The Zero-State Singularity Framework: A Formal Information-Theoretic and Computational Model of Iterative Biological Optimization and Architectural Criteria for Artificial General Intelligence

We recast the Zero-State Singularity (ZSS) framework as a set of formally stated postulates, definitions, propositions and testable hypotheses. The framework holds that biological evolution can be read as an iterative optimization run on a "Base Codebase" with three invariants: Zero Spacetime Coordinates (ZST), Zero-State Vibration (ZSV) and Singularity-to-Duality Knowledge (SDK). We give each invariant a precise counterpart in existing physics and computer science: ZST as a timeless global constraint with relational time (Page-Wootters), ZSV as a pure global quantum state of zero von Neumann entropy that is conserved under unitary evolution, and SDK as the Schmidt data of a bipartition together with an algorithmic-information description. We prove that a zero-entropy global state necessarily produces entropic, "dual" subsystems, and that knowing the set of all configurations does not determine, or shortcut, any particular realized trajectory (the "Phenomenological Gap"). The Tri-Agent architecture (Creation, Preservation, Termination) is formalized as a composite stochastic operator \mathcal{F}=\mathcal{T}\circ\mathcal{P}\circ C with thermodynamic and demographic observables. The "Survival Trap" is modeled as a bandwidth-budget threshold effect, and the framework's teleological claim is converted into a falsifiable statistical test (passive versus driven trends with a reflecting wall), for which we derive an analytic signature and confirm it by simulation. Finally, the three AGI criteria are stated as measurable conditions, linked to planning-as-inference, integration-segregation measures, and the instrumental-convergence literature. We state clearly which results are theorems, which are toy-model illustrations, and which remain postulates, and we list the observations that would falsify the framework.