Pith Number

pith:2PT4BGYQ

pith:2008:2PT4BGYQ3KFKXTU5E5KLJIRQI5

not attested not anchored not stored refs pending

On Relations Between Urbanik and Mehler Semigroups

Zbigniew J. Jurek

arxiv:0811.2989 v1 · 2008-11-18 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2PT4BGYQ3KFKXTU5E5KLJIRQI5}

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	2026-05-18T04:40:57.441994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3e7c09b10da8aabce9d2754b4a230476ada9727312e894867a72a39ad0ced2b

Aliases

arxiv: 0811.2989 · arxiv_version: 0811.2989v1 · doi: 10.48550/arxiv.0811.2989 · pith_short_12: 2PT4BGYQ3KFK · pith_short_16: 2PT4BGYQ3KFKXTU5 · pith_short_8: 2PT4BGYQ

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/2PT4BGYQ3KFKXTU5E5KLJIRQI5 \
  | 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: d3e7c09b10da8aabce9d2754b4a230476ada9727312e894867a72a39ad0ced2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c408c4a8f317a1d54a2a548c949624e62ca0eff31912fe22cf1f3f230317d6a7",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-11-18T20:33:09Z",
    "title_canon_sha256": "2f13659eb0313b2da564bf90d28d1f1335053dbe5411fb55b3d9b83dc5d5499a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.2989",
    "kind": "arxiv",
    "version": 1
  }
}