Pith Number

pith:MAKBXANJ

pith:2002:MAKBXANJ5UNTDK67CIDZ6OABMC

not attested not anchored not stored refs pending

On the ubiquity of the Levy integral, its relationship with the generalised Euler-Jacobi series, and their asymptotics beyond all orders

N.E. Frankel, T.M. Garoni

arxiv:math-ph/0211011 v1 · 2002-11-08 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MAKBXANJ5UNTDK67CIDZ6OABMC}

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	2026-05-18T03:40:16.653788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60141b81a9ed1b31abdf12079f380160ab462aac2597eae3d48b44fc2b518d62

Aliases

arxiv: math-ph/0211011 · arxiv_version: math-ph/0211011v1 · doi: 10.48550/arxiv.math-ph/0211011 · pith_short_12: MAKBXANJ5UNT · pith_short_16: MAKBXANJ5UNTDK67 · pith_short_8: MAKBXANJ

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/MAKBXANJ5UNTDK67CIDZ6OABMC \
  | 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: 60141b81a9ed1b31abdf12079f380160ab462aac2597eae3d48b44fc2b518d62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdcccb85d5b339a104c5e80cc86288e83f8c461000e9843ee87218e1fbda928c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2002-11-08T00:43:35Z",
    "title_canon_sha256": "9be0acf8fb2b1956a52daf9fedda49b67970864bcbdc00b2853c74ff1c8f2df9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0211011",
    "kind": "arxiv",
    "version": 1
  }
}