Pith Number

pith:U4C6GLAR

pith:2026:U4C6GLARTSZSBFS6DBDU2P6DYG

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Finite Generation in Polynomial Semirings

Mohammad El Asal, Wael Mahboub

Finite generation of the additive monoid N_0[alpha] forces the algebraic number alpha to be a weak Perron number.

arxiv:2604.11569 v2 · 2026-04-13 · math.AC

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\usepackage{pith}
\pithnumber{U4C6GLARTSZSBFS6DBDU2P6DYG}

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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

Our second main result shows that finite generation forces alpha to be a weak Perron number.

C2weakest assumption

The analysis assumes the atomic case where atoms are precisely the powers alpha^n up to a certain n, and relies on divisibility conditions involving negative-tail polynomials without independent verification of atomicity in all cases.

C3one line summary

Finite generation of the additive monoid N_0[alpha] is fully characterized for minimal polynomials of the form p(X) - c and implies that alpha must be a weak Perron number, with applications to cubic cases and rank-3 monoids.

Receipt and verification

First computed	2026-06-02T02:04:53.022346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a705e32c119cb320965e18474d3fc3c1a294abe75f65fd5bffc6969f958dfc0b

Aliases

arxiv: 2604.11569 · arxiv_version: 2604.11569v2 · doi: 10.48550/arxiv.2604.11569 · pith_short_12: U4C6GLARTSZS · pith_short_16: U4C6GLARTSZSBFS6 · pith_short_8: U4C6GLAR

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/U4C6GLARTSZSBFS6DBDU2P6DYG \
  | 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: a705e32c119cb320965e18474d3fc3c1a294abe75f65fd5bffc6969f958dfc0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e358191404e921efd804a9213e01edfe5f18429123e770012efbe0f5ebcf715d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-04-13T14:50:35Z",
    "title_canon_sha256": "0cfbf483b6501d7856fa97b8b4d2dbbfd47a859ba3778594d881aa17a18d7f74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.11569",
    "kind": "arxiv",
    "version": 2
  }
}