Pith Number

pith:IZXXRHWQ

pith:2011:IZXXRHWQHB5BBK7X6FHM6UX6BN

not attested not anchored not stored refs pending

Asymptotics for products of characteristic polynomials in classical $\beta$-Ensembles

Dang-Zheng Liu, Patrick Desrosiers

arxiv:1112.1119 v3 · 2011-12-05 · math-ph · math.CA · math.MP · 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{IZXXRHWQHB5BBK7X6FHM6UX6BN}

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	2026-05-18T03:14:30.555243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

466f789ed0387a10abf7f14ecf52fe0b754b228c2c2dbda4094b029308dbe346

Aliases

arxiv: 1112.1119 · arxiv_version: 1112.1119v3 · doi: 10.48550/arxiv.1112.1119 · pith_short_12: IZXXRHWQHB5B · pith_short_16: IZXXRHWQHB5BBK7X · pith_short_8: IZXXRHWQ

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/IZXXRHWQHB5BBK7X6FHM6UX6BN \
  | 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: 466f789ed0387a10abf7f14ecf52fe0b754b228c2c2dbda4094b029308dbe346

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7809605fb4bb015ce072b7e26a49977194e3c90fe4271da9a909556952a767e4",
    "cross_cats_sorted": [
      "math.CA",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-12-05T23:23:18Z",
    "title_canon_sha256": "2e18b9b9ec1f9b5fc03089f1b9228bb2ebffd6735d51e6f78cba4e4cc859b660"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1119",
    "kind": "arxiv",
    "version": 3
  }
}