Pith Number

pith:4TGV6NTD

pith:2013:4TGV6NTDK3FLDZT6ZHDPRFZZIO

not attested not anchored not stored refs pending

On the semicircular law of large dimensional random quaternion matrices

Jiang Hu, Yanqing Yin, Zhidong Bai

arxiv:1309.6937 v2 · 2013-09-26 · 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{4TGV6NTDK3FLDZT6ZHDPRFZZIO}

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	2026-05-18T02:23:58.873380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4cd5f366356cab1e67ec9c6f89739438b04196090f4031f6b9d1c277ec2bf05

Aliases

arxiv: 1309.6937 · arxiv_version: 1309.6937v2 · doi: 10.48550/arxiv.1309.6937 · pith_short_12: 4TGV6NTDK3FL · pith_short_16: 4TGV6NTDK3FLDZT6 · pith_short_8: 4TGV6NTD

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/4TGV6NTDK3FLDZT6ZHDPRFZZIO \
  | 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: e4cd5f366356cab1e67ec9c6f89739438b04196090f4031f6b9d1c277ec2bf05

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad208a134b5a2bde58e213551527911bd40eff7d5893e153201f5391611841d5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-09-26T15:22:06Z",
    "title_canon_sha256": "7457e2160b991e1723ee3026ff26d2a8cb95ae31c9f0d1cdddf9d001f4924da1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6937",
    "kind": "arxiv",
    "version": 2
  }
}