Pith Number

pith:L5DWYCBK

pith:2016:L5DWYCBKUIA3C5635T5YJXSXAO

not attested not anchored not stored refs pending

Turan numbers of extensions of some sparse hypergraphs via Lagrangians

Biao Wu, Tao Jiang, Yuejian Peng

arxiv:1609.08983 v1 · 2016-09-28 · 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{L5DWYCBKUIA3C5635T5YJXSXAO}

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	2026-05-18T01:03:41.452248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f476c082aa201b177dbecfb84de57038d8a0b6e013cd83173d2e3ab427be1ab

Aliases

arxiv: 1609.08983 · arxiv_version: 1609.08983v1 · doi: 10.48550/arxiv.1609.08983 · pith_short_12: L5DWYCBKUIA3 · pith_short_16: L5DWYCBKUIA3C563 · pith_short_8: L5DWYCBK

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/L5DWYCBKUIA3C5635T5YJXSXAO \
  | 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: 5f476c082aa201b177dbecfb84de57038d8a0b6e013cd83173d2e3ab427be1ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af0cc603254516732dc42b9051f0d25aecac6cfc683c3e13fb5d6ffe91190694",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-28T16:06:40Z",
    "title_canon_sha256": "f1648636b288c26fff00f64c516ffed73eb41f86f7ff202721ffe4aae3590236"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.08983",
    "kind": "arxiv",
    "version": 1
  }
}