Pith Number

pith:3VZCXCAF

pith:2014:3VZCXCAF3YJBZBFS65PTTJV6Q4

not attested not anchored not stored refs pending

Amenability and ergodic properties of topological groups: from Bogolyubov onwards

Pierre de la Harpe, Rostislav Grigorchuk

arxiv:1404.7030 v2 · 2014-04-28 · 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{3VZCXCAF3YJBZBFS65PTTJV6Q4}

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	2026-05-18T01:36:25.963842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd722b8805de121c84b2f75f39a6be87373669e2d817f971b53ca4ee2dd9449e

Aliases

arxiv: 1404.7030 · arxiv_version: 1404.7030v2 · doi: 10.48550/arxiv.1404.7030 · pith_short_12: 3VZCXCAF3YJB · pith_short_16: 3VZCXCAF3YJBZBFS · pith_short_8: 3VZCXCAF

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/3VZCXCAF3YJBZBFS65PTTJV6Q4 \
  | 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: dd722b8805de121c84b2f75f39a6be87373669e2d817f971b53ca4ee2dd9449e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71ea89bfafd412a4a6488fc722150c0b3c406d937fe9dfff929822b17c369148",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-04-28T15:52:52Z",
    "title_canon_sha256": "fb8247d3193bd0019de2c9ef10c53fa6d0bdeda76ad736247417d368e2fe881a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.7030",
    "kind": "arxiv",
    "version": 2
  }
}