Pith Number

pith:K5IRLRED

pith:2018:K5IRLREDTYNI5OGODNZ5FPCVFM

not attested not anchored not stored refs pending

Apollonian metric, uniformity and Gromov hyperbolicity

Matti Vuorinen, Qingshan Zhou, Yaxiang Li

arxiv:1805.07481 v2 · 2018-05-19 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K5IRLREDTYNI5OGODNZ5FPCVFM}

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	2026-05-17T23:58:14.273744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

575115c4839e1a8eb8ce1b73d2bc552b049d15647f0a474ceb8f64c23b2fc7e8

Aliases

arxiv: 1805.07481 · arxiv_version: 1805.07481v2 · doi: 10.48550/arxiv.1805.07481 · pith_short_12: K5IRLREDTYNI · pith_short_16: K5IRLREDTYNI5OGO · pith_short_8: K5IRLRED

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/K5IRLREDTYNI5OGODNZ5FPCVFM \
  | 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: 575115c4839e1a8eb8ce1b73d2bc552b049d15647f0a474ceb8f64c23b2fc7e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23792034876b7e4749b454366f8b54e9618317ecc303da8cad55fd9b8bc9917d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2018-05-19T00:14:42Z",
    "title_canon_sha256": "1422e383370bc2761a95112b0af4ea319e9fa616ee95f1a678c5f413a126fded"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.07481",
    "kind": "arxiv",
    "version": 2
  }
}