Pith Number

pith:UMINVIXT

pith:2012:UMINVIXTECFYC5M7V2L7BEEZG5

not attested not anchored not stored refs pending

Operator-valued free multiplicative convolution: analytic subordination theory and applications to random matrix theory

Carlos Vargas, John Treilhard, Roland Speicher, Serban T. Belinschi

arxiv:1209.3508 v1 · 2012-09-16 · math.OA · 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{UMINVIXTECFYC5M7V2L7BEEZG5}

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	2026-05-18T03:45:30.790392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a310daa2f3208b81759fae97f090993771cc83e1889e830ef6c487b982f785ec

Aliases

arxiv: 1209.3508 · arxiv_version: 1209.3508v1 · doi: 10.48550/arxiv.1209.3508 · pith_short_12: UMINVIXTECFY · pith_short_16: UMINVIXTECFYC5M7 · pith_short_8: UMINVIXT

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/UMINVIXTECFYC5M7V2L7BEEZG5 \
  | 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: a310daa2f3208b81759fae97f090993771cc83e1889e830ef6c487b982f785ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4919d9e172d6bced137b24309f0d4e2b62ba9de6775730457adbda8464d01e74",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-09-16T18:03:03Z",
    "title_canon_sha256": "7c9a2f21104980eb07797b452731475793ecfaca43dd899e7363a5bde1fee91e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3508",
    "kind": "arxiv",
    "version": 1
  }
}