Pith Number

pith:RKVJJCM4

pith:2012:RKVJJCM4U4TLMVP6LUO5WZCUHT

not attested not anchored not stored refs pending

Free Brownian motion and free convolution semigroups: multiplicative case

Ping Zhong

arxiv:1210.6090 v3 · 2012-10-23 · math.FA · math.PR

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

Receipt and verification

First computed	2026-05-18T03:06:22.473907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8aaa94899ca726b655fe5d1ddb64543cd03aeebac74cb447ea3070f43873151d

Aliases

arxiv: 1210.6090 · arxiv_version: 1210.6090v3 · doi: 10.48550/arxiv.1210.6090

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/RKVJJCM4U4TLMVP6LUO5WZCUHT \
  | 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: 8aaa94899ca726b655fe5d1ddb64543cd03aeebac74cb447ea3070f43873151d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e4e42cd94f5b266f2c06e4ab22c604b9f93c65b830b6d0f3dffbf1fd0544afc",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-10-23T00:08:18Z",
    "title_canon_sha256": "a6a4203a778598b4a9f0a45731ca477828cb5d8ec677c28fcaeab08068e3e606"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6090",
    "kind": "arxiv",
    "version": 3
  }
}