Pith Number

pith:SCLLTUHB

pith:2015:SCLLTUHBXNHY5HTPNFNKSPP2VC

not attested not anchored not stored refs pending

The splitting process in free probability theory

Frederic Patras, Kurusch Ebrahimi-Fard

arxiv:1502.02748 v1 · 2015-02-10 · math.CO · 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{SCLLTUHBXNHY5HTPNFNKSPP2VC}

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	2026-05-18T01:14:45.543074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9096b9d0e1bb4f8e9e6f695aa93dfaa8b17126c65a1f584e714b724aabec18d0

Aliases

arxiv: 1502.02748 · arxiv_version: 1502.02748v1 · doi: 10.48550/arxiv.1502.02748 · pith_short_12: SCLLTUHBXNHY · pith_short_16: SCLLTUHBXNHY5HTP · pith_short_8: SCLLTUHB

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/SCLLTUHBXNHY5HTPNFNKSPP2VC \
  | 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: 9096b9d0e1bb4f8e9e6f695aa93dfaa8b17126c65a1f584e714b724aabec18d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c49559619acd1a41994607b697c4b899361627d92260cbdfd4b04fd5cac5fdc7",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-02-10T01:01:30Z",
    "title_canon_sha256": "f23c74750963a7f84714bbf47b9e14a9cba0b1b0fb255d6ee88918e0c3a251d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02748",
    "kind": "arxiv",
    "version": 1
  }
}