No present-day theories explain why the fifteen properties appear so widely; only particular cases are understood, not the general pervasiveness.

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

• The fifteen properties emerge directly and inevitably from the unfolding of the whole; it is these fifteen properties that guide all differentiations during development.claim0.833
  Alexander's claim that living structure properties are not incidental but are the operative mechanisms of wholeness-preserving transformation
• The fifteen properties appear in nature because they are structural complements to the formation of stable and semistable systems, contributing to coherence and stability.hypothesis0.829
• Individual mechanical explanations for each property are too specific to provide a general explanation for why living structure repeatedly appears across all domains.claim0.827
  Alexander's argument that case-by-case mechanical explanations fail to address the universal recurrence of living structure
• The fifteen structural properties are not the most fundamental aspect of the theory; they are consequences of the existence of centers and their interdependence.claim0.822
  Alexander's retrospective account of how his theory evolved, demoting the fifteen properties from foundational to derivative status.
• The fifteen properties appear in nature as a direct result of repeated structure-preserving transformations unfolding the wholeness.claim0.816
  Interpretation that the geometric properties of living structure are not arbitrary but arise inevitably from the smooth unfolding process.
• The fifteen properties come into existence naturally as a result of the structure-preserving process.claim0.816
  Claim that the properties are not applied artificially but are consequences of correct unfolding.
• The fifteen properties are not merely visual features which appear in works of art. ... they must be fundamental to the appearance of life in all centers that are generated or created in any system.quote0.814
  Foundation of the chapter's argument that the properties transcend aesthetics and are fundamental to all physical reality.
• Even with non-linear dynamics and complexity theory, the specific appearance of the fifteen properties and emergence of living centers in the world remains largely unexplained.claim0.810
  Alexander's critical assessment of the limits of current complexity science relative to his explanatory target