Pith Number

pith:WYO32ZA7

pith:2012:WYO32ZA7O3L2S6VFLLV2GZQWPQ

not attested not anchored not stored refs pending

On convergence and growth of sums $\sum c_k f(kx)$

Istvan Berkes

arxiv:1211.4446 v1 · 2012-11-19 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WYO32ZA7O3L2S6VFLLV2GZQWPQ}

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	2026-05-18T03:40:26.873522Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b61dbd641f76d7a97aa55aeba366167c290cde65cf7c54521c8db84814fe7940

Aliases

arxiv: 1211.4446 · arxiv_version: 1211.4446v1 · doi: 10.48550/arxiv.1211.4446 · pith_short_12: WYO32ZA7O3L2 · pith_short_16: WYO32ZA7O3L2S6VF · pith_short_8: WYO32ZA7

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/WYO32ZA7O3L2S6VFLLV2GZQWPQ \
  | 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: b61dbd641f76d7a97aa55aeba366167c290cde65cf7c54521c8db84814fe7940

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c99855866c9939c75d823407c01829295815b2ad84deb95eb1b83a8f8eee9d77",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-11-19T14:48:04Z",
    "title_canon_sha256": "213a60aee02469bdf59e6e025aa6bd73ba60d26bc32d9cba3e91669a86d74bd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4446",
    "kind": "arxiv",
    "version": 1
  }
}