Pith Number

pith:ULXZVXKN

pith:2012:ULXZVXKNJIBFN7MQPWRNN26WNK

not attested not anchored not stored refs pending

Analytical approximation for Landau's constants by using BPES method

Karem Boubaker, Lin Zhang

arxiv:1206.0345 v1 · 2012-06-02 · math-ph · math.FA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ULXZVXKNJIBFN7MQPWRNN26WNK}

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	2026-05-18T01:16:27.973492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2ef9add4d4a0256fd907da2d6ebd66a988d3ba3899352af2d477ceb506aa826

Aliases

arxiv: 1206.0345 · arxiv_version: 1206.0345v1 · doi: 10.48550/arxiv.1206.0345 · pith_short_12: ULXZVXKNJIBF · pith_short_16: ULXZVXKNJIBFN7MQ · pith_short_8: ULXZVXKN

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/ULXZVXKNJIBFN7MQPWRNN26WNK \
  | 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: a2ef9add4d4a0256fd907da2d6ebd66a988d3ba3899352af2d477ceb506aa826

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d75f682662b2dff79f7c15167b822c54653197c42f6e0274bb2dbbb62822c83",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-06-02T06:14:38Z",
    "title_canon_sha256": "80975d41ffff34038e42abf121a2cd706f80217b39d21aacaeab5051e9857c3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0345",
    "kind": "arxiv",
    "version": 1
  }
}