Chain Obstructions and Deflation in the Invariant Subspace Problem

Reformulates the invariant subspace problem as a fixed-point problem on the lattice of closed subspaces and provides a structural analysis of chain-based methods. Proves that chains from both extremes of the lattice are forced to triviality — the Adámek construction and its dual are both structurally obstructed. Identifies stabilization and properness as jointly sufficient conditions for nontrivial invariant subspaces, and proves three new sufficient conditions: a deflation theorem, a lattice intermediate value theorem, and a descending chain condition theorem. The deflation theorem abstracts the order-theoretic component of Lomonosov's theorem. Independence results show the abstract lattice axiom system neither forces nor precludes nontrivial fixed points. Formalized in Lean 4 with zero sorry.