Pith Number

pith:X56Q5TL4

pith:2016:X56Q5TL4X4CUSJJWFYKG5FGWSW

not attested not anchored not stored refs pending

Effective equidistribution of horocycle lifts

Ilya Vinogradov

arxiv:1607.04769 v1 · 2016-07-16 · math.DS · 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{X56Q5TL4X4CUSJJWFYKG5FGWSW}

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	2026-05-18T01:10:56.727519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf7d0ecd7cbf054925362e146e94d6959004bc6d2c2524138fa5ac5f42ea6489

Aliases

arxiv: 1607.04769 · arxiv_version: 1607.04769v1 · doi: 10.48550/arxiv.1607.04769 · pith_short_12: X56Q5TL4X4CU · pith_short_16: X56Q5TL4X4CUSJJW · pith_short_8: X56Q5TL4

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/X56Q5TL4X4CUSJJWFYKG5FGWSW \
  | 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: bf7d0ecd7cbf054925362e146e94d6959004bc6d2c2524138fa5ac5f42ea6489

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "188d24c5bc895d4d9e65b23a5bf30e90dd92bec9425f1a1b65abf409dedaf0c2",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-07-16T17:11:37Z",
    "title_canon_sha256": "0222f1b491ef0a8628a848a3c7251429471900120dddeb13694e111e8d0a9d8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.04769",
    "kind": "arxiv",
    "version": 1
  }
}