Pith Number

pith:ZWKQH4MW

pith:2011:ZWKQH4MW2FATCSDTSJZ34S6JBO

not attested not anchored not stored refs pending

Nontrivial independent sets of bipartite graphs and cross-intersecting families

Huajun Zhang, Jun Wang

arxiv:1101.2257 v1 · 2011-01-12 · 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{ZWKQH4MW2FATCSDTSJZ34S6JBO}

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	2026-05-18T04:31:43.256924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd9503f196d1413148739273be4bc90b8084c95da2e750fea7b6c576ae560983

Aliases

arxiv: 1101.2257 · arxiv_version: 1101.2257v1 · doi: 10.48550/arxiv.1101.2257 · pith_short_12: ZWKQH4MW2FAT · pith_short_16: ZWKQH4MW2FATCSDT · pith_short_8: ZWKQH4MW

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/ZWKQH4MW2FATCSDTSJZ34S6JBO \
  | 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: cd9503f196d1413148739273be4bc90b8084c95da2e750fea7b6c576ae560983

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bd16c491f823b52b80dc8153aba82ab1c74b6645d1a590786b2b5ce1b5e1780",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-01-12T02:18:21Z",
    "title_canon_sha256": "8e1e0a4c65b44e9f87fff03ee3aedc72d0369a2cd25aeeedfb4a478cf6b8f983"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2257",
    "kind": "arxiv",
    "version": 1
  }
}