Pith Number

pith:ODXMZPJP

pith:2024:ODXMZPJPKQX7AX4SJZBMKE6RRG

not attested not anchored not stored refs pending

Further analysis on the second frequency of union-closed set families

Saintan Wu

arxiv:2412.03863 v2 · 2024-12-05 · 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{ODXMZPJPKQX7AX4SJZBMKE6RRG}

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	2026-07-05T09:46:00.210539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70eeccbd2f542ff05f924e42c513d189a5500f2b2c1e00dbb3e3b7caf0a2f255

Aliases

arxiv: 2412.03863 · arxiv_version: 2412.03863v2 · doi: 10.48550/arxiv.2412.03863 · pith_short_12: ODXMZPJPKQX7 · pith_short_16: ODXMZPJPKQX7AX4S · pith_short_8: ODXMZPJP

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/ODXMZPJPKQX7AX4SJZBMKE6RRG \
  | 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: 70eeccbd2f542ff05f924e42c513d189a5500f2b2c1e00dbb3e3b7caf0a2f255

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2e9a07f846fa95a86be8f4d8bfcaca2dd838749bde2db22404051d4779ef761",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-05T04:19:16Z",
    "title_canon_sha256": "2b1addd47d8d9a345b11b0e0f6aa7b8fa1d39ea635a3fc7a7a1a78e97b69816c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.03863",
    "kind": "arxiv",
    "version": 2
  }
}