Pith Number

pith:RJX7OEJX

pith:2011:RJX7OEJXSBDT5ZUST7CTLR5PPI

not attested not anchored not stored refs pending

A characterisation of virtually free groups

Derek F. Holt, Robert H. Gilman, Sarah Rees, S. Hermiller

arxiv:1111.0771 v1 · 2011-11-03 · 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{RJX7OEJXSBDT5ZUST7CTLR5PPI}

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	2026-05-18T04:09:36.970546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a6ff7113790473ee6929fc535c7af7a0efd45c7adaf73fa587c9a91c06f969c

Aliases

arxiv: 1111.0771 · arxiv_version: 1111.0771v1 · doi: 10.48550/arxiv.1111.0771 · pith_short_12: RJX7OEJXSBDT · pith_short_16: RJX7OEJXSBDT5ZUS · pith_short_8: RJX7OEJX

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/RJX7OEJXSBDT5ZUST7CTLR5PPI \
  | 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: 8a6ff7113790473ee6929fc535c7af7a0efd45c7adaf73fa587c9a91c06f969c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8476eb25e831e7b79a37b81494e1bb901337765854401616e4ef2110f42ff803",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-11-03T10:25:44Z",
    "title_canon_sha256": "1950e60b30d642904bd14b6b31b8af7ecceedd3f12f9e36fa5a6da3e5b346e97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0771",
    "kind": "arxiv",
    "version": 1
  }
}