Pith Number

pith:OAILO4QK

pith:2017:OAILO4QKL2OPZXHKQUCGDTTGIN

not attested not anchored not stored refs pending

Spatial Statistics of Apollonian Gaskets

Amita Malik, Calvin Kessler, Mo Jiao, Weiru Chen, Xin Zhang

arxiv:1705.06212 v2 · 2017-05-17 · math.MG · math-ph · math.DS · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OAILO4QKL2OPZXHKQUCGDTTGIN}

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	2026-05-18T00:44:15.134583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7010b7720a5e9cfcdcea850461ce6643693b69e1cb763d8836dddab984bf1729

Aliases

arxiv: 1705.06212 · arxiv_version: 1705.06212v2 · doi: 10.48550/arxiv.1705.06212 · pith_short_12: OAILO4QKL2OP · pith_short_16: OAILO4QKL2OPZXHK · pith_short_8: OAILO4QK

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/OAILO4QKL2OPZXHKQUCGDTTGIN \
  | 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: 7010b7720a5e9cfcdcea850461ce6643693b69e1cb763d8836dddab984bf1729

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "525135e6f1f9e50cea521615895f17a5fb56c5077a432312daa58c2444e84d66",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2017-05-17T15:32:43Z",
    "title_canon_sha256": "4cd9dcf9315a3b1412c2e2d31c0b5d04ef455401c3fb638eedc22dc486e786e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.06212",
    "kind": "arxiv",
    "version": 2
  }
}