Pith Number

pith:YOS2Z75Z

pith:2013:YOS2Z75ZMNN6JTKV2BL5SWRYAJ

not attested not anchored not stored refs pending

On relative hyperbolicity for a group and relative quasiconvexity for a subgroup

Saeko Yamagata, Shin-ichi Oguni, Yoshifumi Matsuda

arxiv:1301.4029 v1 · 2013-01-17 · 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{YOS2Z75ZMNN6JTKV2BL5SWRYAJ}

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	2026-05-18T03:36:14.580110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3a5acffb9635be4cd55d057d95a38024e7cf84e9e4f203e68dce8646450b2d4

Aliases

arxiv: 1301.4029 · arxiv_version: 1301.4029v1 · doi: 10.48550/arxiv.1301.4029 · pith_short_12: YOS2Z75ZMNN6 · pith_short_16: YOS2Z75ZMNN6JTKV · pith_short_8: YOS2Z75Z

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/YOS2Z75ZMNN6JTKV2BL5SWRYAJ \
  | 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: c3a5acffb9635be4cd55d057d95a38024e7cf84e9e4f203e68dce8646450b2d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6950e2d14871c66ac010231a76360b8c8f330345218d46eb68251047adfce4b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-01-17T09:47:40Z",
    "title_canon_sha256": "8374a55f4b00e5f89e7f987b562b40ac30e99cd4146a1aa4809ec9f17c01c046"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.4029",
    "kind": "arxiv",
    "version": 1
  }
}