{
  "absolute_threshold": 0.6,
  "case_studies": [
    {
      "code": "C040",
      "id": "centralized-local-food-systems",
      "observation": "Its sixth-ranked relation is only 0.383; the rank lens still draws six direct relations.",
      "role": "Weak forced edge",
      "title": "Centralized/local food systems"
    },
    {
      "code": "C150",
      "id": "post-car-choreographed-flow-city",
      "observation": "Its strongest relation is 0.597, below the fixed threshold, so the absolute lens draws none.",
      "role": "Threshold boundary isolate",
      "title": "Post-Car Choreographed Flow City"
    },
    {
      "code": "C012",
      "id": "ai-externalized-thought-flow",
      "observation": "It has 46 direct relations at the fixed threshold, showing why absolute topology can saturate.",
      "role": "Dense threshold region",
      "title": "AI-Externalized Thought Flow"
    },
    {
      "code": "C143",
      "id": "persistent-ai-mediated-externalized-cognition-loop",
      "observation": "Three-hop reach changes from 18 to 114 when membership changes from rank to absolute similarity.",
      "role": "Largest reach divergence",
      "title": "Persistent AI-Mediated Externalized Cognition Loop"
    }
  ],
  "concept_count": 184,
  "decisions": [
    {
      "decision": "retain as baseline",
      "lens_id": "ranked-path",
      "reason": "It guarantees a bounded, stable navigation signature, but the page labels its variable sixth-edge strength so rank is not read as distance."
    },
    {
      "decision": "retain as an absolute-connectivity lens",
      "lens_id": "absolute-threshold",
      "reason": "Its zero-degree nodes and variable degree expose evidence that forced rank suppresses, while its dense-component reach warns against using it as the only navigation topology."
    },
    {
      "decision": "retain as the main bounded gradient",
      "lens_id": "origin-affinity",
      "reason": "It preserves comparable reach membership while directly answering whether each reached node remains similar to the selected origin."
    },
    {
      "decision": "keep experimental",
      "lens_id": "path-cohesion",
      "reason": "It can expose coherent routes and bridges, but averaging across a path can conceal one weak edge and needs comparison with bottleneck scoring."
    }
  ],
  "field_correlations": [
    {
      "correlation": 1.0,
      "left_id": "ranked-path",
      "right_id": "ranked-path"
    },
    {
      "correlation": 0.5369116930216292,
      "left_id": "ranked-path",
      "right_id": "absolute-threshold"
    },
    {
      "correlation": 0.9137294128623814,
      "left_id": "ranked-path",
      "right_id": "origin-affinity"
    },
    {
      "correlation": 0.9530801419764421,
      "left_id": "ranked-path",
      "right_id": "path-cohesion"
    },
    {
      "correlation": 0.5369116930216291,
      "left_id": "absolute-threshold",
      "right_id": "ranked-path"
    },
    {
      "correlation": 1.0,
      "left_id": "absolute-threshold",
      "right_id": "absolute-threshold"
    },
    {
      "correlation": 0.6320413151057935,
      "left_id": "absolute-threshold",
      "right_id": "origin-affinity"
    },
    {
      "correlation": 0.5284848168347531,
      "left_id": "absolute-threshold",
      "right_id": "path-cohesion"
    },
    {
      "correlation": 0.9137294128623813,
      "left_id": "origin-affinity",
      "right_id": "ranked-path"
    },
    {
      "correlation": 0.6320413151057934,
      "left_id": "origin-affinity",
      "right_id": "absolute-threshold"
    },
    {
      "correlation": 0.9999999999999998,
      "left_id": "origin-affinity",
      "right_id": "origin-affinity"
    },
    {
      "correlation": 0.8994497141342255,
      "left_id": "origin-affinity",
      "right_id": "path-cohesion"
    },
    {
      "correlation": 0.9530801419764422,
      "left_id": "path-cohesion",
      "right_id": "ranked-path"
    },
    {
      "correlation": 0.5284848168347532,
      "left_id": "path-cohesion",
      "right_id": "absolute-threshold"
    },
    {
      "correlation": 0.8994497141342255,
      "left_id": "path-cohesion",
      "right_id": "origin-affinity"
    },
    {
      "correlation": 1.0,
      "left_id": "path-cohesion",
      "right_id": "path-cohesion"
    }
  ],
  "lens_count": 4,
  "lenses": [
    {
      "caution": "Six relations are guaranteed even when all are weak.",
      "claim": "bounded navigational identity; membership does not claim that the sixth neighbor is absolutely close",
      "direct_degree": {
        "count": 184,
        "maximum": 6.0,
        "mean": 6.0,
        "median": 6.0,
        "minimum": 6.0,
        "q10": 6.0,
        "q90": 6.0,
        "zero_count": 0
      },
      "field_nonzero_fraction": 0.2924149338374291,
      "graph": "ranked",
      "id": "ranked-path",
      "interpretation": "A stable local identity and bounded navigator. Variation in the weakest shown edge reveals how much absolute meaning rank discards.",
      "label": "Nearest six · path product",
      "non_root_strength": {
        "count": 9716,
        "maximum": 0.8551723373977896,
        "mean": 0.3303801059723837,
        "median": 0.295254969729683,
        "minimum": 0.0902817791972039,
        "q10": 0.1845816520531647,
        "q90": 0.5392153521312013,
        "zero_count": 0
      },
      "score": "path-product",
      "status": "baseline",
      "three_hop_reach": {
        "count": 184,
        "maximum": 94.0,
        "mean": 53.80434782608695,
        "median": 54.0,
        "minimum": 17.0,
        "q10": 32.0,
        "q90": 78.0,
        "zero_count": 0
      }
    },
    {
      "caution": "Dense regions can dominate reach and sparse regions disappear.",
      "claim": "absolute connectivity; concepts with no qualifying edge remain visibly isolated and dense regions may have more than six edges",
      "direct_degree": {
        "count": 184,
        "maximum": 46.0,
        "mean": 7.195652173913044,
        "median": 3.0,
        "minimum": 0.0,
        "q10": 0.0,
        "q90": 21.700000000000017,
        "zero_count": 43
      },
      "field_nonzero_fraction": 0.3231332703213611,
      "graph": "absolute-threshold",
      "id": "absolute-threshold",
      "interpretation": "A literal view of qualifying similarity. Isolation and dense degree are results rather than rendering failures.",
      "label": "Cosine ≥ 0.60 · path product",
      "non_root_strength": {
        "count": 10756,
        "maximum": 0.855172,
        "mean": 0.3809164830770111,
        "median": 0.37765245696349997,
        "minimum": 0.22050349505518768,
        "q10": 0.2490946778926733,
        "q90": 0.6115165,
        "zero_count": 0
      },
      "score": "path-product",
      "status": "keep",
      "three_hop_reach": {
        "count": 184,
        "maximum": 118.0,
        "mean": 59.45652173913044,
        "median": 79.0,
        "minimum": 1.0,
        "q10": 1.0,
        "q90": 109.70000000000002,
        "zero_count": 0
      },
      "threshold": 0.6
    },
    {
      "caution": "It ignores whether several independent paths support the relation.",
      "claim": "bounded reach membership with intensity set by each reached concept's direct cosine similarity to the selected origin",
      "direct_degree": {
        "count": 184,
        "maximum": 6.0,
        "mean": 6.0,
        "median": 6.0,
        "minimum": 6.0,
        "q10": 6.0,
        "q90": 6.0,
        "zero_count": 0
      },
      "field_nonzero_fraction": 0.2561141304347826,
      "graph": "ranked",
      "id": "origin-affinity",
      "interpretation": "A bounded topology whose gradient asks whether every reached node remains directly similar to the original focus.",
      "label": "Nearest-six reach · origin affinity",
      "non_root_strength": {
        "count": 9716,
        "maximum": 1.0,
        "mean": 0.2444152188143269,
        "median": 0.222086,
        "minimum": 0.0,
        "q10": 0.0,
        "q90": 0.5109160000000001,
        "zero_count": 1229
      },
      "score": "origin-affinity",
      "status": "keep",
      "three_hop_reach": {
        "count": 184,
        "maximum": 94.0,
        "mean": 53.80434782608695,
        "median": 54.0,
        "minimum": 17.0,
        "q10": 32.0,
        "q90": 78.0,
        "zero_count": 0
      }
    },
    {
      "caution": "A mean can conceal one weak bridge edge.",
      "claim": "bounded reach membership with intensity set by the candidate's mean cosine similarity to every earlier concept on its chosen path",
      "direct_degree": {
        "count": 184,
        "maximum": 6.0,
        "mean": 6.0,
        "median": 6.0,
        "minimum": 6.0,
        "q10": 6.0,
        "q90": 6.0,
        "zero_count": 0
      },
      "field_nonzero_fraction": 0.2923558601134216,
      "graph": "ranked",
      "id": "path-cohesion",
      "interpretation": "A contextual gradient that rewards candidates compatible with all earlier nodes on their selected route.",
      "label": "Nearest-six reach · path cohesion",
      "non_root_strength": {
        "count": 9716,
        "maximum": 1.0,
        "mean": 0.41506612951145877,
        "median": 0.41186750000000005,
        "minimum": 0.0,
        "q10": 0.23627616666666673,
        "q90": 0.5963035,
        "zero_count": 2
      },
      "score": "path-cohesion",
      "status": "experimental",
      "three_hop_reach": {
        "count": 184,
        "maximum": 94.0,
        "mean": 53.80434782608695,
        "median": 54.0,
        "minimum": 17.0,
        "q10": 32.0,
        "q90": 78.0,
        "zero_count": 0
      }
    }
  ],
  "maximum_depth": 3,
  "oracles": {
    "absolute_threshold_permits_zero_degree": true,
    "bounded_intensity_lenses_preserve_ranked_membership": true,
    "every_lens_spans_every_origin": true,
    "every_strength_is_calibrated": true,
    "forced_rank_has_constant_direct_degree": true
  },
  "report_fingerprint": "sha256:0e6f06560d283ce9b10e2e5ca696ed9d79f43b7d33344b57352749e6e4785c80",
  "sixth_similarity_histogram": [
    {
      "count": 18,
      "label": "<0.45"
    },
    {
      "count": 18,
      "label": "0.45–0.50"
    },
    {
      "count": 33,
      "label": "0.50–0.55"
    },
    {
      "count": 45,
      "label": "0.55–0.60"
    },
    {
      "count": 36,
      "label": "0.60–0.65"
    },
    {
      "count": 34,
      "label": "≥0.65"
    }
  ],
  "snapshot_id": "sha256:3d58c75318b5e9786f57910940dea086c7b594a867beead2f671d7ee4b330e02",
  "source_ego_world_fingerprint": "sha256:1a9d7ce82cef6dd110c641ea579549d54f50ff3f77ba8f610ae704902b6e2299",
  "source_ego_world_version": "recursive-ego-world-r59-connectivity-lenses",
  "threshold_degree_histogram": [
    {
      "count": 43,
      "label": "0"
    },
    {
      "count": 47,
      "label": "1–2"
    },
    {
      "count": 24,
      "label": "3–5"
    },
    {
      "count": 30,
      "label": "6–11"
    },
    {
      "count": 26,
      "label": "12–23"
    },
    {
      "count": 14,
      "label": "24+"
    }
  ],
  "version": "ego-connectivity-experiment-v1"
}