Pith Number

pith:KJGS3WYZ

pith:2019:KJGS3WYZLJI7IS2LEPHXM2BU65

not attested not anchored not stored refs pending

Regularity properties of free multiplicative convolution on the positive line

Hong Chang Ji

arxiv:1903.02326 v2 · 2019-03-06 · 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{KJGS3WYZLJI7IS2LEPHXM2BU65}

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.

Cited by

1 paper in Pith

Extremal eigenvalues of sample covariance matrices with general population

Receipt and verification

First computed	2026-07-05T01:08:22.948196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

524d2ddb195a51f44b4b23cf766834f7597de9f0652b3fec7c47b569f03328e2

Aliases

arxiv: 1903.02326 · arxiv_version: 1903.02326v2 · doi: 10.48550/arxiv.1903.02326 · pith_short_12: KJGS3WYZLJI7 · pith_short_16: KJGS3WYZLJI7IS2L · pith_short_8: KJGS3WYZ

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/KJGS3WYZLJI7IS2LEPHXM2BU65 \
  | 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: 524d2ddb195a51f44b4b23cf766834f7597de9f0652b3fec7c47b569f03328e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6eeb456a81cf2dd4cacca945eb800ffe8fe70f0b55605b6280ebe50bd6567f90",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-03-06T11:32:44Z",
    "title_canon_sha256": "4f8c59aaf48e38b48931db63ec29ff2ab930b85ab3cd6eb844f07226b0df7199"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.02326",
    "kind": "arxiv",
    "version": 2
  }
}