Pith Number

pith:YZHFSW4R

pith:2021:YZHFSW4RYYZKO4QTPV2JN7KUNX

not attested not anchored not stored refs pending

Polynomial convolutions and (finite) free probability

Adam W. Marcus

arxiv:2108.07054 v1 · 2021-08-16 · math.CO · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YZHFSW4RYYZKO4QTPV2JN7KUNX}

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

10 papers in Pith

Finite free perpetuities

The Rectangular Finite Free Heat Flow

P\'olya--Schur problems and free probability

Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators

Cumulants in rectangular finite free probability and beta-deformed singular values

Receipt and verification

First computed	2026-07-05T03:06:00.586870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c64e595b91c632a772137d7496fd546deec7292773ea029295a4d26813b750a3

Aliases

arxiv: 2108.07054 · arxiv_version: 2108.07054v1 · doi: 10.48550/arxiv.2108.07054 · pith_short_12: YZHFSW4RYYZK · pith_short_16: YZHFSW4RYYZKO4QT · pith_short_8: YZHFSW4R

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/YZHFSW4RYYZKO4QTPV2JN7KUNX \
  | 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: c64e595b91c632a772137d7496fd546deec7292773ea029295a4d26813b750a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10dd33a82dd18dcf8938f8f3aadf46878f81d5336af9a1ca6bc2cc0fd9491573",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-08-16T12:46:54Z",
    "title_canon_sha256": "e293b6aae0320f07470a33898ae16d45d0fd1afc73ad0c184822bf1670257441"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.07054",
    "kind": "arxiv",
    "version": 1
  }
}