Pith Number

pith:25F3HJII

pith:2005:25F3HJII7LHVC46REHY2PW6HI3

not attested not anchored not stored refs pending

Free Probability on a Direct Product of Noncommutative Probability Spaces

Ilwoo Cho

arxiv:math/0509643 v1 · 2005-09-27 · 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{25F3HJII7LHVC46REHY2PW6HI3}

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	2026-05-18T01:05:23.055503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d74bb3a508facf5173d121f1a7dbc746d55a7d5204783215ee665ef7d9a1d16c

Aliases

arxiv: math/0509643 · arxiv_version: math/0509643v1 · doi: 10.48550/arxiv.math/0509643 · pith_short_12: 25F3HJII7LHV · pith_short_16: 25F3HJII7LHVC46R · pith_short_8: 25F3HJII

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/25F3HJII7LHVC46REHY2PW6HI3 \
  | 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: d74bb3a508facf5173d121f1a7dbc746d55a7d5204783215ee665ef7d9a1d16c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d6a6cd7960ed1fa5ebb16462990eadba867be3b8baaf34f0cfd1b7d8c2e3f22",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2005-09-27T18:50:49Z",
    "title_canon_sha256": "548e31059c5691b0d9ba7eb13fc5e8e3e64ce0ca60897a7232193a38d6dcbb05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509643",
    "kind": "arxiv",
    "version": 1
  }
}