Quantum Mechanics and Gravity from Conserved Informational Throughput

Standard quantum mechanics introduces Hilbert space, unitary evolution, the Born rule, and tensor-product composition as foundational elements of its formalism. General relativity introduces curved spacetime geometry and Einstein field equations. This work develops a conserved informational-throughput framework in which normalized quantum-state structure and Newtonian-limit gravitational time dilation arise from a common set of relations connecting local energy density to finite informational capacity. Starting from the informational demand relation κ = ρ_E V A₀/(ħc), the throughput field χ(r) = √(1 − 2κ/r), and the derived Capacity-Conservation Law (CCL), χ² + L = 1, we develop a unified informational route to a normalized Hilbert-compatible state structure, Schrödinger-type evolution, Born-style probability weighting, Tsirelson-limited shared-capacity correlations, and gravitational time dilation via χ(r) ≡ proper time rate k(r). In this framework, quantum coherence, superposition, entanglement, and probability are interpreted as consequences of conserved informational throughput rather than as independent postulates. The same scalar χ links quantum-state normalization with gravitational clock suppression.