Pith Number

pith:63WW37WV

pith:2014:63WW37WVDPBYFVBJPQ7XWWINHU

not attested not anchored not stored refs pending

Finite generating sets of relatively hyperbolic groups and applications to geodesic languages

Laura Ciobanu, Yago Antol\'in

arxiv:1402.2985 v3 · 2014-02-12 · 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{63WW37WVDPBYFVBJPQ7XWWINHU}

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	2026-05-18T01:13:38.425416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6ed6dfed51bc382d4297c3f7b590d3d27dec05f37a9c6777bae999bdca99dec

Aliases

arxiv: 1402.2985 · arxiv_version: 1402.2985v3 · doi: 10.48550/arxiv.1402.2985 · pith_short_12: 63WW37WVDPBY · pith_short_16: 63WW37WVDPBYFVBJ · pith_short_8: 63WW37WV

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/63WW37WVDPBYFVBJPQ7XWWINHU \
  | 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: f6ed6dfed51bc382d4297c3f7b590d3d27dec05f37a9c6777bae999bdca99dec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f23c0ac07f67cd272233e8bf80f0e04b4428c1438ab99123c3a77d2e8e90294d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-02-12T21:12:18Z",
    "title_canon_sha256": "75d508460b2eff3dbc3b76a2d0a33b652e08274e50737c773b64f2513af89f5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.2985",
    "kind": "arxiv",
    "version": 3
  }
}