Pith Number

pith:LQSAFYPA

pith:2016:LQSAFYPAJ7BROVTHPUPVFMYAVB

not attested not anchored not stored refs pending

$L^2$-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices

Andreas Thom, Henrik Densing Petersen, Roman Sauer

arxiv:1612.04559 v3 · 2016-12-14 · math.GR · math.AT · 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{LQSAFYPAJ7BROVTHPUPVFMYAVB}

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	2026-05-18T00:21:55.189788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c2402e1e04fc31756677d1f52b300a879bfb80ee4c4515fb195b1b6278a3f94

Aliases

arxiv: 1612.04559 · arxiv_version: 1612.04559v3 · doi: 10.48550/arxiv.1612.04559 · pith_short_12: LQSAFYPAJ7BR · pith_short_16: LQSAFYPAJ7BROVTH · pith_short_8: LQSAFYPA

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/LQSAFYPAJ7BROVTHPUPVFMYAVB \
  | 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: 5c2402e1e04fc31756677d1f52b300a879bfb80ee4c4515fb195b1b6278a3f94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76ec7a98fdbd093cde92c7e67493771e1cbed1c0a4106c57acccd3fe3058417f",
    "cross_cats_sorted": [
      "math.AT",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-12-14T10:14:25Z",
    "title_canon_sha256": "97723fa003773feb26a84ba66bf6898e5490018c1a2203485f5076d2a39c639c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04559",
    "kind": "arxiv",
    "version": 3
  }
}