Pith Number

pith:WKNWOT4M

pith:2015:WKNWOT4MFVDZPBSXHNKPN7QIS2

not attested not anchored not stored refs pending

The complete $p$-elliptic integrals and a computation formula of $\pi_p$ for $p=4$

Shingo Takeuchi

arxiv:1503.02394 v1 · 2015-03-09 · math.CA · math.AP · 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{WKNWOT4MFVDZPBSXHNKPN7QIS2}

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	2026-05-17T23:51:44.731525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b29b674f8c2d479786573b54f6fe0896a032dbdd59351c0ddc3c680e70b0277b

Aliases

arxiv: 1503.02394 · arxiv_version: 1503.02394v1 · doi: 10.48550/arxiv.1503.02394 · pith_short_12: WKNWOT4MFVDZ · pith_short_16: WKNWOT4MFVDZPBSX · pith_short_8: WKNWOT4M

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/WKNWOT4MFVDZPBSXHNKPN7QIS2 \
  | 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: b29b674f8c2d479786573b54f6fe0896a032dbdd59351c0ddc3c680e70b0277b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "989feda0ae8872de332d62e34ed52a968c0f0ff51fd88f1e251f8347b6c55e7f",
    "cross_cats_sorted": [
      "math.AP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-03-09T08:38:58Z",
    "title_canon_sha256": "156df2861152c9fe1d3bc9876e0a1e06fd74c95c5c463c70b3c7e266fb84eb80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02394",
    "kind": "arxiv",
    "version": 1
  }
}