Pith Number

pith:HUBQMEAE

pith:2012:HUBQMEAEUQV62J3WECDIOEOQOC

not attested not anchored not stored refs pending

On partial sums of the M\"obius and Liouville functions for number fields

Makoto Minamide, Yusuke Fujisawa

arxiv:1212.4348 v1 · 2012-12-18 · 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{HUBQMEAEUQV62J3WECDIOEOQOC}

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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

M\"obius formulas for densities of sets of prime ideals

Receipt and verification

First computed	2026-05-18T03:38:13.252467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d03061004a42bed277620868711d070b9d9e2c4f35623097ebbbf91781bc5cf

Aliases

arxiv: 1212.4348 · arxiv_version: 1212.4348v1 · doi: 10.48550/arxiv.1212.4348 · pith_short_12: HUBQMEAEUQV6 · pith_short_16: HUBQMEAEUQV62J3W · pith_short_8: HUBQMEAE

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/HUBQMEAEUQV62J3WECDIOEOQOC \
  | 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: 3d03061004a42bed277620868711d070b9d9e2c4f35623097ebbbf91781bc5cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "841bad3b93df4368ed2ea7a1d72d594ec7a335e65f67c5180a70f60a8d697bdc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-18T13:36:36Z",
    "title_canon_sha256": "1728a778d04dd628e7a08070ac20ca8fb03f55d410367ef50dd48e6dc175aa0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4348",
    "kind": "arxiv",
    "version": 1
  }
}