Pith Number

pith:CYHXWJTS

pith:2013:CYHXWJTSOELKOUBC7UOZKXMB2X

not attested not anchored not stored refs pending

The journey of the union-closed sets conjecture

Henning Bruhn, Oliver Schaudt

arxiv:1309.3297 v2 · 2013-09-12 · math.CO · 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{CYHXWJTSOELKOUBC7UOZKXMB2X}

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.

Cited by

1 paper in Pith

On Boolean polynomials and the Union-Closed Conjecture

Receipt and verification

First computed	2026-05-18T03:08:26.673498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

160f7b26727116a75022fd1d955d81d5e14a3bbbfda36206012a661b09ba6c91

Aliases

arxiv: 1309.3297 · arxiv_version: 1309.3297v2 · doi: 10.48550/arxiv.1309.3297 · pith_short_12: CYHXWJTSOELK · pith_short_16: CYHXWJTSOELKOUBC · pith_short_8: CYHXWJTS

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/CYHXWJTSOELKOUBC7UOZKXMB2X \
  | 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: 160f7b26727116a75022fd1d955d81d5e14a3bbbfda36206012a661b09ba6c91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b94cdf43e16d3fede8eb88797de9a61b87255829249a2e8042a28969e8daf38",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-12T20:45:36Z",
    "title_canon_sha256": "9b4780439d4f451a49e018f765a9d6db80ab7503fdf1627c3f5254e948811c41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3297",
    "kind": "arxiv",
    "version": 2
  }
}