Open Research Index

Linear upper bounds for the first Betti number of four-generated numerical semigroups

Ben Keene

Palomar Registrypalomar/PALOMAR-2026-10-07-000005Oct 7, 2026math.ACscore 0

A Lean 4 formalization, against Mathlib, of the theorem that the first Betti number (minimal number of generators of the toric ideal) of a numerical semigroup minimally generated by four elements n0 = 4 (an informal companion result; sharpness is not formalized).

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