Pith Number

pith:WRODWO42

pith:2012:WRODWO423T7NF2YUNQKHNXG4CH

not attested not anchored not stored refs pending

Embedding relatively hyperbolic groups in products of trees

Alessandro Sisto, John M. Mackay

arxiv:1207.3008 v2 · 2012-07-12 · math.GT · 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{WRODWO423T7NF2YUNQKHNXG4CH}

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	2026-05-18T02:41:43.043044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b45c3b3b9adcfed2eb146c1476dcdc11febe77bac8133561e65a30bf81cb4c11

Aliases

arxiv: 1207.3008 · arxiv_version: 1207.3008v2 · doi: 10.48550/arxiv.1207.3008 · pith_short_12: WRODWO423T7N · pith_short_16: WRODWO423T7NF2YU · pith_short_8: WRODWO42

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/WRODWO423T7NF2YUNQKHNXG4CH \
  | 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: b45c3b3b9adcfed2eb146c1476dcdc11febe77bac8133561e65a30bf81cb4c11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "438b774210a702ef4d5320ca3d8744bde789efe8d20062ceb40295874ed4ec1f",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-07-12T16:04:57Z",
    "title_canon_sha256": "1d0e0d7a98e3f33e6cd7aff81aefdaadc0cb575719fba7d32ea3fe2a22246cb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3008",
    "kind": "arxiv",
    "version": 2
  }
}