Pith Number

pith:CB3UAXFT

pith:2009:CB3UAXFTJG3TKBJKYKUBSUKYQ7

not attested not anchored not stored refs pending

Ergodic properties of Bogoliubov automorphisms in free probability

Farrukh Mukhamedov, Francesco Fidaleo

arxiv:0905.3026 v2 · 2009-05-19 · math.OA · math.DS · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CB3UAXFTJG3TKBJKYKUBSUKYQ7}

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	2026-05-18T04:36:59.463052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1077405cb349b735052ac2a819515887c31b5ed8091e59aba5b2868ba1959d7a

Aliases

arxiv: 0905.3026 · arxiv_version: 0905.3026v2 · doi: 10.48550/arxiv.0905.3026 · pith_short_12: CB3UAXFTJG3T · pith_short_16: CB3UAXFTJG3TKBJK · pith_short_8: CB3UAXFT

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/CB3UAXFTJG3TKBJKYKUBSUKYQ7 \
  | 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: 1077405cb349b735052ac2a819515887c31b5ed8091e59aba5b2868ba1959d7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6cd7df0725d25f646f30e7681ac5e8fb787390e6eb4c10a139a3f62f36c858a",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-05-19T05:43:51Z",
    "title_canon_sha256": "9ce89f29e34df309c17f980cacf10ad5e660179bcf124c0ef1ed14cacac47a0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.3026",
    "kind": "arxiv",
    "version": 2
  }
}