Graph Representation via Elements of Discrete Morse and Cobordism Theories BAEDMM7YM5

URI	`m2://res/BAEDMM7YM5`
Kind	preprint
Creators	Jennifer Rozenblit, Chenguang Yang, Yuxin Liu, Yuzhou Chen, Yulia Gel
Date	2026-10-01
Subjects	arxiv cs.LG, arxiv math.GN
Scope	border

Expressions

e1: version, preprint

Date	2026-10-01
Ids	arXiv 2610.01937

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
$H_0$-faithfulness (component agreement	definition	definition 26	arxiv
$\mathcal{V}$-paths (Forman	definition	definition 17	arxiv
Maximality under entry-time compatibility	definition	definition 49	arxiv
Non-identifiability of descending manifolds from persistence	statement	proposition 48	arxiv
Descending (Stable) Manifold	definition	definition 10	arxiv
Descending set / discrete unstable manifold	definition	definition 18	arxiv
Compatibility notions	definition	definition 16	arxiv
Morse Function	definition	definition 8	arxiv
Skeleton-preserving perturbation	definition	definition 32	arxiv
Outdegree bound	statement	lemma 22	arxiv
Discrete Morse function	definition	definition 1	arxiv
Discrete gradient vector field	definition	definition 15	arxiv
Acyclicity (Forman $\mathcal{V}$-path condition on graphs	definition	definition 20	arxiv
Forested pairing (optional strengthening	definition	definition 27	arxiv
Exact invariance under skeleton-preserving perturbations	statement	lemma 33	arxiv
H4QF0KRP7K	statement	theorem	arxiv
Decision margin	definition	definition 41	arxiv
Ascending (Unstable) Manifold	definition	definition 11	arxiv
Morse Skeleton Representation of Graphs	definition	definition 3	arxiv
Acyclicity implies no directed cycles	statement	lemma 23	arxiv
Critical Simplex	definition	definition 2	arxiv
Decision margin	definition	definition 5	arxiv
Critical Cell	definition	definition 14	arxiv
Discrete Morse Function	definition	definition 13	arxiv
Morse Index	definition	definition 9	arxiv
Paired-edge orientation and the induced directed graph	definition	definition 21	arxiv
Anchor map on the full graph	definition	definition 24	arxiv
Cobordism	definition	definition 12	arxiv
Critical edges carry cycle rank under component-faithful forested pairing	statement	proposition 29	arxiv
Skeletal Informativeness	statement	proposition 4	arxiv
Margin implies skeleton preservation	statement	theorem 6	arxiv
Critical point	definition	definition 7	arxiv

Catalogue records

arxiv: 2610.01937 (work)