Pith Number

pith:3MKQR7SE

pith:2011:3MKQR7SESHJBVEBQ62RYY6YUNV

not attested not anchored not stored refs pending

On $(\le k)$-edges, crossings, and halving lines of geometric drawings of $K_n$

Bernardo M. \'Abrego, Gelasio Salazar, Jes\'us Lea\~nos, Mario Cetina, Silvia Fern\'andez-Merchant

arxiv:1102.5065 v2 · 2011-02-24 · math.CO · cs.CG · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3MKQR7SESHJBVEBQ62RYY6YUNV}

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	2026-05-18T02:22:31.185873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db1508fe4491d21a9030f6a38c7b146d5e7cebed6fa2a12b1dfb12fe393cd261

Aliases

arxiv: 1102.5065 · arxiv_version: 1102.5065v2 · doi: 10.48550/arxiv.1102.5065 · pith_short_12: 3MKQR7SESHJB · pith_short_16: 3MKQR7SESHJBVEBQ · pith_short_8: 3MKQR7SE

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/3MKQR7SESHJBVEBQ62RYY6YUNV \
  | 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: db1508fe4491d21a9030f6a38c7b146d5e7cebed6fa2a12b1dfb12fe393cd261

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab605e5b9dc3db3dc0cddd29d7f370fd76a77d5b4d43b91083051af76326740c",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-24T19:02:55Z",
    "title_canon_sha256": "915cea4a0eb282ef44ecb484e27b1d574d8539db329e8e1febff2990110730e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.5065",
    "kind": "arxiv",
    "version": 2
  }
}