Pith Number

pith:QY6FOFQD

pith:2010:QY6FOFQD4I4TYOSCBYKONONGEW

not attested not anchored not stored refs pending

Free Products and the Lack of State Preserving Approximations of Nuclear C*-algebras

Caleb Eckhardt

arxiv:1011.2452 v1 · 2010-11-10 · math.OA · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QY6FOFQD4I4TYOSCBYKONONGEW}

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	2026-05-18T03:20:45.701109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

863c571603e2393c3a420e14e6b9a625aa4f4925716cec535777eb7fc7895b52

Aliases

arxiv: 1011.2452 · arxiv_version: 1011.2452v1 · doi: 10.48550/arxiv.1011.2452 · pith_short_12: QY6FOFQD4I4T · pith_short_16: QY6FOFQD4I4TYOSC · pith_short_8: QY6FOFQD

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/QY6FOFQD4I4TYOSCBYKONONGEW \
  | 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: 863c571603e2393c3a420e14e6b9a625aa4f4925716cec535777eb7fc7895b52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01ceeb3a6af3ef835449e1d4703f2213bb8b83437aa24b6726b03f2977719814",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-11-10T18:30:02Z",
    "title_canon_sha256": "e93b222a54e5408380f574e94c276af599b7f10e1b482ec4f5deff4b5ca2c07d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2452",
    "kind": "arxiv",
    "version": 1
  }
}