Pith Number

pith:S4SLH6XM

pith:2011:S4SLH6XM4TKIBXM462QA2FDRNP

not attested not anchored not stored refs pending

Cesaro convergence of spherical averages for measure-preserving actions of Markov semigroups and groups

Alexander Bufetov, Alexey Klimenko, Mikhail Khristoforov

arxiv:1101.5459 v1 · 2011-01-28 · math.DS · math.GR · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S4SLH6XM4TKIBXM462QA2FDRNP}

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	2026-05-18T02:46:38.068634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9724b3faece4d480dd9cf6a00d14716bfdc95f720625700718d9d9289b549f53

Aliases

arxiv: 1101.5459 · arxiv_version: 1101.5459v1 · doi: 10.48550/arxiv.1101.5459 · pith_short_12: S4SLH6XM4TKI · pith_short_16: S4SLH6XM4TKIBXM4 · pith_short_8: S4SLH6XM

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/S4SLH6XM4TKIBXM462QA2FDRNP \
  | 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: 9724b3faece4d480dd9cf6a00d14716bfdc95f720625700718d9d9289b549f53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d55a7417c67968bfe4847a34187d1b7ac58070079306d569eb1bac8c769b6145",
    "cross_cats_sorted": [
      "math.GR",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-01-28T05:57:33Z",
    "title_canon_sha256": "1f12c753476990c738d3fffc80fe06a406b1ffab93fdae4d0c9dd3a4fcddfe93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5459",
    "kind": "arxiv",
    "version": 1
  }
}