Starflower Inheritance III: Toward Magnification via Negation-Width-Preserving Reductions

Abstract:

Building on the Starflower Inheritance Theorem, we develop a framework for constructing negation-width-preserving reductions from robustly hard monotone functions to the Minimum Circuit Size Problem (MCSP). Our main contribution is a conceptual and technical template showing how the exponential lower bound for bipartite matching with bounded negation width — strengthened by the recent breakthrough matching bounds of Çalar et al. (2025) — can be funneled into MCSP hardness via controlled gadget composition. We prove that if MCSP admits circuits of size N to the power of 1 plus delta for small delta greater than zero and simultaneously maintains negation width below a fixed subpolynomial bound, then bipartite matching would admit circuits of negation width below the Brazil Threshold, contradicting Starflower Inheritance. This provides an explicit three-step pathway from structural monotone hardness to MCSP lower bounds of the right shape to trigger hardness magnification toward NP not contained in P/poly.

This paper is the third in the Starflower series. The first established the Starflower Inheritance Theorem and its application to five explicit function families. The second extended the Negation Ladder to nine function families and established a formal convergence with the Magnetically Tunable Synthetic Myelin (MTSM) robotic nervous system cable architecture — a hardware system for which a patent application is pending with the United States Patent and Trademark Office. The present paper develops the magnification pathway, connecting bounded-negation lower bounds to MCSP via a structurally controlled reduction framework. All results are fully rigorous; proven results are clearly separated from exploratory conjectures.

Originally composed and submitted March 26, 2026.