The deepest invariant of all living structures is that local symmetries are so densely packed that the highest possible density of local symmetries occurs, without having an overall symmetry.

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

• Local symmetries are pervasive in nature (sun, trees, crystals, bodies) and are associated with minimum energy and least-action principles.claim0.808
• The deepest living structure in buildings is not attainable without some new understanding, without a new faith based on a new physical and intellectual grasp of the nature of the material universe.claim0.792
  A strong conditional: the creation of the highest living structure requires a cosmology that reunites self and matter in terms consistent with modern science.
• Overall symmetry in a system, by itself, is not a strong source of life or wholeness; local symmetries create coherence while overall symmetry is often naive and even brutalclaim0.792
  Claim distinguishing the deadening effect of large-scale neoclassicist symmetry from the vitalizing effect of numerous overlapping local symmetries
• Local symmetries act as a kind of glue which holds space together; the more glue there is, the more the space is one, solid, unified, coherent—and the symmetrical segments must overlap for the glue to be effectiveclaim0.788
  Interpretation of the experimental finding: overlapping local symmetries are the hidden structural feature that creates perceived wholeness
• In nature, unfolding often consists of a process that establishes local symmetries one by one.claim0.786
  Connects biological morphogenesis to architectural process.
• The profound wholeness of living structure, almost every time it has been done most profoundly, has been done in a mystical‑religious context.claim0.775
  A sweeping historical observation that grounds the claim that mystical context is a near‑universal condition for the highest living structure.
• Individual mechanical explanations for each property are too specific to provide a general explanation for why living structure repeatedly appears across all domains.claim0.768
  Alexander's argument that case-by-case mechanical explanations fail to address the universal recurrence of living structure
• The deep symmetry between problem-solving in anatomical, physiological, transcriptional, and 3D spaces drives specific hypotheses.claim0.767
  Evolution pivoted the same problem-solving strategies across different domains.