Pith Number

pith:QYU7JWCA

pith:2016:QYU7JWCAAX7BSBUSGKES5RRYUK

not attested not anchored not stored refs pending

Ergodicity of inhomogeneous Markov chains through asymptotic pseudotrajectories

Bertrand Cloez (MISTEA), Florian Bouguet (Inria, IECL), Michel Bena\"im (UNINE)

arxiv:1601.06266 v3 · 2016-01-23 · 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{QYU7JWCAAX7BSBUSGKES5RRYUK}

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	2026-05-18T00:31:05.604055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8629f4d84005fe19069232892ec638a2960a5c557f927bb239ab680df2310d37

Aliases

arxiv: 1601.06266 · arxiv_version: 1601.06266v3 · doi: 10.48550/arxiv.1601.06266 · pith_short_12: QYU7JWCAAX7B · pith_short_16: QYU7JWCAAX7BSBUS · pith_short_8: QYU7JWCA

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/QYU7JWCAAX7BSBUSGKES5RRYUK \
  | 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: 8629f4d84005fe19069232892ec638a2960a5c557f927bb239ab680df2310d37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cbb803257fc42314409f5e4bf892a4581ad00f53e215e9ff5a0c1676d0bd6584",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-01-23T13:22:30Z",
    "title_canon_sha256": "b6d89fc3457d9029f3b5a4e4495675da4b2cc6bc304c35998a8497668f2d6f31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.06266",
    "kind": "arxiv",
    "version": 3
  }
}