Pith Number

pith:LE7NCEP3

pith:2013:LE7NCEP33CUM6ICHQGGUF7CPN3

not attested not anchored not stored refs pending

A Short Proof of Stirling's Formula

Hongwei Lou

arxiv:1312.5019 v1 · 2013-12-18 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LE7NCEP33CUM6ICHQGGUF7CPN3}

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	2026-05-18T03:04:16.543529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

593ed111fbd8a8cf2047818d42fc4f6ef62241bdd1b6078d4a5c55ca1acb4b84

Aliases

arxiv: 1312.5019 · arxiv_version: 1312.5019v1 · doi: 10.48550/arxiv.1312.5019 · pith_short_12: LE7NCEP33CUM · pith_short_16: LE7NCEP33CUM6ICH · pith_short_8: LE7NCEP3

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/LE7NCEP33CUM6ICHQGGUF7CPN3 \
  | 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: 593ed111fbd8a8cf2047818d42fc4f6ef62241bdd1b6078d4a5c55ca1acb4b84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77d628dbd6f414e8cbc19c29bbf1e6da511c4b2212544ab6713a0b58ad631bb7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-12-18T02:04:08Z",
    "title_canon_sha256": "f2d8956ff197ed3f00d1488e0e8f192e1166972aa844d8dd3afdb73a62780dfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5019",
    "kind": "arxiv",
    "version": 1
  }
}