Pith Number

pith:4B7WR3CU

pith:2026:4B7WR3CUZVHNTIWTRGMLXD45EE

not attested not anchored not stored refs pending

Freely infinitely divisible $R$-diagonal elements and Brown measure

Mihai Popa, Ping Zhong, Yu Kitagawa

arxiv:2605.25434 v1 · 2026-05-25 · math.OA · 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{4B7WR3CUZVHNTIWTRGMLXD45EE}

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	2026-05-26T02:04:34.904554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e07f68ec54cd4ed9a2d38998bb8f9d210184d0845c1a2d30d5f8ee732ebf21e9

Aliases

arxiv: 2605.25434 · arxiv_version: 2605.25434v1 · doi: 10.48550/arxiv.2605.25434 · pith_short_12: 4B7WR3CUZVHN · pith_short_16: 4B7WR3CUZVHNTIWT · pith_short_8: 4B7WR3CU

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/4B7WR3CUZVHNTIWTRGMLXD45EE \
  | 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: e07f68ec54cd4ed9a2d38998bb8f9d210184d0845c1a2d30d5f8ee732ebf21e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "968c31cc901a56caaf86e246d212b8208517bf9f557ad1b46a54e8eca867f313",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-25T05:17:10Z",
    "title_canon_sha256": "eb2a5de5653fe0cea69b123fc40668b8b9cb336707257ec6c78fc71152afe973"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.25434",
    "kind": "arxiv",
    "version": 1
  }
}