Pith Number

pith:ROMZ6UGN

pith:2009:ROMZ6UGN3SEGDGY5JAMOI5Z3ZB

not attested not anchored not stored refs pending

The minimal density of triangles in tripartite graphs

John Talbot, J. Robert Johnson, Rahil Baber

arxiv:0910.1237 v1 · 2009-10-07 · 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{ROMZ6UGN3SEGDGY5JAMOI5Z3ZB}

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	2026-05-17T23:53:19.895173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b999f50cddc88619b1d4818e4773bc8710e35e747e9e237eb78f9c329f2c77e

Aliases

arxiv: 0910.1237 · arxiv_version: 0910.1237v1 · doi: 10.48550/arxiv.0910.1237 · pith_short_12: ROMZ6UGN3SEG · pith_short_16: ROMZ6UGN3SEGDGY5 · pith_short_8: ROMZ6UGN

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/ROMZ6UGN3SEGDGY5JAMOI5Z3ZB \
  | 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: 8b999f50cddc88619b1d4818e4773bc8710e35e747e9e237eb78f9c329f2c77e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dfa0cc25bc33862e86b859ba98bbd587c73ab4f8a9136d8959206f911de0327",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-10-07T12:35:07Z",
    "title_canon_sha256": "8f094869432b7ed0add0be179affc7b28d1ed2ac0aefa66a323c1d778d0fe6eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.1237",
    "kind": "arxiv",
    "version": 1
  }
}