Pith Number

pith:KKKWJ5V5

pith:2011:KKKWJ5V5SCVSBNIJYPOVXB72HS

not attested not anchored not stored refs pending

Aspects of Recurrence and Transience for Levy Processes in Transformation Groups and Non-Compact Riemannian Symmetric Pairs

David Applebaum

arxiv:1103.4004 v1 · 2011-03-21 · math.PR · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KKKWJ5V5SCVSBNIJYPOVXB72HS}

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	2026-05-18T04:26:22.000984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

529564f6bd90ab20b509c3dd5b87fa3c934898af3f1dfb575442cbbc700e92c4

Aliases

arxiv: 1103.4004 · arxiv_version: 1103.4004v1 · doi: 10.48550/arxiv.1103.4004 · pith_short_12: KKKWJ5V5SCVS · pith_short_16: KKKWJ5V5SCVSBNIJ · pith_short_8: KKKWJ5V5

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/KKKWJ5V5SCVSBNIJYPOVXB72HS \
  | 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: 529564f6bd90ab20b509c3dd5b87fa3c934898af3f1dfb575442cbbc700e92c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85b19bc220238d02f8fa8fc898b72a4c7851da76ebc33d45c6a06438c4860b14",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-21T13:30:28Z",
    "title_canon_sha256": "74f0794a9015be03a168881b6a63cd0458ce7907cad456221b88daccd4454aa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4004",
    "kind": "arxiv",
    "version": 1
  }
}