Pith Number

pith:3HZRPEUE

pith:2023:3HZRPEUEN4MGXAP3TTTLNEECS6

not attested not anchored not stored refs pending

Group rings and hyperbolic geometry

Grigori Avramidi, Thomas Delzant

arxiv:2309.16791 v2 · 2023-09-28 · math.GT · math.GR · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3HZRPEUEN4MGXAP3TTTLNEECS6}

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	2026-06-12T01:09:03.830225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9f31792846f186b81fb9ce6b6908297809b6534c9afd07e7e5c3b20c1619bec

Aliases

arxiv: 2309.16791 · arxiv_version: 2309.16791v2 · doi: 10.48550/arxiv.2309.16791 · pith_short_12: 3HZRPEUEN4MG · pith_short_16: 3HZRPEUEN4MGXAP3 · pith_short_8: 3HZRPEUE

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/3HZRPEUEN4MGXAP3TTTLNEECS6 \
  | 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: d9f31792846f186b81fb9ce6b6908297809b6534c9afd07e7e5c3b20c1619bec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f123bbd94827d860a0e87a88d480a99a727fc9f0c6ed9c6d422461d9367d63d4",
    "cross_cats_sorted": [
      "math.GR",
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2023-09-28T18:38:33Z",
    "title_canon_sha256": "a22782303613c9be015a6150bb5c1bd25144da6c1dfea98c25d5daa96c4e5dab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2309.16791",
    "kind": "arxiv",
    "version": 2
  }
}