Pith Number

pith:3VEHHAPL

pith:2011:3VEHHAPLJLOHXOBTMXU2KVOJEH

not attested not anchored not stored refs pending

The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups

Saeko Yamagata, Shin-ichi Oguni, Yoshifumi Matsuda

arxiv:1106.5288 v3 · 2011-06-27 · 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{3VEHHAPLJLOHXOBTMXU2KVOJEH}

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	2026-05-18T03:55:57.611993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd487381eb4adc7bb83365e9a555c921d37e5416e52aa9b591c03a8788818287

Aliases

arxiv: 1106.5288 · arxiv_version: 1106.5288v3 · doi: 10.48550/arxiv.1106.5288 · pith_short_12: 3VEHHAPLJLOH · pith_short_16: 3VEHHAPLJLOHXOBT · pith_short_8: 3VEHHAPL

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/3VEHHAPLJLOHXOBTMXU2KVOJEH \
  | 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: dd487381eb4adc7bb83365e9a555c921d37e5416e52aa9b591c03a8788818287

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa6444818e597f1f08e23ac641ef98f4533db6e883ff4dbb2a2d88907f77bc3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-06-27T02:38:38Z",
    "title_canon_sha256": "8b1a9be3869163827a7d9907306f17e40d7c8747ebb9f492ee22fda09c554bef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5288",
    "kind": "arxiv",
    "version": 3
  }
}