R59 · measured connectivity comparison
The centroid petals locate each concept against fixed reference directions. The inner stencil asks a different question: which concepts count as connected, and how strongly should reached nodes appear? This experiment holds the world, concepts, embedding matrix, and three-hop limit fixed while changing only that connectivity claim.
No arm is allowed to inherit another arm's interpretation. Rank is a navigation contract, the threshold is an absolute edge rule, origin affinity is a direct-root gradient, and path cohesion is contextual evidence.
bounded navigational identity; membership does not claim that the sixth neighbor is absolutely close
Interpretation. A stable local identity and bounded navigator. Variation in the weakest shown edge reveals how much absolute meaning rank discards.
Do not infer. Six relations are guaranteed even when all are weak.
absolute connectivity; concepts with no qualifying edge remain visibly isolated and dense regions may have more than six edges
Interpretation. A literal view of qualifying similarity. Isolation and dense degree are results rather than rendering failures.
Do not infer. Dense regions can dominate reach and sparse regions disappear.
bounded reach membership with intensity set by each reached concept's direct cosine similarity to the selected origin
Interpretation. A bounded topology whose gradient asks whether every reached node remains directly similar to the original focus.
Do not infer. It ignores whether several independent paths support the relation.
bounded reach membership with intensity set by the candidate's mean cosine similarity to every earlier concept on its chosen path
Interpretation. A contextual gradient that rewards candidates compatible with all earlier nodes on their selected route.
Do not infer. A mean can conceal one weak bridge edge.
A fixed cutoff reveals both genuine isolation and dense regions. Its median direct degree is 3, but it ranges from 0 to 46. The forced-rank baseline always has 6. The second chart shows why that constant degree is not constant evidence: the sixth-ranked similarity varies substantially.
Pearson correlation is calculated over every ordered origin–target pair, with absent reach represented as zero. High correlation means two lenses paint similar fields; it does not mean they make the same scientific claim.
| Lens | Nearest six · path product | Cosine ≥ 0.60 · path product | Nearest-six reach · origin affinity | Nearest-six reach · path cohesion |
|---|---|---|---|---|
| Nearest six · path product | 1.000 | 0.537 | 0.914 | 0.953 |
| Cosine ≥ 0.60 · path product | 0.537 | 1.000 | 0.632 | 0.528 |
| Nearest-six reach · origin affinity | 0.914 | 0.632 | 1.000 | 0.899 |
| Nearest-six reach · path cohesion | 0.953 | 0.528 | 0.899 | 1.000 |
These cases are selected by declared extrema rather than hand-picked for narrative fit.
| Diagnostic role | Concept | Observation |
|---|---|---|
| Weak forced edge | C040 · Centralized/local food systems | Its sixth-ranked relation is only 0.383; the rank lens still draws six direct relations. |
| Threshold boundary isolate | C150 · Post-Car Choreographed Flow City | Its strongest relation is 0.597, below the fixed threshold, so the absolute lens draws none. |
| Dense threshold region | C012 · AI-Externalized Thought Flow | It has 46 direct relations at the fixed threshold, showing why absolute topology can saturate. |
| Largest reach divergence | C143 · Persistent AI-Mediated Externalized Cognition Loop | Three-hop reach changes from 18 to 114 when membership changes from rank to absolute similarity. |
It guarantees a bounded, stable navigation signature, but the page labels its variable sixth-edge strength so rank is not read as distance.
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.
It preserves comparable reach membership while directly answering whether each reached node remains similar to the selected origin.
It can expose coherent routes and bridges, but averaging across a path can conceal one weak edge and needs comparison with bottleneck scoring.