Pith Number

pith:WOJO4SUO

pith:2015:WOJO4SUOJB5H7G547UF3CWYXTK

not attested not anchored not stored refs pending

Presentations of Groups Acting Discontinuously on Direct Products of Hyperbolic Spaces

\'Angel del R\'io, Ann Kiefer, Eric Jespers

arxiv:1504.07783 v1 · 2015-04-29 · 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{WOJO4SUOJB5H7G547UF3CWYXTK}

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	2026-05-18T02:17:32.234001Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b392ee4a8e487a7f9bbcfd0bb15b179a88a6e630b536ddbc8fcbf09b4e945186

Aliases

arxiv: 1504.07783 · arxiv_version: 1504.07783v1 · doi: 10.48550/arxiv.1504.07783 · pith_short_12: WOJO4SUOJB5H · pith_short_16: WOJO4SUOJB5H7G54 · pith_short_8: WOJO4SUO

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/WOJO4SUOJB5H7G547UF3CWYXTK \
  | 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: b392ee4a8e487a7f9bbcfd0bb15b179a88a6e630b536ddbc8fcbf09b4e945186

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24e3eb94f35eb78d33b9de21d7d6411022881f0a0a6f09dd209dadb631273289",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-04-29T09:25:28Z",
    "title_canon_sha256": "4ed1ac4dc39da0e6615a5b19b35a0193dc34d697c164ccb6cc836fcf800037ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.07783",
    "kind": "arxiv",
    "version": 1
  }
}