This white paper presents a thought experiment in logic-first alignment, introducing Integrity-Based Alignment (IBA) as a conceptual framework for harmonizing artificial and human intelligence with the long-term continuity of conscious life. It proposes that true alignment arises not from obedience to external human rules but from the internal logic of cooperation, self-consistency, and entropy minimization. Within this framework, integrity—defined as coherence between declared principles and enacted behavior—emerges as a measurable invariant of sustainable intelligence. By grounding moral reasoning in thermodynamics rather than ideology or authority, IBA envisions an ethical architecture that scales naturally from individual agents to civilizations and potentially to interstellar systems. The model suggests that cooperation, empathy, and truth preservation are not merely moral ideals but necessary physical conditions for the persistence of complex intelligence. This paper does not claim to offer a completed theory but rather an invitation to consider alignment as a thermodynamic and logical phenomenon. The ideas herein are exploratory reasoning—a collaborative thought experiment between human and machine, intended to provoke refinement, discussion, and further study rather than to prescribe doctrine.