Computational Adjudication of Topological Freezing and Decoupled Dark Cores: Classical Topological Features and Quantum Algorithmic Verification based on the O1 Diagnoser

The existence of the superheavy island of stability currently relies on macroscopic-microscopic models, yet anomalous fission barriers and exceptionally long high-spin isomer lifetimes suggest deeper physical mechanisms. This paper proposes a conceptual framework: the stability of superheavy nuclei may originate from a "spatial topological phase transition." When shell-closure rigidity crosses a critical threshold, the topological charge of the nuclear core becomes over-locked, forming a "decoupled dark core" impenetrable to strong/electromagnetic probes. To translate this hypothesis into rigorous algorithmic adjudication, we introduce the O1 Theory Reachability Diagnoser and propose a dual joint criterion of "space (geometric bottleneck)—time (homological deadlock)". On real proxy graphs of nuclides, the algorithm successfully captures topological signatures: Se77 is classified as [Torsion] due to an incontractible homological deadlock, while the doubly magic nucleus Pb208 falls into the [Boundary] critical state due to extreme geometric rigidity. Independence tests further reveal that topological conductance has no linear correlation with static shell corrections of the WS4 model and can capture odd-A pairing-blocking anomalies missed by macroscopic barriers. Furthermore, to address the computational disaster caused by the scale expansion of nuclear configuration graphs, we explore the quantum mapping of this criterion. Using Quantum Phase Estimation (QPE) to extract the Laplacian spectral gap on a NISQ simulator, we verify the feasibility of the algorithm on graph sets up to nodes (93/93 samples with error ). This paper provides a fully computable adjudication tool for the "topological freezing" hypothesis and delineates the computational boundary of topological diagnostics in the NISQ era. Keywords: superheavy nuclei; decoupled dark core; topological freezing; O1 Diagnoser; homological deadlock; Quantum Phase Estimation (QPE)