Pith Number

pith:AGKWKEUL

pith:2011:AGKWKEULWFKAS32M4THL7HRLKK

not attested not anchored not stored refs pending

Apollonian packings as physical fractals

Francesco Varrato, Giuseppe Foffi

arxiv:1111.5256 v1 · 2011-11-22 · cond-mat.stat-mech · math.NT · physics.comp-ph · physics.data-an

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AGKWKEULWFKAS32M4THL7HRLKK}

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	2026-05-18T04:07:53.042112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

019565128bb154096f4ce4cebf9e2b52aa90b298825385011ef5e926ff7c06f8

Aliases

arxiv: 1111.5256 · arxiv_version: 1111.5256v1 · doi: 10.48550/arxiv.1111.5256 · pith_short_12: AGKWKEULWFKA · pith_short_16: AGKWKEULWFKAS32M · pith_short_8: AGKWKEUL

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/AGKWKEULWFKAS32M4THL7HRLKK \
  | 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: 019565128bb154096f4ce4cebf9e2b52aa90b298825385011ef5e926ff7c06f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2211216e18224b0267554c42e3faa02d55c792d79d2137de94de0fa587d10f0d",
    "cross_cats_sorted": [
      "math.NT",
      "physics.comp-ph",
      "physics.data-an"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2011-11-22T17:12:39Z",
    "title_canon_sha256": "6a5eb60872a0cf194fc79744b149a27fd8653e212328489d7c32227ff97323d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5256",
    "kind": "arxiv",
    "version": 1
  }
}