Pith Number

pith:V3JQ5FSH

pith:2004:V3JQ5FSHC4GTNZPTVQ26ZXOKNE

not attested not anchored not stored refs pending

Series expansions for the third incomplete elliptic integral via partial fraction decompositions

A. Savenkova, D. Karp, S.M. Sitnik

arxiv:math/0410009 v3 · 2004-10-01 · 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{V3JQ5FSHC4GTNZPTVQ26ZXOKNE}

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	2026-05-18T02:28:05.737840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aed30e9647170d36e5f3ac35ecddca6917fabc03a5b3643619ceb2205e55a5c1

Aliases

arxiv: math/0410009 · arxiv_version: math/0410009v3 · doi: 10.48550/arxiv.math/0410009 · pith_short_12: V3JQ5FSHC4GT · pith_short_16: V3JQ5FSHC4GTNZPT · pith_short_8: V3JQ5FSH

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/V3JQ5FSHC4GTNZPTVQ26ZXOKNE \
  | 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: aed30e9647170d36e5f3ac35ecddca6917fabc03a5b3643619ceb2205e55a5c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ace78486dc2459e9925c4e0d8210554bee1f8f8bfe8ae6dfd929a1091d27d728",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2004-10-01T08:48:58Z",
    "title_canon_sha256": "cc2ec77b908309a9acbdec8e6814b58e1e6806ce17faacfc790ff4929f66d82f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0410009",
    "kind": "arxiv",
    "version": 3
  }
}