Pith Number

pith:OY5Z7VFJ

pith:2008:OY5Z7VFJEVJ3LRR2O47UT52NIZ

not attested not anchored not stored refs pending

Approximation properties and entropy estimates for crossed products by actions of amenable discrete quantum groups

Adam Skalski, Joachim Zacharias

arxiv:0807.2827 v4 · 2008-07-17 · 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{OY5Z7VFJEVJ3LRR2O47UT52NIZ}

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	2026-05-18T02:58:11.358585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

763b9fd4a92553b5c63a773f49f74d4644c050df944e78f9bc120245d6ae9df2

Aliases

arxiv: 0807.2827 · arxiv_version: 0807.2827v4 · doi: 10.48550/arxiv.0807.2827 · pith_short_12: OY5Z7VFJEVJ3 · pith_short_16: OY5Z7VFJEVJ3LRR2 · pith_short_8: OY5Z7VFJ

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/OY5Z7VFJEVJ3LRR2O47UT52NIZ \
  | 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: 763b9fd4a92553b5c63a773f49f74d4644c050df944e78f9bc120245d6ae9df2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "011dbbeceea387f0598a2f71b42327c1a6d93c282cf0c4bf5a19879b3bb09994",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2008-07-17T16:26:58Z",
    "title_canon_sha256": "708a7c023a44775ed854e54fddd197f9081cd6ce22e8a22cad551f9a432570ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.2827",
    "kind": "arxiv",
    "version": 4
  }
}