Semimeander Knot Diagrams: Complexity Bounds and Slice Dichotomy — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Knot theory yields no direct quasi-cobordism or Maslov potential data in these sources; instead, the strongest concrete result is a new complexity bound for semimeander knot diagrams, plus the slice/semimeander dichotomy. | MATH: Semimeander diagram complexity: for a knot with crossing number \(c\), the minimal number of crossings in a semimeander diagram \(sm(K)\) satisfies \(sm(K) \leq c^2\) (rough bound improved to \(O(c^{3/2})\) per arXiv:2312.05014v2 abstract — exact constant not stated in snippet). Dowker notation: each crossing assigned two integers \(1,\dots,2n\), yielding a permutation \(\pi\) with \(\pi(\pi(i)) = i\) and parity condition \(\pi(i) \not\equiv i \pmod{2}\). Conway knot non-slice: Rasmussen invariant \(s(K) \neq 0\) or Khovanov homology grading shift — Piccirillo's proof uses a 4-ball genus bound via a knot with same Alexander polynomial but different slice status. | CONNECTION: No explicit golden ratio, base-60, or crystallographic symmetry appears. How Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212141355
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