Pith Number

pith:ZB5CUWBG

pith:2021:ZB5CUWBGLK2K7FCMOUC2XOBGES

not attested not anchored not stored refs pending

Linear growth of translation lengths of random isometries on Gromov hyperbolic spaces and Teichm\"uller spaces

Dongryul M. Kim, Hyungryul Baik, Inhyeok Choi

arxiv:2103.13616 v2 · 2021-03-25 · math.GT · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZB5CUWBGLK2K7FCMOUC2XOBGES}

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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

Acylindrically hyperbolic groups and counting problems

Receipt and verification

First computed	2026-07-05T06:58:03.361307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c87a2a58265ab4af944c7505abb82624bd652c354759e872d5d982feda1332ea

Aliases

arxiv: 2103.13616 · arxiv_version: 2103.13616v2 · doi: 10.48550/arxiv.2103.13616 · pith_short_12: ZB5CUWBGLK2K · pith_short_16: ZB5CUWBGLK2K7FCM · pith_short_8: ZB5CUWBG

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/ZB5CUWBGLK2K7FCMOUC2XOBGES \
  | 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: c87a2a58265ab4af944c7505abb82624bd652c354759e872d5d982feda1332ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9433fe9101df48d1f4d76919d550df1a73aa90989ecaa26340d6d7a361de82af",
    "cross_cats_sorted": [
      "math.DS",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-03-25T05:49:39Z",
    "title_canon_sha256": "09b4c33e1fbd3b9c74196d774db7a9fb5f2f59e1cc1a00b9fe9391acfafbb529"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.13616",
    "kind": "arxiv",
    "version": 2
  }
}