Pith Number

pith:4LMHYJ4J

pith:2022:4LMHYJ4JMAHFBGCY4RAGA37KFF

not attested not anchored not stored refs pending

Sums of singular series with large sets and the tail of the distribution of primes

Vivian Kuperberg

arxiv:2210.09775 v2 · 2022-10-18 · 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{4LMHYJ4JMAHFBGCY4RAGA37KFF}

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.

Cited by

1 paper in Pith

Holder continuity of an alternating Erdos series on prime K-tuples

Receipt and verification

First computed	2026-07-05T06:20:37.367084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2d87c2789600e509858e440606fea2959ae0cadd66a1d4c4d32e0adc94df490

Aliases

arxiv: 2210.09775 · arxiv_version: 2210.09775v2 · doi: 10.48550/arxiv.2210.09775 · pith_short_12: 4LMHYJ4JMAHF · pith_short_16: 4LMHYJ4JMAHFBGCY · pith_short_8: 4LMHYJ4J

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/4LMHYJ4JMAHFBGCY4RAGA37KFF \
  | 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: e2d87c2789600e509858e440606fea2959ae0cadd66a1d4c4d32e0adc94df490

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2c460922bc0b1ad45f31352e41f65723fc1c76bcb4df2d98efef2bb22b1dd2a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-10-18T11:42:39Z",
    "title_canon_sha256": "1ea0748704f31a0f0e253679b7d00ebc382fc09bbdb9b009de74598695d1f0bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2210.09775",
    "kind": "arxiv",
    "version": 2
  }
}