Pith Number

pith:7TDQXAVH

pith:2011:7TDQXAVHG4OSJI2XHPPI5VBHZZ

not attested not anchored not stored refs pending

Numerical calculation of Bessel, Hankel and Airy functions

E. L\"otstedt, U. D. Jentschura

arxiv:1112.0072 v1 · 2011-12-01 · math.NA · physics.atom-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7TDQXAVHG4OSJI2XHPPI5VBHZZ}

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	2026-05-18T03:56:22.266668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcc70b82a7371d24a3573bde8ed427ce51f48871088981201229b156ddb2ee85

Aliases

arxiv: 1112.0072 · arxiv_version: 1112.0072v1 · doi: 10.48550/arxiv.1112.0072 · pith_short_12: 7TDQXAVHG4OS · pith_short_16: 7TDQXAVHG4OSJI2X · pith_short_8: 7TDQXAVH

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/7TDQXAVHG4OSJI2XHPPI5VBHZZ \
  | 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: fcc70b82a7371d24a3573bde8ed427ce51f48871088981201229b156ddb2ee85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a5e7c3515f87aac209d2e86664fc4b443396ce4ad2b0df209194f957c571e9e",
    "cross_cats_sorted": [
      "physics.atom-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-12-01T03:05:08Z",
    "title_canon_sha256": "e03bbae9baafff1eeab46ecc06f2711763e473d4f09f8b2b9487731557e91c33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0072",
    "kind": "arxiv",
    "version": 1
  }
}