Pith Number

pith:4JF6HSEM

pith:2022:4JF6HSEM4G7UZPN4E2REG3WBSW

not attested not anchored not stored refs pending

The number of abundant elements in union-closed families without small sets

Adam Kabela, Jakub Teska, Michal Pol\'ak

arxiv:2212.09279 v2 · 2022-12-19 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4JF6HSEM4G7UZPN4E2REG3WBSW}

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

A lemma on a finite union-closed family of finite sets and its applications

Receipt and verification

First computed	2026-07-05T06:15:19.999188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e24be3c88ce1bf4cbdbc26a2436ec195899800dc3b1a22b65872a6a28652a0f0

Aliases

arxiv: 2212.09279 · arxiv_version: 2212.09279v2 · doi: 10.48550/arxiv.2212.09279 · pith_short_12: 4JF6HSEM4G7U · pith_short_16: 4JF6HSEM4G7UZPN4 · pith_short_8: 4JF6HSEM

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/4JF6HSEM4G7UZPN4E2REG3WBSW \
  | 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: e24be3c88ce1bf4cbdbc26a2436ec195899800dc3b1a22b65872a6a28652a0f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2807a3362f17cf81525b1398075075637cfc7f25c6d4a700943245863a6fff28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-12-19T07:20:41Z",
    "title_canon_sha256": "0ec762a570fcacc7956881470423688d1f7da4118f9f9ce6803b60e3b44f9330"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.09279",
    "kind": "arxiv",
    "version": 2
  }
}