Pith Number

pith:AB3CV2OR

pith:2019:AB3CV2ORP35RAOYDUU7Q236QR3

not attested not anchored not stored refs pending

On the geometry of van Kampen diagrams of graph products of groups

Anthony Genevois

arxiv:1901.04538 v2 · 2019-01-14 · 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{AB3CV2ORP35RAOYDUU7Q236QR3}

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.

Cited by

1 paper in Pith

Polynomial hyperbolicity and products of free groups

Receipt and verification

First computed	2026-05-17T23:54:21.702753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00762ae9d17efb103b03a53f0d6fd08efc082833a02c21be429af9cb864b673b

Aliases

arxiv: 1901.04538 · arxiv_version: 1901.04538v2 · doi: 10.48550/arxiv.1901.04538 · pith_short_12: AB3CV2ORP35R · pith_short_16: AB3CV2ORP35RAOYD · pith_short_8: AB3CV2OR

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/AB3CV2ORP35RAOYDUU7Q236QR3 \
  | 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: 00762ae9d17efb103b03a53f0d6fd08efc082833a02c21be429af9cb864b673b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0fbd164c041fc6cf05f411f4a6b8d3213fabd6f0d16ce1e5502128e36e9def24",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-01-14T19:49:29Z",
    "title_canon_sha256": "be202387fcb00ac3a5eed587425634dd37cbe02b4cb600fcb5e22f4aa9f37ea1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.04538",
    "kind": "arxiv",
    "version": 2
  }
}