Pith Number

pith:CAKIFDXO

pith:2025:CAKIFDXOAZ5NHBOVZ5HRGHXGDK

not attested not anchored not stored refs pending

Free positive multiplicative Brownian motion and the free additive convolution of semicircle and uniform distribution

Martin Auer

arxiv:2505.05984 v1 · 2025-05-09 · math.PR · math.CO · math.FA · 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{CAKIFDXOAZ5NHBOVZ5HRGHXGDK}

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	2026-07-05T11:00:51.672967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1014828eee067ad385d5cf4f131ee61abf0d9a6b208b87dbf5fac2558a5ae7e6

Aliases

arxiv: 2505.05984 · arxiv_version: 2505.05984v1 · doi: 10.48550/arxiv.2505.05984 · pith_short_12: CAKIFDXOAZ5N · pith_short_16: CAKIFDXOAZ5NHBOV · pith_short_8: CAKIFDXO

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/CAKIFDXOAZ5NHBOVZ5HRGHXGDK \
  | 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: 1014828eee067ad385d5cf4f131ee61abf0d9a6b208b87dbf5fac2558a5ae7e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b6b48e7f7d308cfd693adbf2a956fb5e088866f6a6a701d2b2ef04903b877c4",
    "cross_cats_sorted": [
      "math.CO",
      "math.FA",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-05-09T12:16:29Z",
    "title_canon_sha256": "f8e560423f4031982ab5b587d5e5d85016c7a9afd80b39a36077788aefcbe8d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.05984",
    "kind": "arxiv",
    "version": 1
  }
}