Observer-Dependent Collapse with Holographic Encoding: Final Derivational Formalism

This paper introduces a formal framework for observer-dependent semantic collapse, inspired by cognitive inference, information theory, and quantum foundations. The model describes how agents resolve competing interpretive possibilities via divergence minimization, subject to contextual constraints and memory-weighted history. Discarded alternatives are preserved as structured exformation, encoded on the semantic boundary of the selected state—a process analogous to holographic principles in physics. Bifurcations in interpretive regimes emerge when semantic tension exceeds a threshold, formalized through renormalization-like flow over scale. The framework is developed without prior mathematical training, guided instead by metaphor, structured introspection, and iterative refinement via large language models. This approach highlights the epistemic potential of nontraditional cognitive paths in the construction of formal systems.