Pith Number

pith:FLMK7BEY

pith:2018:FLMK7BEYN4VY76FWTZELGX7JLG

not attested not anchored not stored refs pending

Asymptotic relation for zeros of cross-product of Bessel functions and applications

Vladimir Bobkov

arxiv:1803.09972 v2 · 2018-03-27 · math.CA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FLMK7BEYN4VY76FWTZELGX7JLG}

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	2026-05-17T23:57:59.484922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ad8af84986f2b8ff8b69e48b35fe959b6823e9abfb8e6fef2521e17f9dcecd4

Aliases

arxiv: 1803.09972 · arxiv_version: 1803.09972v2 · doi: 10.48550/arxiv.1803.09972 · pith_short_12: FLMK7BEYN4VY · pith_short_16: FLMK7BEYN4VY76FW · pith_short_8: FLMK7BEY

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/FLMK7BEYN4VY76FWTZELGX7JLG \
  | 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: 2ad8af84986f2b8ff8b69e48b35fe959b6823e9abfb8e6fef2521e17f9dcecd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "999532a30a73d58bbb56ab6bbf98ddf986e1f76656973f86cf5c5a48fa40cdfd",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-03-27T09:10:43Z",
    "title_canon_sha256": "6659ec9f419f58d5ae2c16e8f445e4621a461f18e5bc580e9cb439b56c255bf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.09972",
    "kind": "arxiv",
    "version": 2
  }
}