Pith Number

pith:MBUISNPB

pith:2021:MBUISNPBZFNSO3UDT64HI2NA6G

not attested not anchored not stored refs pending

The 3-adic valuations of Stirling numbers of the first kind

Long Chen, Min Qiu, Zongbing Lin

arxiv:2109.13458 v2 · 2021-09-28 · 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{MBUISNPBZFNSO3UDT64HI2NA6G}

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	2026-05-20T00:02:44.405221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60688935e1c95b276e839fb87469a0f191bdd4533dae5f29f5c00e04cee84521

Aliases

arxiv: 2109.13458 · arxiv_version: 2109.13458v2 · doi: 10.48550/arxiv.2109.13458 · pith_short_12: MBUISNPBZFNS · pith_short_16: MBUISNPBZFNSO3UD · pith_short_8: MBUISNPB

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/MBUISNPBZFNSO3UDT64HI2NA6G \
  | 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: 60688935e1c95b276e839fb87469a0f191bdd4533dae5f29f5c00e04cee84521

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ec327c22e2e24229d321d9809fd7e7187ddbf056a81144a567f30325fdbc34d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-09-28T03:16:51Z",
    "title_canon_sha256": "12fa80c0f38ee4ec7a61b70d8f8b63c76efdf7643073150462530c481b8fb7cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.13458",
    "kind": "arxiv",
    "version": 2
  }
}