Pith Number

pith:TMBBP7YD

pith:2010:TMBBP7YDMLRJOR2XMYLRJSPSIG

not attested not anchored not stored refs pending

On the generalized higher-order q-Bernoulli numbers and polynomials

Byungje Lee, C. S. Ryoo, T. Kim

arxiv:1008.1435 v1 · 2010-08-09 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TMBBP7YDMLRJOR2XMYLRJSPSIG}

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	2026-05-18T04:42:24.307045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b0217ff0362e2974757661714c9f24192050cb0bab6e6d162ca89ad07ba872e

Aliases

arxiv: 1008.1435 · arxiv_version: 1008.1435v1 · doi: 10.48550/arxiv.1008.1435 · pith_short_12: TMBBP7YDMLRJ · pith_short_16: TMBBP7YDMLRJOR2X · pith_short_8: TMBBP7YD

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/TMBBP7YDMLRJOR2XMYLRJSPSIG \
  | 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: 9b0217ff0362e2974757661714c9f24192050cb0bab6e6d162ca89ad07ba872e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4287bfb5121d72ef8e0db242f28b89362ff5d2e2b5a3b26e57c351e4c00e8a0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-08-09T01:16:29Z",
    "title_canon_sha256": "9166fadbe79089787b689212dc843448f42816764967c64015b1222bd33c4d8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1435",
    "kind": "arxiv",
    "version": 1
  }
}