Pith Number

pith:BFTRDQN5

pith:2017:BFTRDQN5D22ZE3QBXCTBZSFTPF

not attested not anchored not stored refs pending

On a generalization of the Bessel function Neumann expansion

Antti Koskela, Elias Jarlebring

arxiv:1712.04387 v1 · 2017-12-12 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BFTRDQN5D22ZE3QBXCTBZSFTPF}

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	2026-05-18T00:28:08.154946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

096711c1bd1eb5926e01b8a61cc8b37940bbabc78ef8230d5413e537414fe20a

Aliases

arxiv: 1712.04387 · arxiv_version: 1712.04387v1 · doi: 10.48550/arxiv.1712.04387 · pith_short_12: BFTRDQN5D22Z · pith_short_16: BFTRDQN5D22ZE3QB · pith_short_8: BFTRDQN5

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/BFTRDQN5D22ZE3QBXCTBZSFTPF \
  | 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: 096711c1bd1eb5926e01b8a61cc8b37940bbabc78ef8230d5413e537414fe20a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ba8e483f379ceb31514d8d1cd50210c219ef6b9d0ba7decec7e34326c4a9e6e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2017-12-12T16:54:37Z",
    "title_canon_sha256": "c8f2b420c10eea9d13ebbef033b3a57b613005f25f00ec88052f0b8980f2e4c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.04387",
    "kind": "arxiv",
    "version": 1
  }
}