Pith Number

pith:A2KYCGC3

pith:2011:A2KYCGC3M3OCHS3M55R2TJRW6X

not attested not anchored not stored refs pending

Improved lower bounds for the 2-page crossing numbers of K_{m,n} and K_n via semidefinite programming

Dmitrii V. Pasechnik, Etienne de Klerk

arxiv:1110.4824 v1 · 2011-10-21 · math.CO · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A2KYCGC3M3OCHS3M55R2TJRW6X}

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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	2026-05-18T03:50:21.990822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

069581185b66dc23cb6cef63a9a636f5cc1738cb5094ef0b3b22f93fccbf6bb3

Aliases

arxiv: 1110.4824 · arxiv_version: 1110.4824v1 · doi: 10.48550/arxiv.1110.4824 · pith_short_12: A2KYCGC3M3OC · pith_short_16: A2KYCGC3M3OCHS3M · pith_short_8: A2KYCGC3

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/A2KYCGC3M3OCHS3M55R2TJRW6X \
  | 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: 069581185b66dc23cb6cef63a9a636f5cc1738cb5094ef0b3b22f93fccbf6bb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90cc194b91bfa456581fd5c7bed4061b2dc9c98448bbffd91630a27a9b99b4f1",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-10-21T15:27:27Z",
    "title_canon_sha256": "675b6b9f4029e45e08f4bc7bab721da1647c9ee90acff08b11c48e61cd689214"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4824",
    "kind": "arxiv",
    "version": 1
  }
}