Pith Number

pith:3VY7AUU5

pith:2026:3VY7AUU5XUWFGJZXUA3APNT34C

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On numerical semigroups with embedding dimension four

Kazimierz Chomicz

A geometric procedure determines the Apéry set for any numerical semigroup with embedding dimension four.

arxiv:2604.25653 v2 · 2026-04-28 · math.NT

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\usepackage{pith}
\pithnumber{3VY7AUU5XUWFGJZXUA3APNT34C}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

We develop a geometric procedure for finding the Apéry set of any numerical semigroup with embedding dimension four.

C2weakest assumption

The geometric procedure correctly identifies the Apéry set for every numerical semigroup with exactly four minimal generators, without hidden restrictions on the generators or the semigroup.

C3one line summary

A geometric procedure computes Apéry sets for numerical semigroups with embedding dimension four, yielding Frobenius numbers, genera, Betti elements, minimal presentations, and catenary degrees for semigroups generated by four consecutive squares and four consecutive triangular numbers.

Receipt and verification

First computed	2026-05-27T01:05:55.024866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd71f0529dbd2c532737a03607b67be092d80008f6a313294d056a1b114712c9

Aliases

arxiv: 2604.25653 · arxiv_version: 2604.25653v2 · doi: 10.48550/arxiv.2604.25653 · pith_short_12: 3VY7AUU5XUWF · pith_short_16: 3VY7AUU5XUWFGJZX · pith_short_8: 3VY7AUU5

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/3VY7AUU5XUWFGJZXUA3APNT34C \
  | 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: dd71f0529dbd2c532737a03607b67be092d80008f6a313294d056a1b114712c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9dd76d2a19a6993b35afe09a02729b826bce37089b1e56d2b4a96be20c5a8fd4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-04-28T13:50:06Z",
    "title_canon_sha256": "331e237d56d5d36e3f1fa1f9c8b366cc0f2303e028d8e8c004f211fbb268c750"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25653",
    "kind": "arxiv",
    "version": 2
  }
}