Pith Number

pith:B2KDGEPS

pith:2014:B2KDGEPST4V2GKHZAHPG4YSDPS

not attested not anchored not stored refs pending

Treewidth is a lower bound on graph gonality

Dion Gijswijt, Josse van Dobben de Bruyn

arxiv:1407.7055 v2 · 2014-07-25 · 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{B2KDGEPST4V2GKHZAHPG4YSDPS}

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.

Cited by

1 paper in Pith

Chip-Firing Games and Critical Groups

Receipt and verification

First computed	2026-07-05T03:44:48.083643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e943311f29f2ba328f901de6e62437c938309fe43834a6169ddc227db4ce9be

Aliases

arxiv: 1407.7055 · arxiv_version: 1407.7055v2 · doi: 10.48550/arxiv.1407.7055 · pith_short_12: B2KDGEPST4V2 · pith_short_16: B2KDGEPST4V2GKHZ · pith_short_8: B2KDGEPS

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/B2KDGEPST4V2GKHZAHPG4YSDPS \
  | 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: 0e943311f29f2ba328f901de6e62437c938309fe43834a6169ddc227db4ce9be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5dc3c30ed29777264a400d2338380068c9a8dab1516dae7e2e29c3767a9f9e34",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-07-25T20:50:30Z",
    "title_canon_sha256": "7f2624988ab9fe1930429f310df5d2b0d4fdb8ccb2ac68f8386ab2abcbce8edb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.7055",
    "kind": "arxiv",
    "version": 2
  }
}