Pith Number

pith:24IZQ2IX

pith:2011:24IZQ2IXWIYCYWGWQBW5F6N2HE

not attested not anchored not stored refs pending

A Fractional Analogue of Brooks' Theorem

Andrew D. King, Linyuan Lu, Xing Peng

arxiv:1103.3524 v3 · 2011-03-17 · 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{24IZQ2IXWIYCYWGWQBW5F6N2HE}

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	2026-05-18T02:22:18.325868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d711986917b2302c58d6806dd2f9ba393f91d90a87dd98d0cd4a692e26ac0f33

Aliases

arxiv: 1103.3524 · arxiv_version: 1103.3524v3 · doi: 10.48550/arxiv.1103.3524 · pith_short_12: 24IZQ2IXWIYC · pith_short_16: 24IZQ2IXWIYCYWGW · pith_short_8: 24IZQ2IX

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/24IZQ2IXWIYCYWGWQBW5F6N2HE \
  | 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: d711986917b2302c58d6806dd2f9ba393f91d90a87dd98d0cd4a692e26ac0f33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c009ec63660531ac4137a6ec8b0bf5c6f8c77d32e578140170c34cdba2b3efb2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-17T21:10:53Z",
    "title_canon_sha256": "acabeef200606a37924145d6352be4cd3345d63d8056ab8d9b392c87c5990ab9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3524",
    "kind": "arxiv",
    "version": 3
  }
}