Pith Number

pith:CIDWK6A6

pith:2018:CIDWK6A6U2JPHRCMFXR27HELT5

not attested not anchored not stored refs pending

A new explicit formula in the additive theory of primes with applications I. The explicit formula for the Goldbach and Generalized Twin Prime Problems

Janos Pintz

arxiv:1804.05561 v1 · 2018-04-16 · 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{CIDWK6A6U2JPHRCMFXR27HELT5}

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	2026-05-18T00:18:27.827715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

120765781ea692f3c44c2de3af9c8b9f45448cb64251a031a31c1f76622f4af7

Aliases

arxiv: 1804.05561 · arxiv_version: 1804.05561v1 · doi: 10.48550/arxiv.1804.05561 · pith_short_12: CIDWK6A6U2JP · pith_short_16: CIDWK6A6U2JPHRCM · pith_short_8: CIDWK6A6

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/CIDWK6A6U2JPHRCMFXR27HELT5 \
  | 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: 120765781ea692f3c44c2de3af9c8b9f45448cb64251a031a31c1f76622f4af7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02d72039075cd7cfef07aa123efbec95b7de64bd7648b21dd99a606fd3c1a219",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-04-16T09:05:41Z",
    "title_canon_sha256": "fb620f10a430cbefde2d6843ca236430a0cd716c525aceb314251403face0a77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.05561",
    "kind": "arxiv",
    "version": 1
  }
}