Pith Number

pith:BWO7XARC

pith:2021:BWO7XARCYQMO7CDQ7FJHM2MGNE

not attested not anchored not stored refs pending

Product structure of graphs with an excluded minor

Alex Scott, David R. Wood, Freddie Illingworth

arxiv:2104.06627 v6 · 2021-04-14 · 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{BWO7XARCYQMO7CDQ7FJHM2MGNE}

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

Short Paths in the Planar Graph Product Structure Theorem

Receipt and verification

First computed	2026-07-05T09:32:38.073362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d9dfb8222c418ef8870f9527669866916533f864d46fec70bf6a38eccd3e041

Aliases

arxiv: 2104.06627 · arxiv_version: 2104.06627v6 · doi: 10.48550/arxiv.2104.06627 · pith_short_12: BWO7XARCYQMO · pith_short_16: BWO7XARCYQMO7CDQ · pith_short_8: BWO7XARC

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/BWO7XARCYQMO7CDQ7FJHM2MGNE \
  | 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: 0d9dfb8222c418ef8870f9527669866916533f864d46fec70bf6a38eccd3e041

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4c298de6d2d85288897ddf6ba91c60677eaff40337ef9440271d65df4dd4a7d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-04-14T05:11:39Z",
    "title_canon_sha256": "a458adc1d955da924932f5e9e1d7e1ac9e8e8b4f95db079f14d1882ba6d25af2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.06627",
    "kind": "arxiv",
    "version": 6
  }
}