Pith Number

pith:TS3WCVIU

pith:2021:TS3WCVIUOFPKWFQX5IGKP5ONEM

not attested not anchored not stored refs pending

Universality of free random variables: atoms for non-commutative rational functions

Guillaume C\'ebron, Octavio Arizmendi, Roland Speicher, Sheng Yin

arxiv:2107.11507 v2 · 2021-07-24 · 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{TS3WCVIUOFPKWFQX5IGKP5ONEM}

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	2026-07-05T04:24:55.960358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cb7615514715eab1617ea0ca7f5cd23038afa1b9e8d43c049bf9b986df5b5a4

Aliases

arxiv: 2107.11507 · arxiv_version: 2107.11507v2 · doi: 10.48550/arxiv.2107.11507 · pith_short_12: TS3WCVIUOFPK · pith_short_16: TS3WCVIUOFPKWFQX · pith_short_8: TS3WCVIU

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/TS3WCVIUOFPKWFQX5IGKP5ONEM \
  | 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: 9cb7615514715eab1617ea0ca7f5cd23038afa1b9e8d43c049bf9b986df5b5a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c8814e0d91e1c549b93ef055b873716f0f386da7f87a6b01bd23fa11ee284df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2021-07-24T01:43:56Z",
    "title_canon_sha256": "c4eda6b254062ea8bb940dfbcb20fe85c5105d1b20402f512d6b836a37403fc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.11507",
    "kind": "arxiv",
    "version": 2
  }
}