Pith Number

pith:6DFFHCAT

pith:2025:6DFFHCATJ2PBCD6DHI35RUVVJY

not attested not anchored not stored refs pending

Multiple sums with the M\"obius function

Igor E. Shparlinski, William D. Banks

arxiv:2506.08787 v1 · 2025-06-10 · 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{6DFFHCATJ2PBCD6DHI35RUVVJY}

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	2026-07-05T11:19:13.194374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0ca5388134e9e110fc33a37d8d2b54e1196154aba3e170191a333a6c9a3019a

Aliases

arxiv: 2506.08787 · arxiv_version: 2506.08787v1 · doi: 10.48550/arxiv.2506.08787 · pith_short_12: 6DFFHCATJ2PB · pith_short_16: 6DFFHCATJ2PBCD6D · pith_short_8: 6DFFHCAT

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/6DFFHCATJ2PBCD6DHI35RUVVJY \
  | 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: f0ca5388134e9e110fc33a37d8d2b54e1196154aba3e170191a333a6c9a3019a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3550b2b3448e6e22f716b9f53482bb5cf6e85fc8c34063e412eca8822720e5b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-06-10T13:33:41Z",
    "title_canon_sha256": "7f56a90877695fb917992c9c1f649afad46febaba299b81318dd943f193e59d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.08787",
    "kind": "arxiv",
    "version": 1
  }
}