TWIST LIKE BEHAVIOR IN NON-TWIST PATTERNS OF TRIODS

Sourav Bhattacharya, Ashish Yadav

correcthigh confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s Theorem 3.7 (non-decreasing code implies frontier) is proved cleanly via admissible interval loops and a weighted-average argument that uses only the code monotonicity to bound the rotation of each insert, yielding a contradiction if ρ(π) is not an endpoint of I_π. This proof is coherent and aligns with the paper’s formal framework for rotation sets on the oriented graph GP and the definition of the forced rotation interval L(GP) . By contrast, the model’s proof hinges on an unproven “extremal-successor lemma” and a local edge-replacement scheme on GP. The replacement step is stated in the wrong monotonic direction and is not justified to preserve closed loops or to converge to the fundamental loop. Because these gaps affect the core of the argument, the model’s solution is not acceptable as written.

Referee report (LaTeX)

\textbf{Recommendation:} reject

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper’s theorem (non-decreasing code implies frontier) is convincingly established within a clear and self-contained framework and connects neatly to the rotation-interval machinery for triods. By contrast, the model’s alternative proof is not ready for publication: its key “extremal-successor” claim is unproven, and the local replacement scheme is not shown to preserve loops or achieve the claimed optimality; a sign error further clouds the argument. While the model’s approach is interesting and potentially salvageable with substantial additional work (e.g., via rigorous cycle-mean optimization arguments), in its present form it falls short of correctness.