Pith Number

pith:P5QKAL7N

pith:2014:P5QKAL7NEP74WEMK5HYYBJRRCQ

not attested not anchored not stored refs pending

Radial Density in Apollonian Packings

Alexandru Zaharescu, Cristian Cobeli, Jayadev S. Athreya

arxiv:1409.6352 v2 · 2014-09-22 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P5QKAL7NEP74WEMK5HYYBJRRCQ}

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	2026-05-18T02:33:00.931407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f60a02fed23ffcb118ae9f180a631142d5ff875c6fc885e65360b0cf6cfad22

Aliases

arxiv: 1409.6352 · arxiv_version: 1409.6352v2 · doi: 10.48550/arxiv.1409.6352 · pith_short_12: P5QKAL7NEP74 · pith_short_16: P5QKAL7NEP74WEMK · pith_short_8: P5QKAL7N

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/P5QKAL7NEP74WEMK5HYYBJRRCQ \
  | 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: 7f60a02fed23ffcb118ae9f180a631142d5ff875c6fc885e65360b0cf6cfad22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c623549a37db37d7644d8719d54f7f6789c1e8cbc409e1194a56fd05c0016cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-09-22T21:57:42Z",
    "title_canon_sha256": "ed850f46ff623ee95aa19d59c83803708c8491bc15044304a3a6cbf8b75e5efe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.6352",
    "kind": "arxiv",
    "version": 2
  }
}