Pith Number

pith:OA5WGJDE

pith:2009:OA5WGJDERXYHHM2XJIIFTBISBC

not attested not anchored not stored refs pending

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

Attila P\'or, Brad Ballinger, David R. Wood, Ferran Hurtado, Prosenjit Bose, Scott D. Kominers, S\'ebastien Collette, Stefan Langerman, Vida Dujmovi\'c, Zachary Abel

arxiv:0904.0262 v2 · 2009-04-01 · math.CO · cs.CG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OA5WGJDERXYHHM2XJIIFTBISBC}

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	2026-05-18T04:32:19.970294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

703b6324648df073b3574a1059851208b443823f0d3901fb6e0c67198f8c5e5f

Aliases

arxiv: 0904.0262 · arxiv_version: 0904.0262v2 · doi: 10.48550/arxiv.0904.0262 · pith_short_12: OA5WGJDERXYH · pith_short_16: OA5WGJDERXYHHM2X · pith_short_8: OA5WGJDE

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/OA5WGJDERXYHHM2XJIIFTBISBC \
  | 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: 703b6324648df073b3574a1059851208b443823f0d3901fb6e0c67198f8c5e5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccb5064b511d5547fa1c1546f2a27cd32217a4951bb4f4b730c787f6d74e5969",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-04-01T22:49:26Z",
    "title_canon_sha256": "d78e28e51403b2c43cc7796cad43cfb9247a83b6e76f2b0bb9aea45f00a6b2da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.0262",
    "kind": "arxiv",
    "version": 2
  }
}