Correspondence analysis reveals four major clusters of fifteen properties with overlapping membership.

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• Correspondence analysis reveals four clusters of related properties: Cluster 1 (Contrast, Not-Separateness, Roughness, Alternating Repetition, Good Shape), Cluster 2 (Local Symmetries, The Void, Levels of Scale, Good Shape, Positive Space), Cluster 3 (Boundaries, Strong Centers, Deep Interlock and Ambiguity), Cluster 4 (Simplicity and Inner Calm, Echoes, Gradients, Positive Space).finding0.881
  Statistical grouping of properties based on dependency patterns, enabling deeper understanding of their coherence and interaction.
• The fifteen properties form coherent clusters reflecting deep structural interdependencies rather than independent design principles.claim0.824
• Properties in each cluster appear to be similar or interrelatedclaim0.822
  Interpretive claim that the statistically derived clusters reflect conceptual similarity or interdependence among the properties.
• The features are often organized in geometrically-related clusters that share a semantic relationship.claim0.809
  Decoder cosine similarity maps onto concept similarity.
• Combining visualization and statistical analysis enables deeper understanding of the fifteen properties and their interactions.claim0.794
• The fifteen properties are not independent; they overlap, and each property is partly defined in terms of the other fifteen propertiesclaim0.789
  Meta-claim about the logical structure of the properties: the more carefully each is defined, the more it relies on the others, revealing their common origin in the field of centers
• The fifteen structural properties are not the most fundamental aspect of the theory; they are consequences of the existence of centers and their interdependence.claim0.781
  Alexander's retrospective account of how his theory evolved, demoting the fifteen properties from foundational to derivative status.
• Correspondence Analysisconcept0.778
  Statistical technique providing graphic representation of multidimensional relations among variables using χ² distances; applied here to analyze dependencies among the Fifteen Properties.