Pith Number

pith:CN5J2F2Z

pith:2010:CN5J2F2ZOQNIMZIJ3TPX5WBITI

not attested not anchored not stored refs pending

Sieve Procedure for the M\"obius prime-functions, the Infinitude of Primes and the Prime Number Theorem

R. M. Abrarov, S. M. Abrarov

arxiv:1004.1563 v2 · 2010-04-08 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CN5J2F2ZOQNIMZIJ3TPX5WBITI}

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	2026-05-18T04:12:18.713396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

137a9d1759741a866509dcdf7ed8289a0dd4fb8360a48613e21578fae2c57b86

Aliases

arxiv: 1004.1563 · arxiv_version: 1004.1563v2 · doi: 10.48550/arxiv.1004.1563 · pith_short_12: CN5J2F2ZOQNI · pith_short_16: CN5J2F2ZOQNIMZIJ · pith_short_8: CN5J2F2Z

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/CN5J2F2ZOQNIMZIJ3TPX5WBITI \
  | 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: 137a9d1759741a866509dcdf7ed8289a0dd4fb8360a48613e21578fae2c57b86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9ba6d44954969d1b01e628f8d900f0e30fbebf8ef785f89edd4ca7af08321df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2010-04-08T19:27:50Z",
    "title_canon_sha256": "284bf9f9ecd5598a50656fda1b41ed74afc918438d78ab3b3afcd9c501dd27a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.1563",
    "kind": "arxiv",
    "version": 2
  }
}