Pith Number

pith:P4ZGAK35

pith:2010:P4ZGAK35OREJSOWTBQQPL6BZXW

not attested not anchored not stored refs pending

Maximum union-free subfamilies

Benny Sudakov, Choongbum Lee, Jacob Fox

arxiv:1012.3127 v6 · 2010-12-14 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P4ZGAK35OREJSOWTBQQPL6BZXW}

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	2026-05-18T04:26:45.252685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f32602b7d7448993ad30c20f5f839bd8a1187df7f3cd32c94ea5badd899d11f

Aliases

arxiv: 1012.3127 · arxiv_version: 1012.3127v6 · doi: 10.48550/arxiv.1012.3127 · pith_short_12: P4ZGAK35OREJ · pith_short_16: P4ZGAK35OREJSOWT · pith_short_8: P4ZGAK35

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/P4ZGAK35OREJSOWTBQQPL6BZXW \
  | 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: 7f32602b7d7448993ad30c20f5f839bd8a1187df7f3cd32c94ea5badd899d11f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9444867454bc57b9dba7dc1b42e762cc8770566ff5b201b699a9fdc6128d442",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-14T18:44:06Z",
    "title_canon_sha256": "0df06412d67732494a4c91a77fdc5e69e9dc4ae43f20f82aee99eae5c1a0ed5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3127",
    "kind": "arxiv",
    "version": 6
  }
}