Pith Number

pith:WCY5PDWM

pith:2013:WCY5PDWMZB3O3LRIFMSEKNJYLF

not attested not anchored not stored refs pending

On proving some of Ramanujan's formulas for $\frac{1}{\pi}$ with an elementary method

Alexander Aycock

arxiv:1309.1140 v2 · 2013-09-04 · 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{WCY5PDWMZB3O3LRIFMSEKNJYLF}

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	2026-05-18T03:14:08.090958Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0b1d78eccc876edae282b24453538594ddc8ad578b079ed8a24b3b179824290

Aliases

arxiv: 1309.1140 · arxiv_version: 1309.1140v2 · doi: 10.48550/arxiv.1309.1140 · pith_short_12: WCY5PDWMZB3O · pith_short_16: WCY5PDWMZB3O3LRI · pith_short_8: WCY5PDWM

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/WCY5PDWMZB3O3LRIFMSEKNJYLF \
  | 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: b0b1d78eccc876edae282b24453538594ddc8ad578b079ed8a24b3b179824290

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f857d1c2b40add5656a55effbfcf034538786e5c318bc44c7fed3d390f0416b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-04T19:10:51Z",
    "title_canon_sha256": "4a4355b7a16d800cdde7c469d250e9352bf364d6ad386070b5d7731c9210ea8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1140",
    "kind": "arxiv",
    "version": 2
  }
}