Topological Freezing and Decoupled Dark Cores: A Decisive Hypothesis for the Superheavy Island of Stability

The theoretical prediction of the superheavy island of stability (Z≈114, N≈184) rests on shell corrections and fission barriers. Standard macroscopic–microscopic models exhibit a systematic residual structure in the superheavy region, and cannot fully account for phenomena such as the anomalously high fission barriers and the anomalously long lifetimes of high-spin isomers. This paper proposes a decisive hypothesis: the stability of superheavy nuclei is not "falling into an energy valley" but a "spatial topological phase transition." Core Assertion: When the shell-closure rigidity (fission barrier height × shell gap width) crosses a critical threshold, the topological charge of the nuclear core is over-locked and cannot extend outward. In the language of the O1 Theory Reachability Diagnoser, this corresponds to a sheaf-theoretic failure (non-vanishing Čech cohomology, H¹ ≠ 0) of the deconstructive homotopy operator at the nuclear core, forming a "topologically locked region enclosed by a sheaf-failure boundary," i.e., a decoupled dark core. The strong/electromagnetic probes of the dark core are truncated by the boundary, but the inertial/gravitational coupling is retained. We further propose that this locked region is a candidate generation mechanism for dark matter—the mass-electromagnetic decoupling induced by topological tension locking may be the microscopic origin of dark matter's "coupling only through gravity." Adjudication Tool: We deliver the T1–T3 topological criteria (number of components β₀, Fiedler value λ₁, persistent homology H¹ high-persistence loops), a scalar rigidity indicator κ, and a pre-registration protocol. A proof of concept on public-data proxy graphs yields an honest negative result (T1 formally satisfied, T2 and T3 not satisfied). This does not constitute a refutation: proxy graphs do not carry shell-closure rigidity information, and a true adjudication requires a Nilsson multi-quasiparticle configuration graph exported by a nuclear theory group. This is not a "conjecture awaiting verification," but an "assertion directly adjudicable by data." The adjudication protocol is in this paper, the targets are in the observational windows, and the rest is left to the data.