Pith Number

pith:JB4SCHHP

pith:2019:JB4SCHHPJ4BIHOJMQSPGHDITP3

not attested not anchored not stored refs pending

Lecture Notes on "Free Probability Theory"

Roland Speicher

arxiv:1908.08125 v2 · 2019-08-21 · math.OA · 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{JB4SCHHPJ4BIHOJMQSPGHDITP3}

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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

✓ 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.

Cited by

1 paper in Pith

Spectrum of Directed Inhomogeneous Random Graphs

Receipt and verification

First computed	2026-07-05T10:49:01.277044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4879211cef4f0283b92c849e638d137eda6348548d9a5436e706fd7277c1b449

Aliases

arxiv: 1908.08125 · arxiv_version: 1908.08125v2 · doi: 10.48550/arxiv.1908.08125 · pith_short_12: JB4SCHHPJ4BI · pith_short_16: JB4SCHHPJ4BIHOJM · pith_short_8: JB4SCHHP

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/JB4SCHHPJ4BIHOJMQSPGHDITP3 \
  | 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: 4879211cef4f0283b92c849e638d137eda6348548d9a5436e706fd7277c1b449

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2129b50f015d334bc87d9e05f32b96a2ab980c7210bbb0351ef4718abeef95ef",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2019-08-21T21:52:27Z",
    "title_canon_sha256": "f2d2f6fadf03d37b4b3a10f7e44e499546932786a15a022e360609f0f9bea830"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08125",
    "kind": "arxiv",
    "version": 2
  }
}