Pith Number

pith:LPKCVQAB

pith:2010:LPKCVQABSDAWTUQBW7W2YXYP7B

not attested not anchored not stored refs pending

The limit of F_p-Betti numbers of a tower of finite covers with amenable fundamental groups

Peter Linnell, Roman Sauer, Wolfgang Lueck

arxiv:1003.0434 v1 · 2010-03-01 · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPKCVQABSDAWTUQBW7W2YXYP7B}

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	2026-07-04T17:22:41.587112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bd42ac00190c169d201b7edac5f0ff87ddad325804153e2011d9a47c6bdf917

Aliases

arxiv: 1003.0434 · arxiv_version: 1003.0434v1 · doi: 10.48550/arxiv.1003.0434 · pith_short_12: LPKCVQABSDAW · pith_short_16: LPKCVQABSDAWTUQB · pith_short_8: LPKCVQAB

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/LPKCVQABSDAWTUQBW7W2YXYP7B \
  | 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: 5bd42ac00190c169d201b7edac5f0ff87ddad325804153e2011d9a47c6bdf917

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f99219d2781c08dab6a988e8958b01f6ac061bafdb0c7fa7d3d470492c3f1f30",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2010-03-01T19:42:32Z",
    "title_canon_sha256": "afaf3b8ac343bf7ff4bfb338476c324b4683886de2b2b65efecd135b7b6baac6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.0434",
    "kind": "arxiv",
    "version": 1
  }
}