EqR generated maze solution path lengths vary between 101–169 steps

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

• Generated EqR test mazes have wall fraction ≈0.57finding0.795
  Methodological detail characterizing the maze task-instance distribution used.
• Information paths from A to B can exceed C(m+n, n) distinct routes, where m=position displacement and n=layer displacement.finding0.698
  Quantifies extreme redundancy in transformer routing; supports claim that introspection and interference patterns are architecturally permitted.
• DeepSeek-R1 reasons substantially longer than QwQ on average, yet their prompt-side ASR is comparable (17.9% vs 15.2%), suggesting raw reasoning depth is not sufficient for safety.finding0.689
  Evidence that reasoning length does not track safety performance
• Fine-tuning on correct health advice (35 steps) nearly realigns a model trained on insecure code, leaving only 0.5% misalignmentfinding0.689
  Cross-domain realignment is effective but less complete than in-domain realignment
• Less than a trillionth of all the 6 × 10^23 possible sequences actually work well enough to allow smooth unfolding.quote0.685
  Alexander's striking quantification of the rarity of good sequences, underscoring why finding the right order is so difficult and precious.
• Total length of cuts needed: 240 kmfinding0.684
  30 meters of cuts per square meter × 8,000 m².
• FPRM-Maze uncertainty exponent is stable across scale: α=0.853±3e-2finding0.681
  Evidence that FPRM-Maze basins are true (scale-free) fractals, contrasting with EqR-Sudoku's slim fractal.
• The representation-based path and the behavior-based path in Llama-3.1 8B activation space trace out similar curves, demonstrating bidirectional geometry alignment.finding0.680
  Key empirical result showing that optimizing for behavioral outputs and fitting representation geometry produce the same path in activation space.