Pith Number

pith:YA7SPCQZ

pith:2009:YA7SPCQZFZKLWKEIQRUTJL3YL6

not attested not anchored not stored refs pending

Cellular spanning trees and Laplacians of cubical complexes

Art M. Duval, Caroline J. Klivans, Jeremy L. Martin

arxiv:0908.1956 v3 · 2009-08-13 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YA7SPCQZFZKLWKEIQRUTJL3YL6}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:11:49.319221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c03f278a192e54bb2888846934af785f8d6af4381f60fb758b1e85c9a16cbefc

Aliases

arxiv: 0908.1956 · arxiv_version: 0908.1956v3 · doi: 10.48550/arxiv.0908.1956 · pith_short_12: YA7SPCQZFZKL · pith_short_16: YA7SPCQZFZKLWKEI · pith_short_8: YA7SPCQZ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YA7SPCQZFZKLWKEIQRUTJL3YL6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c03f278a192e54bb2888846934af785f8d6af4381f60fb758b1e85c9a16cbefc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cde6595d00e551b1dcd6c7afce1a1f299e13d298bcb42f5f414f375d0c701f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-08-13T19:03:51Z",
    "title_canon_sha256": "675e216bf4a1e4e99c647008d468e398fc0123308b5b0b4ec97bdd3b7a30aecf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.1956",
    "kind": "arxiv",
    "version": 3
  }
}