Pith Number

pith:ULUJA7CB

pith:2011:ULUJA7CB3CB7P24ZQBVUN6QIYR

not attested not anchored not stored refs pending

An extension of Kesten's criterion for amenability to topological Markov chains

Manuel Stadlbauer

arxiv:1110.2942 v3 · 2011-10-13 · math.DS · 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{ULUJA7CB3CB7P24ZQBVUN6QIYR}

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	2026-05-18T03:04:06.957024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2e8907c41d883f7eb99806b46fa08c45f319e9a20a9da26d9ae12ef046535c9

Aliases

arxiv: 1110.2942 · arxiv_version: 1110.2942v3 · doi: 10.48550/arxiv.1110.2942 · pith_short_12: ULUJA7CB3CB7 · pith_short_16: ULUJA7CB3CB7P24Z · pith_short_8: ULUJA7CB

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/ULUJA7CB3CB7P24ZQBVUN6QIYR \
  | 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: a2e8907c41d883f7eb99806b46fa08c45f319e9a20a9da26d9ae12ef046535c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "093937373e963216f8331a73311cfb172d15f0f0ba6bb9f55c41bbdf3db15686",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-10-13T13:45:00Z",
    "title_canon_sha256": "e343b2d77b4da364d5f29c1c97648f63044de5486c429a81c760176f7c567fa2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2942",
    "kind": "arxiv",
    "version": 3
  }
}