Pith Number

pith:Y26XVIES

pith:2012:Y26XVIES2GNBH4MRIO4I44KBSI

not attested not anchored not stored refs pending

The graph formulation of the union-closed sets conjecture

Henning Bruhn, Jan Arne Telle, Oliver Schaudt, Pierre Charbit

arxiv:1212.4175 v2 · 2012-12-17 · 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{Y26XVIES2GNBH4MRIO4I44KBSI}

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	2026-05-18T03:25:34.781212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6bd7aa092d19a13f19143b88e7141921b73d7c7ca7d5969231b22780fcf9846

Aliases

arxiv: 1212.4175 · arxiv_version: 1212.4175v2 · doi: 10.48550/arxiv.1212.4175 · pith_short_12: Y26XVIES2GNB · pith_short_16: Y26XVIES2GNBH4MR · pith_short_8: Y26XVIES

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/Y26XVIES2GNBH4MRIO4I44KBSI \
  | 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: c6bd7aa092d19a13f19143b88e7141921b73d7c7ca7d5969231b22780fcf9846

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c6e30eb1699b7f05a3e18677ff822c9dae648e725b190056397587ca0732879",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-17T21:52:42Z",
    "title_canon_sha256": "937e2217bccc573635a5b505b32696ca54f17e1bb37af8398e8a9da08266c29c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4175",
    "kind": "arxiv",
    "version": 2
  }
}