Pith Number

pith:LOL2LEJH

pith:2022:LOL2LEJHJZZQJA2I3FRMGFOYS6

not attested not anchored not stored refs pending

Dimension-Free Bounds for the Union-Closed Sets Conjecture

Lei Yu

arxiv:2212.00658 v2 · 2022-12-01 · math.CO · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LOL2LEJHJZZQJA2I3FRMGFOYS6}

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

Entropy approach for a generalization of Frankl's conjecture

Receipt and verification

First computed	2026-07-05T06:13:09.259544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b97a591274e73048348d962c315d897bf0296137d8b83e862ba08def6c63948

Aliases

arxiv: 2212.00658 · arxiv_version: 2212.00658v2 · doi: 10.48550/arxiv.2212.00658 · pith_short_12: LOL2LEJHJZZQ · pith_short_16: LOL2LEJHJZZQJA2I · pith_short_8: LOL2LEJH

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/LOL2LEJHJZZQJA2I3FRMGFOYS6 \
  | 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: 5b97a591274e73048348d962c315d897bf0296137d8b83e862ba08def6c63948

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "029bc31abda40266e982aaab33abda4f92aef4df5cf9a6815c743b942e9e5a1d",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-12-01T17:02:58Z",
    "title_canon_sha256": "e2c3bae0e8adfe3448c5d5d96102bb43f16e0ed2750180fe1dfb375dc1f491ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.00658",
    "kind": "arxiv",
    "version": 2
  }
}