Pick a beam and a target, ignite, and burn beam-days. The arithmetic is real (compound nucleus, 3n evaporation); the cross sections are stylized but shaped like the truth: picobarns, one atom per week on a good route, and a quasi-fission penalty that kills exactly the heavy symmetric routes whose arithmetic comes closest to the island. The boats that float fall short; the boat that points at the island sinks. STARK MODE adds the beam that doesn't exist — stamped accordingly.
REAL: the nucleon arithmetic (verified), the record holders plotted (Fl-289 via Ca-48+Pu-244, Og-294 via Ca-48+Cf-249 — Dubna, ~0.5–6 pb, atoms per week), the 6–9 neutron deficit of every existing route, the quasi-fission wall on symmetric heavy projectiles (Ni-64+Pu-244 reaches N=183 on paper and ~nothing in a detector), and N=184 as the predicted shell closure. STYLIZED: cross sections and half-lives here are shaped, not computed — this sheet teaches the structure of the problem, it does not predict experiments. FICTION: the Ca-57 beam. No such beam exists at usable intensity; it is included, stamped, so you can stand on the island once and watch the honest ending: even there, the atom decays. The theorem is the deliverable. The atom never was.