Pith Number

pith:ZTYKU54Q

pith:2011:ZTYKU54Q6AN5XXSWUDQC6TOBBM

not attested not anchored not stored refs pending

La s\'erie enti\`ere $1+\frac z{\Gamma(1+i)}+\frac{z^2}{\Gamma(1+2i)}+\frac{z^3}{\Gamma(1+3i)}+...$ poss\`ede une fronti\`ere naturelle~!

Changgui Zhang

arxiv:1102.1156 v1 · 2011-02-06 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZTYKU54Q6AN5XXSWUDQC6TOBBM}

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	2026-05-18T04:29:54.894127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccf0aa7790f01bdbde56a0e02f4dc10b218c2a259447f1b3543b3c18380da508

Aliases

arxiv: 1102.1156 · arxiv_version: 1102.1156v1 · doi: 10.48550/arxiv.1102.1156 · pith_short_12: ZTYKU54Q6AN5 · pith_short_16: ZTYKU54Q6AN5XXSW · pith_short_8: ZTYKU54Q

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/ZTYKU54Q6AN5XXSWUDQC6TOBBM \
  | 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: ccf0aa7790f01bdbde56a0e02f4dc10b218c2a259447f1b3543b3c18380da508

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba09e937c6453347f65b7fe3725bc0409d1666c37300c756fb70614cbb0cde4f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2011-02-06T14:18:47Z",
    "title_canon_sha256": "d8280c0c7bf629c541a82cade5955bb1c962c5e41cec7552e944492b035e87c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1156",
    "kind": "arxiv",
    "version": 1
  }
}