This study proposes a structural interpretation of low-density, high-temperature hydrogen-rich gas in the halo environment of the Andromeda galaxy under the framework of SOSD-1. The central hypothesis of this work is that some diffuse halo gas structures may not be solely products of internal galactic processes such as stellar feedback, supernova-driven outflows, or recycled fountain flows, but may instead represent primordial hydrogen clouds that were not fully incorporated during early galaxy formation. The main purpose of this paper is not merely to restate that diffuse halo gas exists, since that has already been widely discussed in previous studies, but to reinterpret the origin of a subset of such gas from a structural perspective. The present work argues that the physical state of gas alone cannot determine origin. Low density, high temperature, and even low metallicity may support the primordial interpretation, but these properties are not sufficient by themselves because similar states may also emerge through other astrophysical pathways. For this reason, the paper distinguishes between _state-based conditions_ and _structural origin criteria_. A key element of this study is the conceptual clarification of why low-density, high-temperature gas does not necessarily undergo rapid macroscopic expansion. In ordinary human intuition, high temperature is associated with strong heat, expansion, and energetic activity. However, that intuition is derived from dense environments where particle collisions are frequent. In a highly rarefied halo environment, individual particles may possess high kinetic energy while remaining dynamically decoupled from one another due to extremely low collision rates. Thus, high temperature does not directly imply collective expansion. This distinction is essential to understanding how hot gas may remain diffuse without immediate dispersal. The paper also argues that galaxy formation should not be regarded as a perfectly efficient process in which all primordial gas is inevitably accreted into the galaxy. The early universe was not characterized by complete density uniformity, and therefore not all gas parcels would have experienced identical gravitational conditions. Some regions could become efficiently bound and incorporated, whereas others would remain only weakly bound, marginally coupled, or dynamically separated from the central gravitational collapse. This provides the basis for considering the survival of non-merged primordial gas in halo regions. In addition, the study addresses why such structures may not have been clearly recognized in past observations. Diffuse low-density gas produces weak signals, broad spatial distributions, and low contrast against the background. For this reason, some structures may historically have been treated as noise, background fluctuation, or low-significance artifacts. This does not imply that the gas did not exist; rather, it suggests that the detection and classification frameworks of earlier observations may not have been optimized to distinguish physically real diffuse gas from statistical or instrumental background components. The historical transition in astronomy, in which previously ambiguous diffuse gaseous signals came to be recognized as physically meaningful structures, supports this broader methodological point. Finally, this study introduces both falsification conditions and structural validation conditions. The falsification conditions are derived from the internal logic of the hypothesis itself; if these conditions are violated, the primordial interpretation becomes structurally unsustainable. By contrast, the validation conditions proposed here are not claims that current observations have already confirmed the hypothesis, but rather predictive structural criteria that future observations can use to test it. In this sense, the present work is intended as a structural framework for origin classification rather than as a claim of completed observational proof.