Pith Number

pith:IGRX2POF

pith:2016:IGRX2POFZARLWILVL4R62273FP

not attested not anchored not stored refs pending

Ergodic Theory for Controlled Markov Chains with Stationary Inputs

Ana Bu\v{s}i\'c, Sean Meyn, Yue Chen

arxiv:1604.04013 v2 · 2016-04-14 · cs.PF · cs.IT · math.IT · stat.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IGRX2POFZARLWILVL4R62273FP}

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	2026-05-18T00:05:40.021260Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41a37d3dc5c822bb21755f23ed6bfb2bcc2ae61a24c096bc34f9adda90bae85a

Aliases

arxiv: 1604.04013 · arxiv_version: 1604.04013v2 · doi: 10.48550/arxiv.1604.04013 · pith_short_12: IGRX2POFZARL · pith_short_16: IGRX2POFZARLWILV · pith_short_8: IGRX2POF

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/IGRX2POFZARLWILVL4R62273FP \
  | 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: 41a37d3dc5c822bb21755f23ed6bfb2bcc2ae61a24c096bc34f9adda90bae85a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1298565dcc0e7cbad9fe16a5e7f7d46e8e975796df8267bfcd564f593a5f5e3",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "stat.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.PF",
    "submitted_at": "2016-04-14T02:16:52Z",
    "title_canon_sha256": "cce5c90e187cce5653df47d5380420d26ad857dee02b96ec9d57915274e56a5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.04013",
    "kind": "arxiv",
    "version": 2
  }
}