Pith Number

pith:ACBDFCMO

pith:2022:ACBDFCMOFHNP27TIE4KEPE2QIY

not attested not anchored not stored refs pending

Computing $\pi(N)$: An elementary approach in $\tilde{O}(\sqrt{N})$ time

Dean Hirsch, Ido Kessler, Uri Mendlovic

arxiv:2212.09857 v4 · 2022-12-19 · 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{ACBDFCMOFHNP27TIE4KEPE2QIY}

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

Practical Computations of the Mertens Function: $M(10^{24})$ and $M(10^{25})$

Receipt and verification

First computed	2026-07-05T06:40:31.086345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

008232898e29dafd7e682714479350461ec6a48288d4c058a33f99bf086088a3

Aliases

arxiv: 2212.09857 · arxiv_version: 2212.09857v4 · doi: 10.48550/arxiv.2212.09857 · pith_short_12: ACBDFCMOFHNP · pith_short_16: ACBDFCMOFHNP27TI · pith_short_8: ACBDFCMO

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/ACBDFCMOFHNP27TIE4KEPE2QIY \
  | 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: 008232898e29dafd7e682714479350461ec6a48288d4c058a33f99bf086088a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "edeac8b6be0413a2eddf509d89256705a51db75e2bbfd155da180790d0bbc276",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-12-19T21:05:14Z",
    "title_canon_sha256": "8160fdfaa71ddf372d61a6af18913dec70052139abaa4e831dc99de653511cf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.09857",
    "kind": "arxiv",
    "version": 4
  }
}