Pith Number

pith:77QW2X2K

pith:2015:77QW2X2KWCQ32C2JVFHV6CCIER

not attested not anchored not stored refs pending

Two-color balanced affine urn models with multiple drawings II: large-index and triangular urns

Hosam M. Mahmoud, Markus Kuba

arxiv:1509.09053 v1 · 2015-09-30 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{77QW2X2KWCQ32C2JVFHV6CCIER}

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	2026-05-18T01:31:29.229096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffe16d5f4ab0a1bd0b49a94f5f0848245978863f45dcfbfc78c45a1c86655a36

Aliases

arxiv: 1509.09053 · arxiv_version: 1509.09053v1 · doi: 10.48550/arxiv.1509.09053 · pith_short_12: 77QW2X2KWCQ3 · pith_short_16: 77QW2X2KWCQ32C2J · pith_short_8: 77QW2X2K

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/77QW2X2KWCQ32C2JVFHV6CCIER \
  | 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: ffe16d5f4ab0a1bd0b49a94f5f0848245978863f45dcfbfc78c45a1c86655a36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2e69c9bf779e38250a2326b8a67906f573838732fe2f07405381f8f745f849e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-30T07:57:19Z",
    "title_canon_sha256": "b802284468704c72a4361193869214b48c08281e026f7b646130147c86fbae0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.09053",
    "kind": "arxiv",
    "version": 1
  }
}