Pith Number

pith:M6NICBEB

pith:2026:M6NICBEB355Y2ZIZ6WTIPYLC3K

not attested not anchored not stored refs pending

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

Greg Hurst

arxiv:2607.07566 v1 · 2026-07-08 · 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{M6NICBEB355Y2ZIZ6WTIPYLC3K}

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	2026-07-09T01:20:29.681106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

679a810481df7b8d6519f5a687e162da86544b095f24b710c62a89533bc58dc5

Aliases

arxiv: 2607.07566 · arxiv_version: 2607.07566v1 · doi: 10.48550/arxiv.2607.07566 · pith_short_12: M6NICBEB355Y · pith_short_16: M6NICBEB355Y2ZIZ · pith_short_8: M6NICBEB

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/M6NICBEB355Y2ZIZ6WTIPYLC3K \
  | 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: 679a810481df7b8d6519f5a687e162da86544b095f24b710c62a89533bc58dc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61a5971ee557b027d1b20ac4f31d9937552f0079cadd4826128204c9c4b1593f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-08T15:57:01Z",
    "title_canon_sha256": "e24e5010bada858ebe5648acef364ceead2d69b9d558a28d64b4e544a9977b43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07566",
    "kind": "arxiv",
    "version": 1
  }
}