Pith Number

pith:YZOAW4QO

pith:2013:YZOAW4QO7TSBID6XY3BNRQ7WRB

not attested not anchored not stored refs pending

Exponential ergodicity for Markov processes with random switching

Bertrand Cloez, Martin Hairer

arxiv:1303.6999 v2 · 2013-03-27 · math.PR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YZOAW4QO7TSBID6XY3BNRQ7WRB}

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	2026-05-18T02:19:06.381951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c65c0b720efce4140fd7c6c2d8c3f688470fbdddfc8dc81b70d9fed5dff27e71

Aliases

arxiv: 1303.6999 · arxiv_version: 1303.6999v2 · doi: 10.48550/arxiv.1303.6999 · pith_short_12: YZOAW4QO7TSB · pith_short_16: YZOAW4QO7TSBID6X · pith_short_8: YZOAW4QO

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/YZOAW4QO7TSBID6XY3BNRQ7WRB \
  | 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: c65c0b720efce4140fd7c6c2d8c3f688470fbdddfc8dc81b70d9fed5dff27e71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c26134949ab8c5bd81af8a9e8f7cfa7089daba81d597bf6e2a9e4ded42dd6db",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-03-27T22:52:35Z",
    "title_canon_sha256": "f27968952e75912aabb52b035d6a796a999733ba63033073204ca66efe059b16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.6999",
    "kind": "arxiv",
    "version": 2
  }
}