A cheap gate that survives its controls: the anchor bound

Three statistics failed the same way -- fields agreeing on the number
and disagreeing on recovery -- because each was invented by staring at
the fields rather than by asking what matching needs. The fourth asks
directly: declare half the scenes anchors, hand over their
correspondence, describe the rest by their field rows against the
anchors, and match one-to-one by Hungarian assignment. Seconds to
compute, and it upper-bounds blind recovery because blind recovery must
also discover the anchor correspondence.

Never violated across six fields spanning the full range of outcomes,
and it separates every case the refuted statistics collapsed:

  synth full        bound 0.989  blind 0.958  gap +0.03
  synth noise 0.35  bound 0.984  blind 0.947  gap +0.04
  synth omit size   bound 0.997  blind 0.056  gap +0.94
  synth rank 8      bound 0.930  blind 0.129  gap +0.80
  Visual Genome     bound 0.291  blind 0.000  gap +0.29

This corrects two claims from earlier today. Caption suppression does
not destroy information -- its bound is 0.997 -- it destroys blind
searchability, by making scenes interchangeable under permutation in a
way given anchors break. And Visual Genome's problem was never spectral
width: with the correspondence handed over, seven scenes in ten still
cannot be identified.

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

1 files changed, 66 insertions, 0 deletions

diff --git a/artifacts/vg_5k/anchor_bound.json b/artifacts/vg_5k/anchor_bound.json
new file mode 100644
index 0000000..2de1390
--- /dev/null
+++ b/artifacts/vg_5k/anchor_bound.json
@@ -0,0 +1,66 @@
+{
+  "protocol": "Half the scenes are anchors with their correspondence given. The rest are described by their field rows against the anchors and matched by Hungarian assignment. Upper-bounds blind recovery, which must additionally discover the anchor correspondence.",
+  "rows": [
+    {
+      "label": "synth-full",
+      "correlation": 0.928480988366389,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.9375,
+      "anchor_bound": 0.9890625,
+      "blind_recovery": 0.958,
+      "search_gap": 0.031062499999999993
+    },
+    {
+      "label": "synth-noise035",
+      "correlation": 0.8276655471168534,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.896875,
+      "anchor_bound": 0.984375,
+      "blind_recovery": 0.947,
+      "search_gap": 0.03737500000000005
+    },
+    {
+      "label": "synth-omitsize",
+      "correlation": 0.8301825436675786,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.89375,
+      "anchor_bound": 0.996875,
+      "blind_recovery": 0.056,
+      "search_gap": 0.9408749999999999
+    },
+    {
+      "label": "synth-rank8",
+      "correlation": 0.9058447537972103,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.746875,
+      "anchor_bound": 0.9296875,
+      "blind_recovery": 0.129,
+      "search_gap": 0.8006875
+    },
+    {
+      "label": "natural-best",
+      "correlation": 0.7309253746041517,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.1671875,
+      "anchor_bound": 0.290625,
+      "blind_recovery": 0.0,
+      "search_gap": 0.290625
+    },
+    {
+      "label": "natural-baseline",
+      "correlation": 0.6558829559111277,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.1296875,
+      "anchor_bound": 0.1953125,
+      "blind_recovery": 0.0,
+      "search_gap": 0.1953125
+    }
+  ],
+  "reading": "A low bound means the representation does not identify scenes and no solver will help. A high bound with low blind recovery means the information is present and the search or the landscape is at fault."
+}
\ No newline at end of file