Quantum-Informational History Optimization Theory (QIHOT): A Single-History Selection Framework with Consistency Results

We present Quantum-Informational History Optimization Theory (QIHOT) as a formal proposal for selecting a single realized quantum history from a space of dynamically admissible histories subject to boundary constraints. In the present paper, we restrict attention to finite-dimensional and toy-model settings, where the framework can be stated explicitly. QIHOT separates two levels: a dynamical prior over admissible histories generated by standard quantum evolution, and an informational selection rule that reweights those histories by an entropy-based cost functional. Within this structure, we show that standard Born statistics are recovered in symmetric-cost measurement scenarios when the prior is the usual Hilbert-space quantum prior. We further formulate conditions under which operational no-signaling is preserved, provided the selection functional factorizes locally for spacelike-separated regions. A fully worked two-outcome model illustrates how the framework interpolates between coherent evolution and measurement-like branch selection. We contrast QIHOT with the Many-Worlds Interpretation, the Transactional Interpretation, the Consistent Histories formalism, the Schwinger–Keldysh formalism, and Lagrangian-based retrocausal models, highlighting structural similarities and key differences. We emphasize that the present paper develops QIHOT as a scoped formal proposal with partial consistency results rather than as a complete replacement for quantum theory. Possible extensions to consciousness and cosmology are deferred to brief outlook-level discussion.