Pith Number

pith:F3DTZOPE

pith:2016:F3DTZOPERMEKJ27MMG5AVML66P

not attested not anchored not stored refs pending

A Probabilistic Proof of the Multinomial Theorem

K. K. Kataria

arxiv:1608.01718 v1 · 2016-08-04 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F3DTZOPERMEKJ27MMG5AVML66P}

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	2026-05-17T23:39:42.348256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ec73cb9e48b08a4ebec61ba0ab17ef3eea9a6647f0f6c9123c9aa45be89e846

Aliases

arxiv: 1608.01718 · arxiv_version: 1608.01718v1 · doi: 10.48550/arxiv.1608.01718 · pith_short_12: F3DTZOPERMEK · pith_short_16: F3DTZOPERMEKJ27M · pith_short_8: F3DTZOPE

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/F3DTZOPERMEKJ27MMG5AVML66P \
  | 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: 2ec73cb9e48b08a4ebec61ba0ab17ef3eea9a6647f0f6c9123c9aa45be89e846

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8b22ccb096bcc2560c0c16e5debef4e0aa86572b9a4427dd643d476b7ebcaf2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2016-08-04T23:45:57Z",
    "title_canon_sha256": "17e1a91c42f372e5476574d89d54d8c3f0f41a7576a9d8e08b8b675a30eee4bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.01718",
    "kind": "arxiv",
    "version": 1
  }
}