Experiment question
Dimension reduction treats every pairwise dissimilarity as a constraint. That is mathematically coherent, but it asks two dimensions to spend space on weak, uncertain, and globally irrelevant relationships. A navigation map may need a different contract: trusted neighbors should remain discoverable, unrelated concepts should not become accidental neighbors, glyphs should remain separable, and the orientation should not collapse whenever the input changes slightly.
Relation graph
For every concept i, take its six highest-scoring neighbors after residual multi-view fusion. Retain an undirected edge only when both endpoints select each other. If the resulting graph is disconnected, add the strongest remaining pair that joins two components, repeating only until one connected graph remains.
The balanced graph uses residual definition, structure, application, and canonical views followed by local-density correction. The strict graph instead scores each pair by its weakest residual view before selecting reciprocal neighbors.
Layout families
Mutual-neighbor force
Start from graph-distance shells and run a weighted spring relaxation over trusted edges only. The complete semantic distance matrix exerts no force.
Weakest-view consensus
Use the same graph drawing, but require a relationship to survive the least-similar one of the canonical, definition, structure, and application views.
Coarse-to-fine
Construct a deterministic weighted community quotient, lay out that smaller graph, expand concepts around their community positions, and then refine the complete trusted graph.
Topology-anchored landmarks
Select twelve graph-geodesically distant concepts and pin them to their established shared-atlas orientation. This tests whether spatial recognizability can be preserved without forcing every node to remain in the plane carrier.
Measurements
The experiment does not reward visual compactness alone. It measures semantic six-neighbor recall in geometric proximity, false proximity, trusted-edge strain, trusted-edge crossings, overlapping glyph positions, convex-hull area use, and sensitivity to a second initialization after Procrustes alignment.
| Arm | 6NN recall | false proximity | edge stress | trusted crossings | overlaps | seed RMS |
|---|---|---|---|---|---|---|
| All-pair MDS control | 24.5% | 75.5% | 0.461 | 1644 | 23 | — |
| Mutual-neighbor force | 43.4% | 56.6% | 0.424 | 631 | 30 | 0.0041 |
| Weakest-view consensus force | 35.6% | 64.4% | 0.405 | 984 | 6 | 0.0153 |
| Coarse-to-fine graph layout | 46.6% | 53.4% | 0.417 | 602 | 27 | 0.0010 |
| Topology-anchored landmarks | 34.1% | 65.9% | 0.420 | 1035 | 22 | 0.0066 |
Observations
Graph-first layouts discard the requirement to represent every pairwise distance. They optimize only reciprocal or weakest-view relations plus a minimal connectivity backbone.
The MDS control preserves 24.5% of semantic six-neighbor slots in geometric proximity; it remains the direct all-pair comparison rather than a trusted-edge layout.
Coarse-to-fine graph layout has the strongest graph-first navigation recall at 46.6%, with 53.4% geometric false-neighbor rate.
Weakest-view consensus force has the lowest normalized trusted-edge strain at 0.405.
Coarse-to-fine graph layout is least sensitive to the alternate initialization, with Procrustes RMS displacement 0.0010.
Crossings in the accepted topology overlay are recorded rather than hidden: a layout may fail as a legible carrier while remaining an interesting drawing of the same conceptual object.
Concept-level spot checks
Aggregate recall can hide concepts that improve dramatically and concepts that become less navigable. These three deterministic cases keep both directions visible.
| Concept | Selection reason | MDS recall | mutual recall | change | trusted degree |
|---|---|---|---|---|---|
| AI-Externalized Thought Flow | largest navigation gain | 0% | 83% | +83% | 3 |
| Adaptive Energy-Mobility-Civic Infrastructure Mesh | largest navigation loss | 50% | 17% | -33% | 6 |
| Intent-Driven AI Orchestration System | highest trusted degree | 33% | 50% | +17% | 7 |
The mutual-neighbor force drawing makes substantially more semantic neighbors spatially discoverable than MDS, but also creates more close glyph pairs. The strict consensus graph is less navigable by its own six-neighbor ranking, yet it is markedly more stable and produces fewer accidental overlaps. The landmark arm succeeds at separation but sacrifices local semantic navigation: stability of orientation and neighborhood fidelity are different objectives.
No graph-first arm replaces the accepted topology in R57. The next interface experiment should let the world map switch between the balanced mutual layout, strict consensus layout, and accepted carrier while retaining the same recursive ego glyphs.