Pith Number

pith:XOZFDRGA

pith:2013:XOZFDRGAM7OOT7MPAN6RFDYPNH

not attested not anchored not stored refs pending

On the Local-Global Principle for Integral Apollonian-3 Circle Packings

Xin Zhang

arxiv:1312.4650 v2 · 2013-12-17 · math.NT · math.GR · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XOZFDRGAM7OOT7MPAN6RFDYPNH}

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	2026-05-18T02:18:23.912836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbb251c4c067dce9fd8f037d128f0f69eaff20c07cbce6af8144e0b8f7e67616

Aliases

arxiv: 1312.4650 · arxiv_version: 1312.4650v2 · doi: 10.48550/arxiv.1312.4650 · pith_short_12: XOZFDRGAM7OO · pith_short_16: XOZFDRGAM7OOT7MP · pith_short_8: XOZFDRGA

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/XOZFDRGAM7OOT7MPAN6RFDYPNH \
  | 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: bbb251c4c067dce9fd8f037d128f0f69eaff20c07cbce6af8144e0b8f7e67616

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61294cb7e07df9085369ac7580c3b73673411b3b8a3877587515a912a1cac68f",
    "cross_cats_sorted": [
      "math.GR",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-17T05:32:47Z",
    "title_canon_sha256": "d5f0632519b552cbf0efd1cbbd13abbb22cd5d1c0c176941f448696e08e3d43c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4650",
    "kind": "arxiv",
    "version": 2
  }
}