Pith Number

pith:GWFNYNNS

pith:2011:GWFNYNNSBOPLILP2R6T4PMUSNI

not attested not anchored not stored refs pending

Minimum density of union-closed families

Igor Balla

arxiv:1106.0369 v1 · 2011-06-02 · 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{GWFNYNNSBOPLILP2R6T4PMUSNI}

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	2026-05-18T04:20:50.559830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

358adc35b20b9eb42dfa8fa7c7b2926a0223b35e71e9bd13952eab45cd19fe55

Aliases

arxiv: 1106.0369 · arxiv_version: 1106.0369v1 · doi: 10.48550/arxiv.1106.0369 · pith_short_12: GWFNYNNSBOPL · pith_short_16: GWFNYNNSBOPLILP2 · pith_short_8: GWFNYNNS

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/GWFNYNNSBOPLILP2R6T4PMUSNI \
  | 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: 358adc35b20b9eb42dfa8fa7c7b2926a0223b35e71e9bd13952eab45cd19fe55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ae64a813a2eedd058e8397f4d0aa19a94ae75881c4757154f56eae0e7bd60d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-06-02T06:15:54Z",
    "title_canon_sha256": "62f7a013fce839bc79f4bd3575f245fc798c935f17f2b21d6c2d954c705be456"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0369",
    "kind": "arxiv",
    "version": 1
  }
}