Pith Number

pith:B2DVUXSI

pith:2011:B2DVUXSIQ4HETPNKKGWHROQCGH

not attested not anchored not stored refs pending

On graphs double-critical with respect to the colouring number

Anders Sune Pedersen, Matthias Kriesell

arxiv:1108.1036 v1 · 2011-08-04 · 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{B2DVUXSIQ4HETPNKKGWHROQCGH}

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	2026-05-18T04:16:13.187773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e875a5e48870e49bdaa51ac78ba0231ee2a7324974f841154fc268d7118a260

Aliases

arxiv: 1108.1036 · arxiv_version: 1108.1036v1 · doi: 10.48550/arxiv.1108.1036 · pith_short_12: B2DVUXSIQ4HE · pith_short_16: B2DVUXSIQ4HETPNK · pith_short_8: B2DVUXSI

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/B2DVUXSIQ4HETPNKKGWHROQCGH \
  | 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: 0e875a5e48870e49bdaa51ac78ba0231ee2a7324974f841154fc268d7118a260

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12e7e36313ca6f53259d456017b8e2e8b00b250552b310113ccafd6e4fc257d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-04T10:10:35Z",
    "title_canon_sha256": "b6a423d7f0a6bebd2b7d4aa07196f6ed6009617f2e05b6f64a9fa435ff655bfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1036",
    "kind": "arxiv",
    "version": 1
  }
}