Pith Number

pith:AYYIIJ6Q

pith:2011:AYYIIJ6QPA3R7A6M6KW5CTCWKZ

not attested not anchored not stored refs pending

Computing the Mertens function on a GPU

Eugene Kuznetsov

arxiv:1108.0135 v1 · 2011-07-31 · 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{AYYIIJ6QPA3R7A6M6KW5CTCWKZ}

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	2026-05-18T04:16:31.623856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06308427d078371f83ccf2add14c56564179507a8c2e6fbcaec85d27dcba2b65

Aliases

arxiv: 1108.0135 · arxiv_version: 1108.0135v1 · doi: 10.48550/arxiv.1108.0135 · pith_short_12: AYYIIJ6QPA3R · pith_short_16: AYYIIJ6QPA3R7A6M · pith_short_8: AYYIIJ6Q

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/AYYIIJ6QPA3R7A6M6KW5CTCWKZ \
  | 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: 06308427d078371f83ccf2add14c56564179507a8c2e6fbcaec85d27dcba2b65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b11af19507640829ff203d0da47c25abbb6723e6434dcd4ef637c65ba30a7d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-07-31T05:01:49Z",
    "title_canon_sha256": "ccf1e027ba73a30f67e39707defa8aadf030f3bb37848e1bbb2b428a9d92a90b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0135",
    "kind": "arxiv",
    "version": 1
  }
}