Pith Number

pith:GA4A3MDP

pith:2016:GA4A3MDPKNHAQDCZ57QVIATE2G

not attested not anchored not stored refs pending

Mixed type multiple orthogonal polynomials associated with the modified Bessel functions and products of two coupled random matrices

Lun Zhang

arxiv:1605.01899 v2 · 2016-05-06 · math.CA · math-ph · 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{GA4A3MDPKNHAQDCZ57QVIATE2G}

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	2026-05-18T01:03:49.876955Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30380db06f534e080c59efe1540264d182c2cd0a98724958d6da9f2becc91820

Aliases

arxiv: 1605.01899 · arxiv_version: 1605.01899v2 · doi: 10.48550/arxiv.1605.01899 · pith_short_12: GA4A3MDPKNHA · pith_short_16: GA4A3MDPKNHAQDCZ · pith_short_8: GA4A3MDP

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/GA4A3MDPKNHAQDCZ57QVIATE2G \
  | 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: 30380db06f534e080c59efe1540264d182c2cd0a98724958d6da9f2becc91820

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f715b61d4184f6d1a4a808f247b69de41e82139cec9afb7db9b6159af7c2bd2",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-05-06T11:43:21Z",
    "title_canon_sha256": "2625a180e6b0117bd2d6d6809144ea5a7a41052845a7febf015af57116131a70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.01899",
    "kind": "arxiv",
    "version": 2
  }
}