Pith Number

pith:QJLJO53X

pith:2009:QJLJO53XLU3VBSQP4VEBJLG76L

not attested not anchored not stored refs pending

On Cayley graphs of virtually free groups

Yago Antolin

arxiv:0911.2177 v2 · 2009-11-11 · 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{QJLJO53XLU3VBSQP4VEBJLG76L}

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	2026-05-18T03:22:19.279489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82569777775d3750ca0fe54814acdff2eb3ce3a1395f39c49bbf57c9bfb3bcad

Aliases

arxiv: 0911.2177 · arxiv_version: 0911.2177v2 · doi: 10.48550/arxiv.0911.2177 · pith_short_12: QJLJO53XLU3V · pith_short_16: QJLJO53XLU3VBSQP · pith_short_8: QJLJO53X

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/QJLJO53XLU3VBSQP4VEBJLG76L \
  | 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: 82569777775d3750ca0fe54814acdff2eb3ce3a1395f39c49bbf57c9bfb3bcad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef56b9e4ef41b80414fb31f7437c053818a7f3e40939fbf27bb0b46fdda30493",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-11-11T16:50:11Z",
    "title_canon_sha256": "e7df491124820e947fe8cadcd6658d7c319893defc32a076a52e73e7995c7851"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2177",
    "kind": "arxiv",
    "version": 2
  }
}