Pith Number

pith:3MIIQIJF

pith:2011:3MIIQIJF3ZO4JETIYLCVBPP2CZ

not attested not anchored not stored refs pending

The Distribution of Mixing Times in Markov Chains

Jeffrey J. Hunter

arxiv:1111.0151 v1 · 2011-11-01 · 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{3MIIQIJF3ZO4JETIYLCVBPP2CZ}

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	2026-05-18T02:57:24.409105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db10882125de5dc49268c2c550bdfa1654ae371d58be6214aa71591214c5aecd

Aliases

arxiv: 1111.0151 · arxiv_version: 1111.0151v1 · doi: 10.48550/arxiv.1111.0151 · pith_short_12: 3MIIQIJF3ZO4 · pith_short_16: 3MIIQIJF3ZO4JETI · pith_short_8: 3MIIQIJF

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/3MIIQIJF3ZO4JETIYLCVBPP2CZ \
  | 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: db10882125de5dc49268c2c550bdfa1654ae371d58be6214aa71591214c5aecd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12b9a8897ffd7d5837a50202d26c1842d39d849b8328fd87945e8d34da2f5e4d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-01T09:25:14Z",
    "title_canon_sha256": "4e1e31b80203254332c1884cd88cbeb32ae6d59af87548014c2dcce6bdaa9ac6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0151",
    "kind": "arxiv",
    "version": 1
  }
}