Multi-Anti-Structure Cores and Heterogeneous Gluing Debt: Once All the Known Escape Hatches Are Sealed, Where Does the Difficulty Actually Lie?

The original plan was to find a “multi-anti-structure core” (MASC) that resists all six known quotienting techniques at once, but this is immediately self-corrected: even a genuine find would only prove hardness “against the currently listed arsenal,” not “not in P” — Round 9's OBDD counterexample already demonstrated this trap. This round's real payoff comes from a thought experiment running the other way: let R₊=x∨y∨z and R₋=¬x∨¬y∨¬z; either one alone is trivial (satisfiable by setting everything to 1 or everything to 0), but Monotone 3-SAT, which mixes both, is already known to be NP-complete — local tractability is not closed under simple addition. Schaefer's dichotomy theorem formally confirms this: tractability depends on whether the entire constraint language shares a sufficient polymorphism closure, not on whether each individual constraint is easy on its own. Proposes Heterogeneous Gluing Debt (HGD), which measures local-quotienting cost and global-gluing cost separately, along with a Polymorphism Intersection Spectrum (PIS). The Equals Team counters with Dynamic Algebra Switching — which doesn't require a single algebra to be shared globally, and instead lets the algorithm switch between different solvers according to local structure.