Pith Number

pith:3MGTLEV3

pith:2008:3MGTLEV3DHKIEOVXBBZKTN6E3W

not attested not anchored not stored refs pending

Askey--Wilson polynomials, quadratic harnesses and martingales

Jacek Weso{\l}owski, W{\l}odek Bryc

arxiv:0812.0657 v3 · 2008-12-03 · math.PR · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3MGTLEV3DHKIEOVXBBZKTN6E3W}

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	2026-05-18T02:46:31.797137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db0d3592bb19d4823ab70872a9b7c4dd9333318065feedcf4287c35c67b9a4da

Aliases

arxiv: 0812.0657 · arxiv_version: 0812.0657v3 · doi: 10.48550/arxiv.0812.0657 · pith_short_12: 3MGTLEV3DHKI · pith_short_16: 3MGTLEV3DHKIEOVX · pith_short_8: 3MGTLEV3

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/3MGTLEV3DHKIEOVXBBZKTN6E3W \
  | 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: db0d3592bb19d4823ab70872a9b7c4dd9333318065feedcf4287c35c67b9a4da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dc3e83e530f61f4c1f3072bfcbaf2cf115dfd9093746be98c51c07e9e9c37c1",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-12-03T06:19:03Z",
    "title_canon_sha256": "33f8afcdeacbf9d7a0a90b4e0888f1e79ed44754ee48f4b309343e28267f8faa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.0657",
    "kind": "arxiv",
    "version": 3
  }
}