Pith Number

pith:OBDEFRXU

pith:2025:OBDEFRXUZXXY4G732KAERT5UEC

not attested not anchored not stored refs pending

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

Qian-Qian Zhou, Yi-Ding Shi, Ze-Chun Hu

arxiv:2507.11008 v2 · 2025-07-15 · 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{OBDEFRXUZXXY4G732KAERT5UEC}

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	2026-07-05T12:02:48.269936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

704642c6f4cdef8e1bfbd28048cfb42092ed94006bf9aed1ab7c732ae99122e7

Aliases

arxiv: 2507.11008 · arxiv_version: 2507.11008v2 · doi: 10.48550/arxiv.2507.11008 · pith_short_12: OBDEFRXUZXXY · pith_short_16: OBDEFRXUZXXY4G73 · pith_short_8: OBDEFRXU

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/OBDEFRXUZXXY4G732KAERT5UEC \
  | 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: 704642c6f4cdef8e1bfbd28048cfb42092ed94006bf9aed1ab7c732ae99122e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ea5fb95d2727567b9434cbf86e06b547a4a107ad70d78bd04e59fdc6fd3faeb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-15T05:56:02Z",
    "title_canon_sha256": "ec246f4202d33fe0bd59d65c3c4b54921c99fa45cbead2496a22532e04958dc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.11008",
    "kind": "arxiv",
    "version": 2
  }
}