Pith Number

pith:PO5L7MKZ

pith:2002:PO5L7MKZD65NDTYPFU7ZQGVZKU

not attested not anchored not stored refs pending

Boundaries of hyperbolic groups

Ilya Kapovich, Nadia Benakli

arxiv:math/0202286 v1 · 2002-02-27 · 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{PO5L7MKZD65NDTYPFU7ZQGVZKU}

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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

Growth of Approximate Groups in Hyperbolic Groups

Receipt and verification

First computed	2026-07-04T14:35:56.724000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bbabfb1591fbad1cf0f2d3f981ab9550ddb508760a8adbbb6f9b86aa4cafee6

Aliases

arxiv: math/0202286 · arxiv_version: math/0202286v1 · doi: 10.48550/arxiv.math/0202286 · pith_short_12: PO5L7MKZD65N · pith_short_16: PO5L7MKZD65NDTYP · pith_short_8: PO5L7MKZ

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/PO5L7MKZD65NDTYPFU7ZQGVZKU \
  | 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: 7bbabfb1591fbad1cf0f2d3f981ab9550ddb508760a8adbbb6f9b86aa4cafee6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9974488eee129d5912fa644943987a9e7d24642f1e24ca296a21af8f1c28ac52",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2002-02-27T02:22:23Z",
    "title_canon_sha256": "736bf9c7312fe71ad95d4d7a1bcfd40596c36330c16f2ecc115032adda64ec91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0202286",
    "kind": "arxiv",
    "version": 1
  }
}