Pith Number

pith:P4GMAHS4

pith:2016:P4GMAHS4S7UXU2P7A3MEOJXB6U

not attested not anchored not stored refs pending

Computation of asymptotic expansions of turning point problems via Cauchy's integral formula: Bessel functions

A. Gil, J. Segura, T. M. Dunster

arxiv:1607.08269 v3 · 2016-07-27 · math.CA · 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{P4GMAHS4S7UXU2P7A3MEOJXB6U}

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	2026-05-18T00:50:04.367889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f0cc01e5c97e97a69ff06d84726e1f51a7e45dbb11b23b93e8c8f2d0bccdada

Aliases

arxiv: 1607.08269 · arxiv_version: 1607.08269v3 · doi: 10.48550/arxiv.1607.08269 · pith_short_12: P4GMAHS4S7UX · pith_short_16: P4GMAHS4S7UXU2P7 · pith_short_8: P4GMAHS4

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/P4GMAHS4S7UXU2P7A3MEOJXB6U \
  | 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: 7f0cc01e5c97e97a69ff06d84726e1f51a7e45dbb11b23b93e8c8f2d0bccdada

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a39db4a12e8d1d212b7e68c7e5be127293de3e78098da7218b462c2fb37a82e7",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-07-27T21:28:41Z",
    "title_canon_sha256": "7c2aec580846bc2cd00478aa67685bfe9dc25331ffc1f9edb86538d7623d0ff4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.08269",
    "kind": "arxiv",
    "version": 3
  }
}