Pith Number

pith:W5HKLXGJ

pith:2016:W5HKLXGJ4TMBVWM7RGX55QGVCT

not attested not anchored not stored refs pending

Recurrence and transience of contractive autoregressive processes and related Markov chains

Martin P. W. Zerner

arxiv:1608.01394 v2 · 2016-08-03 · 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{W5HKLXGJ4TMBVWM7RGX55QGVCT}

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	2026-05-18T01:02:12.383218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b74ea5dcc9e4d81ad99f89afdec0d514c57fadf512caf443efef48434d7b78ff

Aliases

arxiv: 1608.01394 · arxiv_version: 1608.01394v2 · doi: 10.48550/arxiv.1608.01394 · pith_short_12: W5HKLXGJ4TMB · pith_short_16: W5HKLXGJ4TMBVWM7 · pith_short_8: W5HKLXGJ

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/W5HKLXGJ4TMBVWM7RGX55QGVCT \
  | 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: b74ea5dcc9e4d81ad99f89afdec0d514c57fadf512caf443efef48434d7b78ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "405208d392b50fe0550bee48cd2b7d32a223a7f2ae1e778c21a77de1c64aaf10",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-08-03T23:18:10Z",
    "title_canon_sha256": "1a8cdf5f56e5aa77d23882cef6f3d143b988e5830c19dc5773fd1cc8e6c643d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.01394",
    "kind": "arxiv",
    "version": 2
  }
}