Pith Number

pith:FLL4UI6T

pith:2015:FLL4UI6TRM54LK2B7A5TSVXJWR

not attested not anchored not stored refs pending

On the multiplication of operator-valued c-free random variables

Jiun-Chau Wang, Mihai Popa, Victor Vinnikov

arxiv:1509.08853 v2 · 2015-09-29 · 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{FLL4UI6TRM54LK2B7A5TSVXJWR}

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	2026-05-18T01:16:07.036181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ad7ca23d38b3bc5ab41f83b3956e9b462fb623d704e51487e1e224cfa151114

Aliases

arxiv: 1509.08853 · arxiv_version: 1509.08853v2 · doi: 10.48550/arxiv.1509.08853 · pith_short_12: FLL4UI6TRM54 · pith_short_16: FLL4UI6TRM54LK2B · pith_short_8: FLL4UI6T

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/FLL4UI6TRM54LK2B7A5TSVXJWR \
  | 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: 2ad7ca23d38b3bc5ab41f83b3956e9b462fb623d704e51487e1e224cfa151114

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b04485bd4d400ecdf1efe8a5fcef28c94e7a64b96923c6e857a1ec982d6ca07",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-09-29T17:07:53Z",
    "title_canon_sha256": "6b5bac971d362fdd5ab88aa25fb5fc1766d51f213d552dc9ce1598d4b03367ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08853",
    "kind": "arxiv",
    "version": 2
  }
}