Pith Number

pith:OY6GZGWH

pith:2016:OY6GZGWHNSM73X4SXWZUYYJIUU

not attested not anchored not stored refs pending

On the number of union-free families

Adam Zsolt Wagner, Jozsef Balogh

arxiv:1601.03659 v1 · 2016-01-14 · 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{OY6GZGWHNSM73X4SXWZUYYJIUU}

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	2026-05-18T01:22:52.911260Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

763c6c9ac76c99fddf92bdb34c6128a510e0c70063741ed5f9d67c9625ac36af

Aliases

arxiv: 1601.03659 · arxiv_version: 1601.03659v1 · doi: 10.48550/arxiv.1601.03659 · pith_short_12: OY6GZGWHNSM7 · pith_short_16: OY6GZGWHNSM73X4S · pith_short_8: OY6GZGWH

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/OY6GZGWHNSM73X4SXWZUYYJIUU \
  | 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: 763c6c9ac76c99fddf92bdb34c6128a510e0c70063741ed5f9d67c9625ac36af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3b02224e270843b97d2e64df2c6a47b2d3825cfa962ad000eee716950861f08",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-01-14T16:47:30Z",
    "title_canon_sha256": "60ce4a0f35770eaf48e339e6f24f1a3adeaba10190c48f7c750157e759ce0771"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.03659",
    "kind": "arxiv",
    "version": 1
  }
}