Pith Number

pith:ZNGYRORL

pith:2013:ZNGYRORLRFOTTKFIB4GZ5DQERE

not attested not anchored not stored refs pending

Matricial circular systems and random matrices

Romuald Lenczewski

arxiv:1311.6420 v5 · 2013-11-25 · 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{ZNGYRORLRFOTTKFIB4GZ5DQERE}

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	2026-05-18T00:15:02.657568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb4d88ba2b895d39a8a80f0d9e8e048922fa5d37983dda302364b599187a7abd

Aliases

arxiv: 1311.6420 · arxiv_version: 1311.6420v5 · doi: 10.48550/arxiv.1311.6420 · pith_short_12: ZNGYRORLRFOT · pith_short_16: ZNGYRORLRFOTTKFI · pith_short_8: ZNGYRORL

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/ZNGYRORLRFOTTKFIB4GZ5DQERE \
  | 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: cb4d88ba2b895d39a8a80f0d9e8e048922fa5d37983dda302364b599187a7abd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55ab22aa08042a79d98cf0de11c323c71caa1a89b733e3e17fa01e59c9deeb23",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-11-25T19:47:42Z",
    "title_canon_sha256": "b77ddb8d7d4cc1e37c6a0a9e250fba35adbf204bee31c3503de92a8718b045b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.6420",
    "kind": "arxiv",
    "version": 5
  }
}