Pith Number

pith:J6LDD4HU

pith:2018:J6LDD4HUBDGQG5ZNWRYILBPMQH

not attested not anchored not stored refs pending

A new explicit formula in the additive theory of primes with applications II. The exceptional set in Goldbach's problem

Janos Pintz

arxiv:1804.09084 v2 · 2018-04-24 · 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{J6LDD4HUBDGQG5ZNWRYILBPMQH}

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	2026-05-18T00:17:16.169581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f9631f0f408cd03772db4708585ec81e2a10ea9c7ced042a52fbf92ecc9e372

Aliases

arxiv: 1804.09084 · arxiv_version: 1804.09084v2 · doi: 10.48550/arxiv.1804.09084 · pith_short_12: J6LDD4HUBDGQ · pith_short_16: J6LDD4HUBDGQG5ZN · pith_short_8: J6LDD4HU

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/J6LDD4HUBDGQG5ZNWRYILBPMQH \
  | 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: 4f9631f0f408cd03772db4708585ec81e2a10ea9c7ced042a52fbf92ecc9e372

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9afbf6077120e2936a58505af488c61757ab05d115b7471dcd4f42efb89b6df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-04-24T15:05:38Z",
    "title_canon_sha256": "d32700f047f8d00f684522e5eb5988b80830f014fc14fe4478f8592eb14d665c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.09084",
    "kind": "arxiv",
    "version": 2
  }
}