Pith Number

pith:YWLQCS3S

pith:2009:YWLQCS3SKMUWMZSYCARU637E6I

not attested not anchored not stored refs pending

On abstract commensurators of groups

Laurent Bartholdi, Oleg Bogopolski

arxiv:0902.4542 v1 · 2009-02-26 · 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{YWLQCS3SKMUWMZSYCARU637E6I}

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	2026-05-18T02:28:32.263680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c597014b72532966665810234f6fe4f211349b5e5b3ea5f7e75c9b4313558164

Aliases

arxiv: 0902.4542 · arxiv_version: 0902.4542v1 · doi: 10.48550/arxiv.0902.4542 · pith_short_12: YWLQCS3SKMUW · pith_short_16: YWLQCS3SKMUWMZSY · pith_short_8: YWLQCS3S

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/YWLQCS3SKMUWMZSYCARU637E6I \
  | 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: c597014b72532966665810234f6fe4f211349b5e5b3ea5f7e75c9b4313558164

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21fa7f1ef8bb79715df7b12d4141bd7110dcb584d77afc2c2933ecc7be351fc4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-02-26T10:07:14Z",
    "title_canon_sha256": "088dd17cf3b906ff5a977e771ec9c0c2b4dcd20fecbb55f9f66bb9f9b7f33324"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.4542",
    "kind": "arxiv",
    "version": 1
  }
}