Pith Number

pith:7AZATMD3

pith:2015:7AZATMD3ZGXFOENMJCCQWDXE6N

not attested not anchored not stored refs pending

Singular values for products of complex Ginibre matrices with a source: hard edge limit and phase transition

Dang-Zheng Liu, Peter J. Forrester

arxiv:1503.07955 v2 · 2015-03-27 · math.PR · math-ph · math.CA · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7AZATMD3ZGXFOENMJCCQWDXE6N}

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	2026-05-18T01:22:40.787368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f83209b07bc9ae5711ac48850b0ee4f349855995e4198eb807db358ab3c696f4

Aliases

arxiv: 1503.07955 · arxiv_version: 1503.07955v2 · doi: 10.48550/arxiv.1503.07955 · pith_short_12: 7AZATMD3ZGXF · pith_short_16: 7AZATMD3ZGXFOENM · pith_short_8: 7AZATMD3

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/7AZATMD3ZGXFOENMJCCQWDXE6N \
  | 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: f83209b07bc9ae5711ac48850b0ee4f349855995e4198eb807db358ab3c696f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f2720ce68a39eb8759569e46fd87d227c63a9209a166018d74035e7e0067cde",
    "cross_cats_sorted": [
      "math-ph",
      "math.CA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-03-27T04:02:20Z",
    "title_canon_sha256": "11ced152abab00a0f759de1d7c4f1402e2c35dc12c9f514877819503016da6c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.07955",
    "kind": "arxiv",
    "version": 2
  }
}