Pith Number

pith:VYIVR7LR

pith:2019:VYIVR7LRHT6ALLTRVRPMNCUPKQ

not attested not anchored not stored refs pending

High-order derivatives of the Bessel functions with an application

R B Paris

arxiv:1905.04673 v1 · 2019-05-12 · 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{VYIVR7LRHT6ALLTRVRPMNCUPKQ}

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	2026-05-17T23:46:23.992480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae1158fd713cfc05ae71ac5ec68a8f542dc40850d2a6a698255b2bbd9179aeb9

Aliases

arxiv: 1905.04673 · arxiv_version: 1905.04673v1 · doi: 10.48550/arxiv.1905.04673 · pith_short_12: VYIVR7LRHT6A · pith_short_16: VYIVR7LRHT6ALLTR · pith_short_8: VYIVR7LR

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/VYIVR7LRHT6ALLTRVRPMNCUPKQ \
  | 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: ae1158fd713cfc05ae71ac5ec68a8f542dc40850d2a6a698255b2bbd9179aeb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b4005ebfd26842a89f0be0c1e39c57642bbc8f7267c2c5cdda41b10330130df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-05-12T09:08:24Z",
    "title_canon_sha256": "50e385782503d46f1344cf1447b7a79ad59e388995755d5330b9ae261c991cb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.04673",
    "kind": "arxiv",
    "version": 1
  }
}