Pith Number

pith:KZCVP5KE

pith:2004:KZCVP5KE5QEUUKNOHPJFN3O3KM

not attested not anchored not stored refs pending

Combinatorial proofs of inverse relations and log-concavity for Bessel numbers

Hyuk Han, Seunghyun Seo

arxiv:math/0406378 v2 · 2004-06-18 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KZCVP5KE5QEUUKNOHPJFN3O3KM}

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	2026-07-04T14:38:43.829420Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

564557f544ec094a29ae3bd256eddb533927fc6a6ea45ad14bfed26d07342526

Aliases

arxiv: math/0406378 · arxiv_version: math/0406378v2 · doi: 10.48550/arxiv.math/0406378 · pith_short_12: KZCVP5KE5QEU · pith_short_16: KZCVP5KE5QEUUKNO · pith_short_8: KZCVP5KE

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/KZCVP5KE5QEUUKNOHPJFN3O3KM \
  | 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: 564557f544ec094a29ae3bd256eddb533927fc6a6ea45ad14bfed26d07342526

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4366420adccbd5a46715bf6b4349540d8e70c3b3b3ac5e8e8360928600f23f47",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2004-06-18T19:16:53Z",
    "title_canon_sha256": "c74937637adce1431f22c25a9c502c6a2297baed3517c215a8a41ddb7022f415"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406378",
    "kind": "arxiv",
    "version": 2
  }
}