Pith Number

pith:DIJ2GLM6

pith:2013:DIJ2GLM6I2LUL3KYAHP5BHICRJ

not attested not anchored not stored refs pending

On the asymptotic behavior of weakly lacunary series

Christoph Aistleitner, Istvan Berkes, Robert Tichy

arxiv:1312.0668 v2 · 2013-12-03 · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DIJ2GLM6I2LUL3KYAHP5BHICRJ}

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	2026-05-18T03:02:46.393362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a13a32d9e469745ed5801dfd09d028a6a8dfedaf4a5ee1762df29f06056faf3

Aliases

arxiv: 1312.0668 · arxiv_version: 1312.0668v2 · doi: 10.48550/arxiv.1312.0668 · pith_short_12: DIJ2GLM6I2LU · pith_short_16: DIJ2GLM6I2LUL3KY · pith_short_8: DIJ2GLM6

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/DIJ2GLM6I2LUL3KYAHP5BHICRJ \
  | 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: 1a13a32d9e469745ed5801dfd09d028a6a8dfedaf4a5ee1762df29f06056faf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c028f380b828e043160f1075d98026f97d009b03464c2e7c332ebbbdcbdde9e",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-03T00:39:27Z",
    "title_canon_sha256": "6e3bab738bf634cbf48071c053da493b16590e9cbbcc9c3b2faf59a42a70dd69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0668",
    "kind": "arxiv",
    "version": 2
  }
}