Pith Number

pith:ATKCO6JO

pith:2011:ATKCO6JOMFQLTWE2TQUYIXHLKS

not attested not anchored not stored refs pending

A Dirichlet principle for non reversible Markov chains and some recurrence theorems

Alexandre Gaudilli\`ere, Claudio Landim

arxiv:1111.2445 v1 · 2011-11-10 · 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{ATKCO6JOMFQLTWE2TQUYIXHLKS}

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	2026-05-18T04:08:34.141067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04d427792e6160b9d89a9c29845ceb54826f4c6016c464c3891f5cd12844af8e

Aliases

arxiv: 1111.2445 · arxiv_version: 1111.2445v1 · doi: 10.48550/arxiv.1111.2445 · pith_short_12: ATKCO6JOMFQL · pith_short_16: ATKCO6JOMFQLTWE2 · pith_short_8: ATKCO6JO

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/ATKCO6JOMFQLTWE2TQUYIXHLKS \
  | 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: 04d427792e6160b9d89a9c29845ceb54826f4c6016c464c3891f5cd12844af8e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca969d1d19e566d1dd59d7c9492bfdf53c78bbe0fb70b39c1030c008fa1c55a2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-10T10:50:06Z",
    "title_canon_sha256": "185e187ee4ba612005ddf9f188c18e62e2d14adc5f0afbe7e6e5585c26226dcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2445",
    "kind": "arxiv",
    "version": 1
  }
}