We establish the Starflower Inheritance Theorem, proving that exponential monotone circuit lower bounds persist under bounded negation width. For any function family with sufficiently large monotone complexity, any circuit with sub-polynomial negation width must retain exponential size. This introduces the Brazil Threshold, a universal formula connecting monotone hardness exponents to negation-width robustness regimes. We apply the theorem to five explicit function families: bipartite perfect matching (Çalar et al. 2025), GEN-TFNP search problems, pigeonhole and clique-coloring functions, Tardos weight functions, and de Rezende–Vinyals CSP P-functions. This establishes a negation ladder of inherited hardness, with bipartite matching achieving the strongest known lower bounds in the bounded-negation regime — a super-polynomial improvement over prior results confirmed as a new unpublished result by Professor Stasys Jukna (personal correspondence, March 17, 2026). The framework unifies monotone and negation-limited complexity and provides stronger input bounds potentially enabling hardness magnification toward P versus NP resolution. All results are fully rigorous. An extended version applying the theorem to nine function families with MTSM hardware convergence is available separately.