Pith Number

pith:DE2OGBNP

pith:2015:DE2OGBNP524JGIVUJHHUJL4NH7

not attested not anchored not stored refs pending

The minimum size of graphs with given rainbow index

Thomas Y.H. Liu

arxiv:1509.07256 v2 · 2015-09-24 · 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{DE2OGBNP524JGIVUJHHUJL4NH7}

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	2026-05-18T01:32:02.618854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1934e305afeeb89322b449cf44af8d3ffe1aab1404de8fa5c73c18c7d7565157

Aliases

arxiv: 1509.07256 · arxiv_version: 1509.07256v2 · doi: 10.48550/arxiv.1509.07256 · pith_short_12: DE2OGBNP524J · pith_short_16: DE2OGBNP524JGIVU · pith_short_8: DE2OGBNP

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/DE2OGBNP524JGIVUJHHUJL4NH7 \
  | 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: 1934e305afeeb89322b449cf44af8d3ffe1aab1404de8fa5c73c18c7d7565157

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18d9883014dd4594d1b4b09eab0683a83f25dcca77a9e6b1a55927a9d6a327ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-24T07:01:52Z",
    "title_canon_sha256": "9d14049e0ab9dbe180cd056c6eadf81f76d6beef6e3155ad4b45ea72123eed23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07256",
    "kind": "arxiv",
    "version": 2
  }
}