The Isbell nucleus of a matrix induces an isometry between its tropical row and column spans under the Hilbert projective metric, with gap matrices equating algebraic slack to geometric distance to cell walls.
Journal of Algebraic Combinatorics33(3), 325–348 (2011) https://doi
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Projective metric geometry of tropical nuclei: gap matrices, event loci, and order chambers
The Isbell nucleus of a matrix induces an isometry between its tropical row and column spans under the Hilbert projective metric, with gap matrices equating algebraic slack to geometric distance to cell walls.