Pith Number

pith:4NBKV5T7

pith:2016:4NBKV5T7UYDTXFWFF3JP3FPZCA

not attested not anchored not stored refs pending

Doubly uniform complete law of large numbers for independent point processes

Tetsuya Hattori

arxiv:1612.09126 v1 · 2016-12-29 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4NBKV5T7UYDTXFWFF3JP3FPZCA}

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	2026-05-18T00:53:46.412289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e342aaf67fa6073b96c52ed2fd95f9103042535e0b366e1aa30face2c369ad5e

Aliases

arxiv: 1612.09126 · arxiv_version: 1612.09126v1 · doi: 10.48550/arxiv.1612.09126 · pith_short_12: 4NBKV5T7UYDT · pith_short_16: 4NBKV5T7UYDTXFWF · pith_short_8: 4NBKV5T7

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/4NBKV5T7UYDTXFWFF3JP3FPZCA \
  | 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: e342aaf67fa6073b96c52ed2fd95f9103042535e0b366e1aa30face2c369ad5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d846cb4e64f896b3312278d99ff0540f0dae9605b1be0575dfd592ee2d4d644",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-29T12:53:01Z",
    "title_canon_sha256": "da7435b53b3ee9f6473b56e15514c56606b2203f75e69c90149bee81228b951b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09126",
    "kind": "arxiv",
    "version": 1
  }
}