Structural Unforcedness in Foundational Problems A Programmatic Explanation of Persistent Non-Resolution

This work presents a unified structural analysis of six major unresolved problems in mathematics and theoretical physics: the Birch–Swinnerton–Dyer Conjecture, the Hodge Conjecture, the Riemann Hypothesis, the P versus NP problem, the Navier–Stokes global regularity problem, and the Yang–Mills mass gap problem. Rather than proposing solutions or technical refinements, the paper argues that the persistent non-resolution of these problems arises from a shared structural property of their prevailing formal frameworks. Each framework permits the conjectured outcome but does not logically enforce it, allowing multiple globally consistent configurations to coexist. This phenomenon is formalized under the notion of structural unforcedness, which manifests as representational, certificational, and dynamical non-closure across arithmetic, analytic, computational, and dynamical domains. From this perspective, non-resolution is interpreted as structural information about the limits of current conceptual languages, rather than as a deficit of technical sophistication. The work is intended as a diagnostic and programmatic contribution, clarifying why incremental refinement has repeatedly failed and outlining the minimal structural conditions any genuine resolution must satisfy.