Tropical Ptolemy label flips on spherical Delaunay triangulations are claimed to yield braid invariants, but the load-bearing pentagon identity is asserted without verification.
Manturov, Knot Theory, Chapman & Hall/CRC Press, Boca Raton, FL
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Tropical Ptolemy Transformations and Invariants of Braids
Tropical Ptolemy label flips on spherical Delaunay triangulations are claimed to yield braid invariants, but the load-bearing pentagon identity is asserted without verification.