Pith Number

pith:HG3MLHT3

pith:2012:HG3MLHT3GM3XJAGQURZQSMEOBH

not attested not anchored not stored refs pending

The Asymptotic Bound of the Lubell Function for Diamond-free Families

Wei-Tian Li

arxiv:1206.0806 v2 · 2012-06-05 · 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{HG3MLHT3GM3XJAGQURZQSMEOBH}

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	2026-05-18T03:53:16.953465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39b6c59e7b33377480d0a47309308e09fea8033413d4f84e23a62950d3ff01bc

Aliases

arxiv: 1206.0806 · arxiv_version: 1206.0806v2 · doi: 10.48550/arxiv.1206.0806 · pith_short_12: HG3MLHT3GM3X · pith_short_16: HG3MLHT3GM3XJAGQ · pith_short_8: HG3MLHT3

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/HG3MLHT3GM3XJAGQURZQSMEOBH \
  | 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: 39b6c59e7b33377480d0a47309308e09fea8033413d4f84e23a62950d3ff01bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d73442a48fce0445c98915707f2634b894b763e34637d831835a43cb76203d67",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-06-05T01:31:32Z",
    "title_canon_sha256": "a3d78737fb9063727efc53cc7ede1f66380c372f533e170f42d947ce32c778a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0806",
    "kind": "arxiv",
    "version": 2
  }
}