Pith Number

pith:B4QPDUUK

pith:2012:B4QPDUUKJNETMDNHV5X4FUXWXM

not attested not anchored not stored refs pending

On the Local-Global Conjecture for integral Apollonian gaskets

Alex Kontorovich, Jean Bourgain

arxiv:1205.4416 v2 · 2012-05-20 · 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{B4QPDUUKJNETMDNHV5X4FUXWXM}

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	2026-05-18T03:25:46.538225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f20f1d28a4b49360da7af6fc2d2f6bb0fabee5434aed911186245c4c52f06ba

Aliases

arxiv: 1205.4416 · arxiv_version: 1205.4416v2 · doi: 10.48550/arxiv.1205.4416 · pith_short_12: B4QPDUUKJNET · pith_short_16: B4QPDUUKJNETMDNH · pith_short_8: B4QPDUUK

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/B4QPDUUKJNETMDNHV5X4FUXWXM \
  | 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: 0f20f1d28a4b49360da7af6fc2d2f6bb0fabee5434aed911186245c4c52f06ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f618d543f8d3e9433a9aa7de73e29940e83e89a1f44c0860c694c01270a91fa5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-05-20T13:11:47Z",
    "title_canon_sha256": "f74941741050edbc11dc0b08cdf93e28b267d7581c1668938ec2424185660c35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.4416",
    "kind": "arxiv",
    "version": 2
  }
}