Pith Number

pith:7EVVV22Y

pith:2016:7EVVV22YHU4YYSBLMTNQJDIVZV

not attested not anchored not stored refs pending

Multivariate Krawtchouk polynomials and composition birth and death processes

Robert Griffiths

arxiv:1603.00196 v2 · 2016-03-01 · 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{7EVVV22YHU4YYSBLMTNQJDIVZV}

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	2026-05-18T01:15:49.344040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f92b5aeb583d398c482b64db048d15cd50ea1b965f71a6bbb26e97645feda551

Aliases

arxiv: 1603.00196 · arxiv_version: 1603.00196v2 · doi: 10.48550/arxiv.1603.00196 · pith_short_12: 7EVVV22YHU4Y · pith_short_16: 7EVVV22YHU4YYSBL · pith_short_8: 7EVVV22Y

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/7EVVV22YHU4YYSBLMTNQJDIVZV \
  | 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: f92b5aeb583d398c482b64db048d15cd50ea1b965f71a6bbb26e97645feda551

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31b6800e9d6e15b27b5eb642d6e62088effba16976395d920c284ee56a4a71ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-03-01T09:23:39Z",
    "title_canon_sha256": "22f71ec78901724f7cd128ea1be1a4b739f092d6638e2435a995dbdee9928020"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.00196",
    "kind": "arxiv",
    "version": 2
  }
}