Pith Number

pith:M4UGRNGA

pith:2014:M4UGRNGAWRRL75EZ2YZ56IF6BV

not attested not anchored not stored refs pending

$K_{s,t}$-saturated bipartite graphs

Benny Sudakov, D\'aniel Kor\'andi, Wenying Gan

arxiv:1402.2471 v3 · 2014-02-11 · 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{M4UGRNGAWRRL75EZ2YZ56IF6BV}

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	2026-05-18T02:32:46.266572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

672868b4c0b462bff499d633df20be0d4aee39c5a01a8ca2d0b1a45d032b98ef

Aliases

arxiv: 1402.2471 · arxiv_version: 1402.2471v3 · doi: 10.48550/arxiv.1402.2471 · pith_short_12: M4UGRNGAWRRL · pith_short_16: M4UGRNGAWRRL75EZ · pith_short_8: M4UGRNGA

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/M4UGRNGAWRRL75EZ2YZ56IF6BV \
  | 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: 672868b4c0b462bff499d633df20be0d4aee39c5a01a8ca2d0b1a45d032b98ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "feb0b64048bcbc8a3cf3248cd80adc4d4162caad3075aff4d2628c239a39dee3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-02-11T12:21:42Z",
    "title_canon_sha256": "b81329786d8e21dd63eab12f8e4bdf3202adfed34b1e9dc2454305935b7411e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.2471",
    "kind": "arxiv",
    "version": 3
  }
}