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cs.AI2026
Reasoning is topologically simple
Chris Kapulkin, Nathan Kershaw
We formulate and investigate the hypothesis that reasoning text has simpler co-occurrence topology than non-reasoning text, and that higher-quality reasoning has simpler co-occurre…
cs.CG2026
Discrete homology computations by reduction to zero differentials
Sterling Ebel, Chris Kapulkin, Nathan Kershaw
We develop a new algorithm for computing (persistent) discrete homology of graphs using reduction to zero differentials and active enumeration. This allows us to compute the fourth…
cs.CG2026
RedZeD: Computing persistent homology by Reduction to Zero Differentials
Chris Kapulkin, Nathan Kershaw
We introduce a new algorithm for computing persistent homology of Vietoris-Rips filtrations, which offers a considerable improvement both in terms of time and memory over the exist…