Pith Number

pith:YQLKTOFK

pith:2007:YQLKTOFKC5RW56NRTJWMYVLO45

not attested not anchored not stored refs pending

Strong wavefront lemma and counting lattice points in sectors

Alexander Gorodnik, Hee Oh, Nimish Shah

arxiv:0708.3188 v1 · 2007-08-23 · math.NT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YQLKTOFKC5RW56NRTJWMYVLO45}

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	2026-05-17T23:53:58.395065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c416a9b8aa17636ef9b19a6ccc556ee75dcc608ba4cd1e5de1b8c74684659ab7

Aliases

arxiv: 0708.3188 · arxiv_version: 0708.3188v1 · doi: 10.48550/arxiv.0708.3188 · pith_short_12: YQLKTOFKC5RW · pith_short_16: YQLKTOFKC5RW56NR · pith_short_8: YQLKTOFK

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/YQLKTOFKC5RW56NRTJWMYVLO45 \
  | 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: c416a9b8aa17636ef9b19a6ccc556ee75dcc608ba4cd1e5de1b8c74684659ab7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10ecbcc6228ecbf9de3986e3c4074d36d6c9d3af8a43ad7ae5ad471f1e2159b6",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-08-23T15:16:28Z",
    "title_canon_sha256": "2ee10c31392ec3fb9314b09158ad53cb20ebd1b247bcb96c3f60d68b9761822c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.3188",
    "kind": "arxiv",
    "version": 1
  }
}