Pith Number

pith:6CCXCE6V

pith:2019:6CCXCE6VIDQ7D7X5IQRZGUQN7P

not attested not anchored not stored refs pending

Asymptotic expoansions of mathieu-Bessel series. I

R B Paris

arxiv:1907.01812 v2 · 2019-07-03 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6CCXCE6VIDQ7D7X5IQRZGUQN7P}

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	2026-05-17T23:41:16.951889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0857113d540e1f1fefd442393520dfbd8f2388fbddc7826ef18445722e3ba51

Aliases

arxiv: 1907.01812 · arxiv_version: 1907.01812v2 · doi: 10.48550/arxiv.1907.01812 · pith_short_12: 6CCXCE6VIDQ7 · pith_short_16: 6CCXCE6VIDQ7D7X5 · pith_short_8: 6CCXCE6V

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/6CCXCE6VIDQ7D7X5IQRZGUQN7P \
  | 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: f0857113d540e1f1fefd442393520dfbd8f2388fbddc7826ef18445722e3ba51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68bb5cdcbb8271bed79011e58b4b49eb820715d9c38213c32e0fcf4ad0375d04",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-07-03T09:28:54Z",
    "title_canon_sha256": "b781e156dc41a5855f9c26327a0c34615f818bf1231b8ea904e1f77b44995544"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.01812",
    "kind": "arxiv",
    "version": 2
  }
}