Pith Number

pith:TEYG4HNU

pith:2012:TEYG4HNUIZU4KAW2XXUQVRKS2T

not attested not anchored not stored refs pending

Symbolic methods for the evaluation of sum rules of Bessel functions

D. Babusci, G. Dattoli, K. A. Penson, K. Gorska

arxiv:1209.5114 v2 · 2012-09-23 · math-ph · math.CA · 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{TEYG4HNUIZU4KAW2XXUQVRKS2T}

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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	2026-05-18T01:54:19.733347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99306e1db44669c502dabde90ac552d4c083c64ab23c8ea52258d8b65b4646bb

Aliases

arxiv: 1209.5114 · arxiv_version: 1209.5114v2 · doi: 10.48550/arxiv.1209.5114 · pith_short_12: TEYG4HNUIZU4 · pith_short_16: TEYG4HNUIZU4KAW2 · pith_short_8: TEYG4HNU

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/TEYG4HNUIZU4KAW2XXUQVRKS2T \
  | 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: 99306e1db44669c502dabde90ac552d4c083c64ab23c8ea52258d8b65b4646bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09f95052bc09d9283ac0dd4b963d00ce19fb2e7d0545804615eb5f3f67f637cb",
    "cross_cats_sorted": [
      "math.CA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-09-23T21:41:11Z",
    "title_canon_sha256": "90f359dc6bc88458325f9ae39d1b942f6c5cce429972e9a2fee3fc088031b327"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5114",
    "kind": "arxiv",
    "version": 2
  }
}