Pith Number

pith:PLOSZQFH

pith:2011:PLOSZQFH2ZNRRI7YSZR3MUFFDV

not attested not anchored not stored refs pending

Amenability and vanishing of L^2-Betti numbers: an operator algebraic approach

David Kyed, Vadim Alekseev

arxiv:1105.3406 v2 · 2011-05-17 · 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{PLOSZQFH2ZNRRI7YSZR3MUFFDV}

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	2026-05-18T00:22:11.428485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7add2cc0a7d65b18a3f89663b650a51d73314067c3d806f992cb2942744d186c

Aliases

arxiv: 1105.3406 · arxiv_version: 1105.3406v2 · doi: 10.48550/arxiv.1105.3406 · pith_short_12: PLOSZQFH2ZNR · pith_short_16: PLOSZQFH2ZNRRI7Y · pith_short_8: PLOSZQFH

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/PLOSZQFH2ZNRRI7YSZR3MUFFDV \
  | 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: 7add2cc0a7d65b18a3f89663b650a51d73314067c3d806f992cb2942744d186c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73c708daac9fa7d6b5f6311b78279dedacc46355e51fb949353029fdab92ea32",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-05-17T15:00:39Z",
    "title_canon_sha256": "57e31b3832bff176ed8a98b9c3fc77518327d648d8dc7161a071a9da0d788cc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.3406",
    "kind": "arxiv",
    "version": 2
  }
}