Pith Number

pith:7BWUFXRR

pith:2015:7BWUFXRRO6CJV6SMWA2BUZE3MA

not attested not anchored not stored refs pending

Small dense subgraphs of polarity graphs and the extremal number for the 4-cycle

Craig Timmons, Michael Tait

arxiv:1502.02722 v1 · 2015-02-09 · 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{7BWUFXRRO6CJV6SMWA2BUZE3MA}

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	2026-05-18T02:27:31.128414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f86d42de3177849afa4cb0341a649b603c84f2dbb692a3a4e27c4bee370ad98c

Aliases

arxiv: 1502.02722 · arxiv_version: 1502.02722v1 · doi: 10.48550/arxiv.1502.02722 · pith_short_12: 7BWUFXRRO6CJ · pith_short_16: 7BWUFXRRO6CJV6SM · pith_short_8: 7BWUFXRR

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/7BWUFXRRO6CJV6SMWA2BUZE3MA \
  | 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: f86d42de3177849afa4cb0341a649b603c84f2dbb692a3a4e27c4bee370ad98c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be3d429a02e13e1a482d933a1a9640fa785a65141ae283e8cdb6b5a1ef731d32",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-02-09T23:06:34Z",
    "title_canon_sha256": "130b07905de2618c69790b7e76b29f676e29fc4135cfd1fa9d9e527aa0a2e254"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02722",
    "kind": "arxiv",
    "version": 1
  }
}