How can treelike versus-relations be axiomatically characterized?

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

• Characterize treelike versus-relations! Can this perhaps be done automatically?question0.872
  Central open question in evolutionary tree analysis: find axioms describing versus-relations derived from trees.
• Treelike versus-relations can be characterized by a single rule: wx | y, ¬wz | y → wx | z.finding0.871
  Empirical discovery via FCA that versus-relations on evolutionary tree leaves satisfy a single Horn rule with variables.
• The tree structure can be reconstructed from its versus relation.claim0.773
  Statement that the versus relation uniquely determines a tree.
• There is a bidirectional relationship between the geometry of representation and behavior across tasks and modalities.claim0.715
  Author’s interpretive claim that the shared geometry is general and robust.
• The feed-forward network truly implements a symbolic, tree-structured algorithm for hierarchical equality, with abstract equality relations not decomposable into input identitiesclaim0.714
  DAS reveals that the neural network encodes abstract relational structure rather than raw input identities.
• These relationships are cognitive architectures regardless of the substrate in which they are implemented.claim0.711
  Asserts that organismic identity is fundamentally a cognitive structure.
• There is a clear bidirectional relationship between the geometry of behavior and representation: steering along representation manifolds follows behavior manifolds, and vice versa.claim0.711
  The paper's finding that the alignment holds in both directions — from representation to behavior and from behavior back to representation space.
• Under the Dependent Origination Axiom, no object in the phenomenal category possesses svabhāva (its representable functor is never isomorphic to a constant functor).claim0.706
  Proposition 4.1, category-theoretic elucidation of śūnyatā.