Pith Number

pith:3PV6ZTT2

pith:2026:3PV6ZTT2MCCV2KKDOZVAR4YHHQ

not attested not anchored not stored refs pending

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis

Sergey Liflandsky

arxiv:2607.09797 v1 · 2026-07-09 · 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{3PV6ZTT2MCCV2KKDOZVAR4YHHQ}

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	2026-07-14T00:18:36.359460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbebecce7a60855d2943766a08f3073c23c20a08a3e942808cd0d777103e37dc

Aliases

arxiv: 2607.09797 · arxiv_version: 2607.09797v1 · doi: 10.48550/arxiv.2607.09797 · pith_short_12: 3PV6ZTT2MCCV · pith_short_16: 3PV6ZTT2MCCV2KKD · pith_short_8: 3PV6ZTT2

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/3PV6ZTT2MCCV2KKDOZVAR4YHHQ \
  | 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: dbebecce7a60855d2943766a08f3073c23c20a08a3e942808cd0d777103e37dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e963eb2807c1c4830bdc183fa6239cd89768a9ac8241be332f296e5f85690207",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-07-09T12:12:21Z",
    "title_canon_sha256": "9d87b0129d7afbea21207213f235e6a04a683121af9ed0bf71587fb1e5ada056"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.09797",
    "kind": "arxiv",
    "version": 1
  }
}