I believe that these properties arise because they are the principal ways in which centers can be strengthened by other centers.

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

• The beauty and force of any building arises always, and in its entirety, from the deep functional nature of the centers that have been created.claim0.824
  Core principle tying beauty directly to deeply functional centers.
• Why do centers arise at all? Why do centers become more intense or more alive?question0.822
  Alexander's deeper formulation of the morphogenetic question in terms of his center-based framework
• It is the field of centers which is primary, not these fifteen properties, and the properties are simply aspects of the field which help us understand concretely how the field worksclaim0.815
  Meta-theoretical claim that the fifteen properties are derivative from the deeper reality of the field of centers; the properties are pedagogical tools rather than fundamental
• I finally recognized that it is the field of centers which is primary, not these fifteen properties, and that the properties are simply aspects of the field which help us to understand concretely how the field works.quote0.812
  Meta-theoretical revelation about the ontological priority of the field of centers over the fifteen properties
• Certain configurations of centers have such organizing force that they create entirely new levels of intensity within the centers themselves and utterly transmute the material character of space.hypothesis0.805
  Suggests that sufficiently intense fields of centers transcend ordinary matter.
• The intricate and beautiful structure of living centers comes about naturally, and most of the time without effort, as a result of the repeated application of structure-preserving transformations to the wholeness which exists.claim0.804
  Central interpretive claim of the chapter, asserting that living structure is an effortless natural outcome of structure-preserving transformations.
• In buildings, especially, the success of the process will be judged by the extent to which these middle-range entities appear with their own distinct symmetries, with their own definite and distinct force as strong centers.claim0.800
  Proposes middle-range entity quality as the criterion for judging the success of a building process
• My claim in Book 2 is that the intricate and beautiful structure of living centers comes about naturally, and most of the time without effort, as a result of the repeated application of structure-preserving transformations to the wholeness which exists.quote0.800
  Central thesis statement of the chapter, encapsulating the core idea that living structure arises effortlessly from structure-preserving transformations.