This paper constructs a new framework for the many-worlds interpretation thatintegrates symplectic geometry, quantum information geometry, and optimal transport theory. The central thesis is that world branches are not static splits in Hilbertspace, but rather a Lagrangian submanifold fibration process on a symplectic manifold driven by decoherence. We prove that the Born rule for the squared magnitudeof wave function amplitudes arises from a strict duality between symplectic volume conservation and the measure transformation induced by the quantum Fishermetric. An optimal transport cost functional between worlds is introduced as adynamical criterion for branch reality: a corresponding branch can support a stable information-recording structure if and only if the transport cost is lower thana critical threshold determined by the spectral gap. This framework transformsthe traditional measure problem of the many-worlds interpretation into a computable geometric optimization problem and achieves an explicit construction ofself-consistent observer conditions within the string theory landscape. The theorypredicts observable geometric phase effects in superconducting quantum simulators,and on cosmological scales, it corresponds to non-Gaussian deviations in primordialdensity perturbations. This work provides a complete mathematical implementation for the many-worlds interpretation, from ontology to phenomenology.