Pith Number

pith:5OVMQRWI

pith:2019:5OVMQRWID2GD7G2HIEOUSXUWDU

not attested not anchored not stored refs pending

Euler and the Multiplication Formula for the Gamma Function

Alexander Aycock

arxiv:1901.03400 v1 · 2019-01-10 · math.HO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5OVMQRWID2GD7G2HIEOUSXUWDU}

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	2026-05-17T23:56:31.329775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebaac846c81e8c3f9b47411d495e961d16dd998dabdd7e9e2cef37d94a959491

Aliases

arxiv: 1901.03400 · arxiv_version: 1901.03400v1 · doi: 10.48550/arxiv.1901.03400 · pith_short_12: 5OVMQRWID2GD · pith_short_16: 5OVMQRWID2GD7G2H · pith_short_8: 5OVMQRWI

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/5OVMQRWID2GD7G2HIEOUSXUWDU \
  | 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: ebaac846c81e8c3f9b47411d495e961d16dd998dabdd7e9e2cef37d94a959491

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42f8cb63f6e998c26aea2e04d1242843e037df028b8a107a54127e76f08d00c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2019-01-10T21:21:42Z",
    "title_canon_sha256": "689b92906dcd420f51cdb99111af478d2868ebd437c48401182c307df730dc59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.03400",
    "kind": "arxiv",
    "version": 1
  }
}