Pith Number

pith:3IJOS33O

pith:2023:3IJOS33ONJELPKRIJO7ITYSJMF

not attested not anchored not stored refs pending

Sparse Graphs of Twin-width 2 Have Bounded Tree-width

Benjamin Bergougnoux, Filip Pokr\'yvka, Grzegorz Gu\'spiel, Jakub Gajarsk\'y, Marek Soko{\l}owski, Petr Hlin\v{e}n\'y

arxiv:2307.01732 v1 · 2023-07-04 · math.CO · cs.DM · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3IJOS33ONJELPKRIJO7ITYSJMF}

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	2026-07-05T06:28:00.126325Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da12e96f6e6a48b7aa284bbe89e249614d39e9bfcdfe6f62968a1e8109264d0d

Aliases

arxiv: 2307.01732 · arxiv_version: 2307.01732v1 · doi: 10.48550/arxiv.2307.01732 · pith_short_12: 3IJOS33ONJEL · pith_short_16: 3IJOS33ONJELPKRI · pith_short_8: 3IJOS33O

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/3IJOS33ONJELPKRIJO7ITYSJMF \
  | 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: da12e96f6e6a48b7aa284bbe89e249614d39e9bfcdfe6f62968a1e8109264d0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2a9e0691502673c0c8de29d50c0a12620669332adfc99f5dd985f9ed4369d0d",
    "cross_cats_sorted": [
      "cs.DM",
      "cs.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-07-04T14:03:10Z",
    "title_canon_sha256": "904f7005c2ea721118f5e1de6ec7b3fc2f45c20b0ea4a11ce2a2212ceee028ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.01732",
    "kind": "arxiv",
    "version": 1
  }
}