Pith. sign in

REVIEW 1 cited by

Cellular Sheaves of Lattices and the Tarski Laplacian

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2007.04099 v2 pith:UDT3RPHN submitted 2020-07-08 math.AT math.CTmath.RA

Robert Ghrist , Hans Riess This is my paper · ORCID
classification math.ATmath.CTmath.RA
keywords applicationscellularlaplacianlatticessheavestarskiagreesbroader
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

This paper initiates a discrete Hodge theory for cellular sheaves taking values in a category of lattices and Galois connections. The key development is the Tarski Laplacian, an endomorphism on the cochain complex whose fixed points yield a cohomology that agrees with the global section functor in degree zero. This has immediate applications in consensus and distributed optimization problems over networks and broader potential applications.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Representing Higher-Order Networks: A Survey of Graph-Based Frameworks

    cs.SI 2026-03 unverdicted novelty 4.0 of 10

    A survey organizing higher-order network formalisms into four families with a master comparison table, plus ~17 new superhypergraph-style definitions whose only supporting theorems are well-definedness checks.

Pith tools