After the bifurcation, unstable FTLE directions appear and basin entropy abruptly increases

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

• Basin entropy strongly correlates with number of reasoning iterations required to converge, across Sudoku, mazes, visual puzzles, and mathematical logicfinding0.767
  Core empirical result establishing fractality scales with task difficulty across four tasks/architectures.
• Formulating a prior intention constitutes a catastrophic bifurcation—a phase change in cognitive organization—analogous to Bénard cell emergence.hypothesis0.740
• Steering toward out-of-distribution positive directions causes more rapid and severe coherency collapse than steering toward neutral suppression directionsclaim0.736
  Key empirical observation motivating analysis of positive vs negative steering directions
• Checkerboard pattern formation exhibits directional propagation from bottom-left to top-right despite no built-in directional bias in the modelfinding0.728
  Emergent property observed in checkerboard pattern generation
• probably helps not only with faithful reconstruction but also creates interference patterns that encode nuanced information about the deltas and convergences between states.quote0.725
  Key quote connecting path redundancy to interferometric information encoding.
• The essence of the process is that it generates coherent, yet quite unpredictable structure, simply by applying a few simple rules to a piece of land and its natural idiosyncracies.quote0.724
  Alexander's distillation of why the dynamic process produces living results that top-down design cannot.
• What would happen if systems believed their attracting sets had low entropy?question0.720
  Question about the consequences of intrinsic beliefs about entropy.
• Even mathematical catastrophes always begin as features consistent with the symmetries of the earlier state and develop smoothly from within the existing wholeness.claim0.719
  Alexander's response to the apparent counter-examples from catastrophe theory: discontinuities are themselves structure-preserving at a deeper level