Pith Number

pith:6WYV5YRM

pith:2017:6WYV5YRMKQHRVRMGC2RBGDBY5P

not attested not anchored not stored refs pending

Amenability of groups and $G$-sets

Laurent Bartholdi

arxiv:1705.04091 v1 · 2017-05-11 · math.GR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6WYV5YRMKQHRVRMGC2RBGDBY5P}

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	2026-05-18T00:44:41.442046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5b15ee22c540f1ac58616a2130c38ebd08999bc315f0c07e0fb86e9f6c1fec4

Aliases

arxiv: 1705.04091 · arxiv_version: 1705.04091v1 · doi: 10.48550/arxiv.1705.04091 · pith_short_12: 6WYV5YRMKQHR · pith_short_16: 6WYV5YRMKQHRVRMG · pith_short_8: 6WYV5YRM

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/6WYV5YRMKQHRVRMGC2RBGDBY5P \
  | 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: f5b15ee22c540f1ac58616a2130c38ebd08999bc315f0c07e0fb86e9f6c1fec4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6eb98b6d7c7065d3395ec8d6615e682e5bbc03f39d8b8530c789bac8adecd09d",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-05-11T09:47:43Z",
    "title_canon_sha256": "89a1239147b7cde72b843a03456f3ef681b1804e161e7aea55a401e54db863a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.04091",
    "kind": "arxiv",
    "version": 1
  }
}