Pith Number

pith:3VUQACSW

pith:2017:3VUQACSWTA6SC6DZYJPCWPYNZ7

not attested not anchored not stored refs pending

Central Limit Theorems for a Stationary Semicircular Sequence in Free Probability

Zhichao Wang

arxiv:1712.03619 v1 · 2017-12-11 · math.PR · 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{3VUQACSWTA6SC6DZYJPCWPYNZ7}

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	2026-05-18T00:28:20.573771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd69000a56983d217879c25e2b3f0dcfde08cb8902825b2232772722744c2eb7

Aliases

arxiv: 1712.03619 · arxiv_version: 1712.03619v1 · doi: 10.48550/arxiv.1712.03619 · pith_short_12: 3VUQACSWTA6S · pith_short_16: 3VUQACSWTA6SC6DZ · pith_short_8: 3VUQACSW

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/3VUQACSWTA6SC6DZYJPCWPYNZ7 \
  | 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: dd69000a56983d217879c25e2b3f0dcfde08cb8902825b2232772722744c2eb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f9f482dc7e1e3863db8658f2b2f42f17348fcae21eb853295f7437fc4deecc1",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-12-11T00:43:54Z",
    "title_canon_sha256": "a92e43c8426557c365991746fa5d7defc9a8df7cd449f5c471dacff75f4e77eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.03619",
    "kind": "arxiv",
    "version": 1
  }
}