Main idea The manuscript is organized in two parts. Part I (Reduction) develops the OS-window analytic and geometric infrastructure and reduces the remaining model-specific target-side burden to one canonical shell-side specialization theorem on a canonical SU (2) family. Part II (Closure) proves that remaining shell-side theorem on one fixed canonical good packet chart and one fixed packet depth, and then follows the already prepared downstream continuation to the final mass-gap conclusion. Global theorem-facing chain The overall route is _ (t₀) > 0 _ (-M) ₆₄₎\, _ (t₀) ² m₀ c₃₎₌\, _ (-M) m₀ c₆₀\, _² > 0, with c₆₀: = c₃₎₌\, ₆₄₎. Thus the main bottleneck is the target-side production of residual-density positivity. What Part I proves Part I develops the OS-window framework, including: the parameter-box feasibility theorem, the residual topology density _, the topological-coercivity-to-gap route, the FRD / KP / CM. 1 / entropy-trace / EVI modules, the strict interchange-of-limits package, OS reconstruction and the global operator-gap transfer. Within this framework, all downstream transfers from residual-density positivity to the mass-gap conclusion are theorem-derived. What Part II proves Part II closes the remaining shell-side theorem on one fixed canonical chart. More precisely, it proves: a shell-center principal separation theorem, a fixed-chart one-point shell-margin theorem via the affine donor chain, a near-good branch entry theorem, a fixed-chart probability-floor transfer theorem, the canonical shell-side activation theorem. These ingredients verify the canonical shell-side specialization theorem and yield ₒ₇₄₋₋^SU (2) 0 _>0 m₀ c₆₀\, _² > 0. Reading guide This manuscript is intended to be read as a single-manuscript reduction-and-closure theorem package for the canonical target SU (2) BT-2 route. The appendices retain the full analytic, geometric, and target-instantiation ledgers, including: proof packs, dependency maps, OS-window feasibility infrastructure, parameter and constants registries, the detailed BT-2 local proof map, the target SU (2) instantiation bridge. Finite contract forms, packet-record forms, and auditable witness interfaces are retained as supplementary certification boundaries, rather than as the primary theorem-facing closure route. ------------------------ *Author: Lee Byoungwoo (leeclinic@protonmail. com)
Byoungwoo Lee (Sun,) studied this question.