Pith Number

pith:MQZ7H62Q

pith:2015:MQZ7H62QQDJQRLR4ZIB5FNTU6N

not attested not anchored not stored refs pending

Mean convergence of Markovian spherical averages for measure-preserving actions of the free group

Alexander Bufetov, Lewis Bowen, Olga Romaskevich

arxiv:1502.01797 v1 · 2015-02-06 · math.DS · math.GR · 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{MQZ7H62QQDJQRLR4ZIB5FNTU6N}

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	2026-05-18T02:27:50.643802Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6433f3fb5080d308ae3cca03d2b674f34fcf980f1a22ec9287e829a321f471d7

Aliases

arxiv: 1502.01797 · arxiv_version: 1502.01797v1 · doi: 10.48550/arxiv.1502.01797 · pith_short_12: MQZ7H62QQDJQ · pith_short_16: MQZ7H62QQDJQRLR4 · pith_short_8: MQZ7H62Q

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/MQZ7H62QQDJQRLR4ZIB5FNTU6N \
  | 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: 6433f3fb5080d308ae3cca03d2b674f34fcf980f1a22ec9287e829a321f471d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efad2f71824fc70740b8b1c23c2da57ced340df6d285c3324e598bae060fa7dd",
    "cross_cats_sorted": [
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-02-06T05:22:33Z",
    "title_canon_sha256": "0c8c1f78176b549f6993f439141a7dd64bc6e1984e98810469d48305a12ec901"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01797",
    "kind": "arxiv",
    "version": 1
  }
}