Pith Number

pith:WDQCJ5MV

pith:2017:WDQCJ5MV24YHUGPTZBGCYRQQHU

not attested not anchored not stored refs pending

All properly ergodic Markov chains over a free group are orbit equivalent

Lewis Bowen

arxiv:1706.09483 v1 · 2017-06-28 · math.DS · math.OA · 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{WDQCJ5MV24YHUGPTZBGCYRQQHU}

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	2026-05-18T00:41:14.962464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0e024f595d7307a19f3c84c2c46103d3f56bb3d3ba30f904c5ab0044e76d501

Aliases

arxiv: 1706.09483 · arxiv_version: 1706.09483v1 · doi: 10.48550/arxiv.1706.09483 · pith_short_12: WDQCJ5MV24YH · pith_short_16: WDQCJ5MV24YHUGPT · pith_short_8: WDQCJ5MV

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/WDQCJ5MV24YHUGPTZBGCYRQQHU \
  | 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: b0e024f595d7307a19f3c84c2c46103d3f56bb3d3ba30f904c5ab0044e76d501

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "448f522cf20a470f1f81de0182d2bacb019aa1a082450e6b62250db8e69b308a",
    "cross_cats_sorted": [
      "math.OA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-06-28T20:51:30Z",
    "title_canon_sha256": "ea9bfec4b1b112dd33fe0be6160a83f8421ffb16cd78a7d96803752be633b3c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.09483",
    "kind": "arxiv",
    "version": 1
  }
}