Pith Number

pith:X2OJ77ID

pith:2012:X2OJ77IDJ266UUVISJTNCM4Y45

not attested not anchored not stored refs pending

From Apollonius To Zaremba: Local-Global Phenomena in Thin Orbits

Alex Kontorovich

arxiv:1208.5460 v1 · 2012-08-27 · 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{X2OJ77IDJ266UUVISJTNCM4Y45}

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	2026-05-18T03:46:59.421540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be9c9ffd034ebdea52a89266d13398e77031022ab2e73e19a2b206d9024cd5d7

Aliases

arxiv: 1208.5460 · arxiv_version: 1208.5460v1 · doi: 10.48550/arxiv.1208.5460 · pith_short_12: X2OJ77IDJ266 · pith_short_16: X2OJ77IDJ266UUVI · pith_short_8: X2OJ77ID

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/X2OJ77IDJ266UUVISJTNCM4Y45 \
  | 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: be9c9ffd034ebdea52a89266d13398e77031022ab2e73e19a2b206d9024cd5d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4564acdf89fb352c86acbb1b4f57d9dc79c0844610943dbf5d66a0492889d55e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-27T18:05:01Z",
    "title_canon_sha256": "81053996ab5ca6f462207db0a56bcfb004ffd80863c07fce59086834148710a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5460",
    "kind": "arxiv",
    "version": 1
  }
}