Pith Number

pith:AI4UDHFR

pith:2009:AI4UDHFRYLON5DMTUS6H4EP7FL

not attested not anchored not stored refs pending

An introduction to hyperlinear and sofic groups

Aleksandra Kwiatkowska, Vladimir G. Pestov

arxiv:0911.4266 v4 · 2009-11-22 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AI4UDHFRYLON5DMTUS6H4EP7FL}

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	2026-05-18T03:29:51.406680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0239419cb1c2dcde8d93a4bc7e11ff2ae1246415aa3159f9e6faebd070721dbd

Aliases

arxiv: 0911.4266 · arxiv_version: 0911.4266v4 · doi: 10.48550/arxiv.0911.4266 · pith_short_12: AI4UDHFRYLON · pith_short_16: AI4UDHFRYLON5DMT · pith_short_8: AI4UDHFR

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/AI4UDHFRYLON5DMTUS6H4EP7FL \
  | 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: 0239419cb1c2dcde8d93a4bc7e11ff2ae1246415aa3159f9e6faebd070721dbd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49180d764ec418003745c6582fcd3fbbb87a41f59e8c0e3d9b15021f2d070648",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-11-22T17:23:29Z",
    "title_canon_sha256": "e1e5bc28a318aef95015c761d2a62c0476c596c05e122616af9518350f97fbba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.4266",
    "kind": "arxiv",
    "version": 4
  }
}