Pith Number

pith:XF57YNDX

pith:2011:XF57YNDXGFS52OPD7NNIEVZDAJ

not attested not anchored not stored refs pending

Mixing and hitting times for finite Markov chains

Roberto Imbuzeiro Oliveira

arxiv:1108.1708 v2 · 2011-08-08 · 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{XF57YNDXGFS52OPD7NNIEVZDAJ}

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	2026-05-18T03:47:01.407567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb

Aliases

arxiv: 1108.1708 · arxiv_version: 1108.1708v2 · doi: 10.48550/arxiv.1108.1708 · pith_short_12: XF57YNDXGFS5 · pith_short_16: XF57YNDXGFS52OPD · pith_short_8: XF57YNDX

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/XF57YNDXGFS52OPD7NNIEVZDAJ \
  | 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: b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c45889d9e4212103c3cac83d7290f0032f9dd897d6d0092f4fb78b8a1a0945c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-08T13:50:42Z",
    "title_canon_sha256": "320bea8ff9b20aafef1e28bab4d44b35e7aa306d4dfee072f72045f751360c2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1708",
    "kind": "arxiv",
    "version": 2
  }
}