The Battle for an Algebraic Invariant: Does Every Easy Problem Have a “Composable Solution Structure”?

Polymorphism offers an elegant candidate: instead of looking at how a formula is written, look at whether the legal tuples can be stably composed by a nontrivial operation — Horn is closed under AND, dual-Horn under OR, 2-SAT under majority, affine under XOR/minority, and the more general finite-domain CSP dichotomy centers on Taylor/WNU-type operations. This is, so far, the first structural tool in the entire game that genuinely transcends surface syntax and unconditionally yields a polynomial-time algorithm. But Team Equal seizes on this round's most important logical distinction: the formal conclusion on the hard side of CSP dichotomy is NP-completeness, and NP-complete does not mean “not in P” unless P≠NP is already known. If P=NP, languages with no tractable polymorphism would still have polynomial-time algorithms. Proposes the Algorithm-to-Algebra Bridge Problem: does every exact P algorithm necessarily induce some independently definable compositional structure on its solution space? This bridge has not yet been built.