Novelty audit

The repository includes a source-by-source audit: NOVELTY_AUDIT.md.

The generic crossing-number route gives only \(\exp(O(N^2))\). However, Gros–Ramirez Alfonsin’s 2025 strong-geometry reconstruction theorem already implies a factorial-scale upper bound by standard sign-pattern counting. The full wedge table gives \(N^{33N+o(N)}\); using only the signs needed in its proof gives \(N^{6N+o(N)}\). These bounds are implicit consequences rather than printed corollaries and are credited in the manuscript.

The new direct self-intersection-discriminant argument gives \(N^{3N+o(N)}\), improving the proof-extracted leading upper exponent from \(6\) to \(3\). The explicit Garside construction gives the lower exponent \(2/3\), while earlier Malyutin–Stupakov and Huh–Oh results already implied a smaller positive factorial exponent.

The defensible contribution is therefore the sharper direct topology-to-algebraic-chambers count, together with the new lower construction and matching order of growth—not a claim that no factorial-scale bound was previously implicit.