Pith Number

pith:JOJ5EFJO

pith:2011:JOJ5EFJOWSMWLRJFMNCBFEGGC2

not attested not anchored not stored refs pending

Quasi-hyperbolic planes in relatively hyperbolic groups

Alessandro Sisto, John M. Mackay

arxiv:1111.2499 v3 · 2011-11-10 · math.GR · math.GT · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JOJ5EFJOWSMWLRJFMNCBFEGGC2}

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.

Cited by

1 paper in Pith

Piecewise Visual, Linearly Connected Metrics on Boundaries of Relatively Hyperbolic Groups

Receipt and verification

First computed	2026-07-05T01:49:33.445343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b93d2152eb49965c52563441290c6168c6464ba914759312a3530cb208576dd

Aliases

arxiv: 1111.2499 · arxiv_version: 1111.2499v3 · doi: 10.48550/arxiv.1111.2499 · pith_short_12: JOJ5EFJOWSMW · pith_short_16: JOJ5EFJOWSMWLRJF · pith_short_8: JOJ5EFJO

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/JOJ5EFJOWSMWLRJFMNCBFEGGC2 \
  | 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: 4b93d2152eb49965c52563441290c6168c6464ba914759312a3530cb208576dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "714535fbc0692f284f176db6475d723d4235110a0130ea23e24f310d4685803d",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-11-10T15:21:30Z",
    "title_canon_sha256": "ade43d07e3815e064e41cb962850bb7ad4c75f3b348d322761ea409db51fff5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2499",
    "kind": "arxiv",
    "version": 3
  }
}