Pith Number

pith:2EUTUZYF

pith:2012:2EUTUZYFI3Y6BCHFC3T5EOSHZU

not attested not anchored not stored refs pending

Local convexity properties of Apollonian and Seittenranta's metric balls

Riku Kl\'en

arxiv:1204.0329 v2 · 2012-04-02 · 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{2EUTUZYFI3Y6BCHFC3T5EOSHZU}

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	2026-05-18T03:07:02.268342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1293a670546f1e088e516e7d23a47cd3428428ffd7614defedd4df0dddcf486

Aliases

arxiv: 1204.0329 · arxiv_version: 1204.0329v2 · doi: 10.48550/arxiv.1204.0329 · pith_short_12: 2EUTUZYFI3Y6 · pith_short_16: 2EUTUZYFI3Y6BCHF · pith_short_8: 2EUTUZYF

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/2EUTUZYFI3Y6BCHFC3T5EOSHZU \
  | 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: d1293a670546f1e088e516e7d23a47cd3428428ffd7614defedd4df0dddcf486

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f66bc951e610e6be7aae3986726e8bf5660f7629a9f9b313cc2dc968c9d19bfe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-04-02T07:27:31Z",
    "title_canon_sha256": "430916b6c917613995e66ef94b21249d41dc3f4515bd8deb56b7adf1a10f1a26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0329",
    "kind": "arxiv",
    "version": 2
  }
}