Pith Number

pith:D52GFPBJ

pith:2014:D52GFPBJXHUPN6WCFBPQWC4JJI

not attested not anchored not stored refs pending

A New Proof of Stirling's Formula

Thorsten Neuschel

arxiv:1407.3775 v1 · 2014-07-10 · math.HO · 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{D52GFPBJXHUPN6WCFBPQWC4JJI}

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	2026-05-18T02:47:41.702291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f7462bc29b9e8f6fac2285f0b0b894a210ebb94c202f99c29070bae376647d7

Aliases

arxiv: 1407.3775 · arxiv_version: 1407.3775v1 · doi: 10.48550/arxiv.1407.3775 · pith_short_12: D52GFPBJXHUP · pith_short_16: D52GFPBJXHUPN6WC · pith_short_8: D52GFPBJ

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/D52GFPBJXHUPN6WCFBPQWC4JJI \
  | 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: 1f7462bc29b9e8f6fac2285f0b0b894a210ebb94c202f99c29070bae376647d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ed312914ee68823585f40c9136e85ddcd346e12fb488fefa5f919c0054bbf5c",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2014-07-10T11:26:39Z",
    "title_canon_sha256": "cb163802c21b597a1a92a7fddb8e43e54ad396c126e480f98bc8cc6800395cb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.3775",
    "kind": "arxiv",
    "version": 1
  }
}