Pith Number

pith:HJ7SIWU7

pith:2011:HJ7SIWU7LI4FCH4BRM5GNLOW7H

not attested not anchored not stored refs pending

Free Deterministic Equivalents, Rectangular Random Matrix Models, and Operator-Valued Free Probability Theory

Carlos Vargas, Roland Speicher, Tobias Mai

arxiv:1110.1237 v1 · 2011-10-06 · cs.IT · math.IT · 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{HJ7SIWU7LI4FCH4BRM5GNLOW7H}

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	2026-05-18T04:11:32.463880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a7f245a9f5a38511f818b3a66add6f9e2dadda2c2d9a3e64c36d34ba025296b

Aliases

arxiv: 1110.1237 · arxiv_version: 1110.1237v1 · doi: 10.48550/arxiv.1110.1237 · pith_short_12: HJ7SIWU7LI4F · pith_short_16: HJ7SIWU7LI4FCH4B · pith_short_8: HJ7SIWU7

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/HJ7SIWU7LI4FCH4BRM5GNLOW7H \
  | 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: 3a7f245a9f5a38511f818b3a66add6f9e2dadda2c2d9a3e64c36d34ba025296b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "671dcb92599dc392562ad3692bef94208da60070bb5b03fe0d835ac3afeeb6ff",
    "cross_cats_sorted": [
      "math.IT",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2011-10-06T12:11:30Z",
    "title_canon_sha256": "63fd7bfefed033075c85b39d4f9fad082765787f698d25174c3b2007268dada2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1237",
    "kind": "arxiv",
    "version": 1
  }
}