Pith Number

pith:ABCIZZXG

pith:2013:ABCIZZXGYO6E3XRB7LQYZI55S6

not attested not anchored not stored refs pending

Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis

Armen Bagdasaryan, Mehmet Acikgoz, Serkan Araci, Yuan He

arxiv:1311.4148 v4 · 2013-11-17 · 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{ABCIZZXGYO6E3XRB7LQYZI55S6}

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	2026-05-17T23:41:37.729480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00448ce6e6c3bc4dde21fae18ca3bd97bbada747a181803bdc0643d1cbf1beeb

Aliases

arxiv: 1311.4148 · arxiv_version: 1311.4148v4 · doi: 10.48550/arxiv.1311.4148 · pith_short_12: ABCIZZXGYO6E · pith_short_16: ABCIZZXGYO6E3XRB · pith_short_8: ABCIZZXG

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/ABCIZZXGYO6E3XRB7LQYZI55S6 \
  | 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: 00448ce6e6c3bc4dde21fae18ca3bd97bbada747a181803bdc0643d1cbf1beeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54fa73df6f5d049e971c936b888a7235bb9052da862200a0389ce8fde31faec8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-17T11:35:00Z",
    "title_canon_sha256": "f5ca4950a84a065c8f4e2100f1ee756ac77359439b19741f784c1281e59c06d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.4148",
    "kind": "arxiv",
    "version": 4
  }
}