Pith Number

pith:Y4DQHRDV

pith:2011:Y4DQHRDVEZIZRHF4FZCSR6OGOP

not attested not anchored not stored refs pending

Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials

Francisco J. Ruiz, Juan L. Varona, Luis M. Navas

arxiv:1102.1493 v2 · 2011-02-08 · 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{Y4DQHRDVEZIZRHF4FZCSR6OGOP}

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	2026-05-18T03:41:32.406265Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c70703c4752651989cbc2e4528f9c673d16d49212d970fac66224af90825ec01

Aliases

arxiv: 1102.1493 · arxiv_version: 1102.1493v2 · doi: 10.48550/arxiv.1102.1493 · pith_short_12: Y4DQHRDVEZIZ · pith_short_16: Y4DQHRDVEZIZRHF4 · pith_short_8: Y4DQHRDV

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/Y4DQHRDVEZIZRHF4FZCSR6OGOP \
  | 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: c70703c4752651989cbc2e4528f9c673d16d49212d970fac66224af90825ec01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d72f6816edbfff909eca34fbdf263a1b68feda98f18358d45170e640150bd0a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-02-08T02:40:53Z",
    "title_canon_sha256": "e5d8292f9fed4f51a6db1d42a69e8f44a8676b6823fdff7e65ae2c99ac2ef4e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1493",
    "kind": "arxiv",
    "version": 2
  }
}