Pith Number

pith:6VFUT2MI

pith:2013:6VFUT2MIVEKOQXOSLLRBSF2KIT

not attested not anchored not stored refs pending

Approximation by normal distribution for a sample sum in sampling without replacement from a finite population

Ibrahim Bin Mohamed (University of Malaya, Malaysia), Sherzod M. Mirakhmedov (Institute of Mathematics, Tashkent)

arxiv:1312.3256 v1 · 2013-12-11 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6VFUT2MIVEKOQXOSLLRBSF2KIT}

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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	2026-05-18T03:05:00.090423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f54b49e988a914e85dd25ae219174a44d6beeb869db9afc6fbae1ed69664b8c1

Aliases

arxiv: 1312.3256 · arxiv_version: 1312.3256v1 · doi: 10.48550/arxiv.1312.3256 · pith_short_12: 6VFUT2MIVEKO · pith_short_16: 6VFUT2MIVEKOQXOS · pith_short_8: 6VFUT2MI

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/6VFUT2MIVEKOQXOSLLRBSF2KIT \
  | 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: f54b49e988a914e85dd25ae219174a44d6beeb869db9afc6fbae1ed69664b8c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02b880d9af44da3d147e1a11b4f18f05fe0e0ea53a4015fcd27188ac6f9b54c2",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2013-12-11T17:41:30Z",
    "title_canon_sha256": "ff6eb8ab3cbfa6a3b051af4cebf88132192af32716978d605a2fe68810065636"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3256",
    "kind": "arxiv",
    "version": 1
  }
}