Pith Number

pith:KQUSRU25

pith:2015:KQUSRU25OYPTULP2DWPXV7W3IL

not attested not anchored not stored refs pending

Minimal genus of a multiple and Frobenius number of a quotient of a numerical semigroup

Francesco Strazzanti

arxiv:1512.00638 v1 · 2015-12-02 · math.GR · math.AC · 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{KQUSRU25OYPTULP2DWPXV7W3IL}

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	2026-05-18T01:25:25.509670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

542928d35d761f3a2dfa1d9f7afedb42d61cfc356ec3b2745b4d5c828df0ee8f

Aliases

arxiv: 1512.00638 · arxiv_version: 1512.00638v1 · doi: 10.48550/arxiv.1512.00638 · pith_short_12: KQUSRU25OYPT · pith_short_16: KQUSRU25OYPTULP2 · pith_short_8: KQUSRU25

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/KQUSRU25OYPTULP2DWPXV7W3IL \
  | 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: 542928d35d761f3a2dfa1d9f7afedb42d61cfc356ec3b2745b4d5c828df0ee8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00e3f571e2393223128e9dd1fa462410de68523f4d40461794b035598fd8cf09",
    "cross_cats_sorted": [
      "math.AC",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-12-02T10:34:56Z",
    "title_canon_sha256": "e127146dbab2d34346564dc886280dfba63512c4c85374faf911772c78e0db50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00638",
    "kind": "arxiv",
    "version": 1
  }
}