Pith Number

pith:UBMMU7SY

pith:2010:UBMMU7SY6XLP6BHRICJINDQ3KD

not attested not anchored not stored refs pending

Sofic representations of amenable groups

Endre Szabo, Gabor Elek

arxiv:1010.3424 v2 · 2010-10-17 · 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{UBMMU7SY6XLP6BHRICJINDQ3KD}

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	2026-05-18T04:38:07.610912Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a058ca7e58f5d6ff04f14092868e1b50e17911a5b07d90eec5c5ba9078c6b16a

Aliases

arxiv: 1010.3424 · arxiv_version: 1010.3424v2 · doi: 10.48550/arxiv.1010.3424 · pith_short_12: UBMMU7SY6XLP · pith_short_16: UBMMU7SY6XLP6BHR · pith_short_8: UBMMU7SY

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/UBMMU7SY6XLP6BHRICJINDQ3KD \
  | 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: a058ca7e58f5d6ff04f14092868e1b50e17911a5b07d90eec5c5ba9078c6b16a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5803327d7f7b9eeb8cf03c215468a9591c11310727dd2965ef6abc5d6e63641a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-10-17T15:59:30Z",
    "title_canon_sha256": "54ad33e2e9d6b832100ee3edd01f0c4450aba6c1ee393453af703738c8871d0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3424",
    "kind": "arxiv",
    "version": 2
  }
}