Pith Number

pith:VCVUYZWM

pith:2012:VCVUYZWMUI2NFTFQZFBWQMYWAD

not attested not anchored not stored refs pending

Derivative formulas for Bessel, Struve and Anger-Weber functions

Robert E. Gaunt

arxiv:1211.2759 v2 · 2012-11-06 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VCVUYZWMUI2NFTFQZFBWQMYWAD}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:40:29.050052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8ab4c66cca234d2ccb0c94368331600da46c066d7ec4d706d51d2db2affd1dc

Aliases

arxiv: 1211.2759 · arxiv_version: 1211.2759v2 · doi: 10.48550/arxiv.1211.2759 · pith_short_12: VCVUYZWMUI2N · pith_short_16: VCVUYZWMUI2NFTFQ · pith_short_8: VCVUYZWM

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/VCVUYZWMUI2NFTFQZFBWQMYWAD \
  | 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: a8ab4c66cca234d2ccb0c94368331600da46c066d7ec4d706d51d2db2affd1dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9335fc3f06e7e1173badf8dd0cd5c16f768e0a219d08150c57d5576bda863d61",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-11-06T15:28:33Z",
    "title_canon_sha256": "8d12f57fffb21b6164937d8a2d443da5575bb47d97362d49dba80460aedf1d0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2759",
    "kind": "arxiv",
    "version": 2
  }
}