Pith Number

pith:WH4JYKNO

pith:2013:WH4JYKNOZPAXBVZBSHH3YX27MR

not attested not anchored not stored refs pending

On the Typical Size and Cancelations Among the Coefficients of Some Modular Forms

Florian Luca, Igor E. Shparlinski, Maksym Radziwill

arxiv:1308.6606 v2 · 2013-08-29 · 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{WH4JYKNOZPAXBVZBSHH3YX27MR}

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	2026-05-18T02:42:25.947937Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1f89c29aecbc170d72191cfbc5f5f646500ef16312ede760126c5d7b8c33d56

Aliases

arxiv: 1308.6606 · arxiv_version: 1308.6606v2 · doi: 10.48550/arxiv.1308.6606 · pith_short_12: WH4JYKNOZPAX · pith_short_16: WH4JYKNOZPAXBVZB · pith_short_8: WH4JYKNO

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/WH4JYKNOZPAXBVZBSHH3YX27MR \
  | 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: b1f89c29aecbc170d72191cfbc5f5f646500ef16312ede760126c5d7b8c33d56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9463ba0be5bcf0f6ad78357629f67d5bc21f5fe6228f7a82ff6468eefa7454f6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-08-29T20:56:46Z",
    "title_canon_sha256": "e134e806364201d040091939f5e1ed9c9713712d2e0e5d08e642c19b2f688f2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.6606",
    "kind": "arxiv",
    "version": 2
  }
}