Pith Number

pith:DBG4BWWG

pith:2009:DBG4BWWGKFENZUERNPDSMC7MQJ

not attested not anchored not stored refs pending

The 2-adic valuations of Stirling numbers of the second kind

Jianrong Zhao, Shaofang Hong, Wei Zhao

arxiv:0907.3412 v2 · 2009-07-20 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DBG4BWWGKFENZUERNPDSMC7MQJ}

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	2026-05-18T03:52:51.738344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

184dc0dac65148dcd0916bc7260bec824d6f0627292308ba30a9e42267be95a0

Aliases

arxiv: 0907.3412 · arxiv_version: 0907.3412v2 · doi: 10.48550/arxiv.0907.3412 · pith_short_12: DBG4BWWGKFEN · pith_short_16: DBG4BWWGKFENZUER · pith_short_8: DBG4BWWG

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/DBG4BWWGKFENZUERNPDSMC7MQJ \
  | 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: 184dc0dac65148dcd0916bc7260bec824d6f0627292308ba30a9e42267be95a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ab981694ffcc8dda8175c92bb84286b489876012764feccb9445ed15d257d54",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-07-20T14:51:34Z",
    "title_canon_sha256": "bcdca85d38ae456677d676690b59fd48b00a0fa5e41405559fb66ca65f5b5674"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.3412",
    "kind": "arxiv",
    "version": 2
  }
}