Pith Number

pith:X6QJURAV

pith:2016:X6QJURAVFSVU4SZUSDTTOOF7SY

not attested not anchored not stored refs pending

Ergodic Markov processes and Poisson equations (lecture notes)

Alexander Veretennikov

arxiv:1610.09661 v3 · 2016-10-30 · 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{X6QJURAVFSVU4SZUSDTTOOF7SY}

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	2026-05-18T00:09:42.431586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfa09a44152cab4e4b3490e73738bf96101fdc6d90c7d02b5a0cf7ac3a6d6b20

Aliases

arxiv: 1610.09661 · arxiv_version: 1610.09661v3 · doi: 10.48550/arxiv.1610.09661 · pith_short_12: X6QJURAVFSVU · pith_short_16: X6QJURAVFSVU4SZU · pith_short_8: X6QJURAV

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/X6QJURAVFSVU4SZUSDTTOOF7SY \
  | 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: bfa09a44152cab4e4b3490e73738bf96101fdc6d90c7d02b5a0cf7ac3a6d6b20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "014b238e8df83586212fd1a0fea03fb16a486da40ffaec9a3e2b336a4b74af15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-10-30T15:28:56Z",
    "title_canon_sha256": "27be327295e2ae00e96c02698a925eca51230c21d3608ad06f1b71b95d0345be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.09661",
    "kind": "arxiv",
    "version": 3
  }
}