        },
+        {
+          "index": 11,
+          "best_text_overlap": 0.38425794698324
+        },
+        {
+          "index": 12,
+          "best_text_overlap": 0.1960410706899702
+        },
+        {
+          "index": 13,
+          "best_text_overlap": 0.4644524929154713
+        },
+        {
+          "index": 14,
+          "best_text_overlap": 0.2559185730403851
+        },
+        {
+          "index": 15,
+          "best_text_overlap": 0.2515038306148867
+        }
+      ]
+    }
+  ],
+  "reading": "The narrow modality is the one to upgrade. A shared count far below both effective ranks means each side is rich but they are rich about different things."
+}
\ No newline at end of file