source	date	role	url
Hulbert--Zaremsky, Word length, Morse theory, and Vietoris--Rips complexes	2026-08-26	Current Morse criterion; two-dimensional RAAG theorem; higher-dimensional prediction	https://arxiv.org/html/2608.25614v1
Gupta--Sarkar--Shukla, On the Vietoris--Rips Complexes of Integer Lattices	2025-11-06	Sharp theorem through dimension five; dimension-six scale-ten theorem; optimality context	https://arxiv.org/html/2511.04238v1
Zaremsky, Contractible Vietoris--Rips complexes of Z^n	2025-08-12	Uniform n^2+n-1 bound and sharp conjecture	https://arxiv.org/abs/2410.11993
Virk, Contractibility of the Rips complexes of Integer lattices via local domination	2025-07-26	Original general contractibility theorem; local crushing; sharp result through dimension three	https://arxiv.org/abs/2405.09134
Chalopin--Chepoi--Genevois--Hirai--Osajda, Helly groups	2025	Different-generating-set control for CAT(0) cubical groups	https://msp.org/gt/2025/29-1/gt-v29-n1-p01-s.pdf
Postnikov, Permutohedra, associahedra, and beyond	2009	Influence on the proposed signed-polytope carrier language; not a proof dependency	https://math.mit.edu/~apost/papers/permutohedron_full.pdf