One State, Many Perspectives: Branch Structure and Born Weights in Everettian Quantum Mechanics

Everettian quantum mechanics retains universal unitary evolution and therefore does not select a unique measurement outcome by collapse. This raises two distinct questions: why quantum alternatives should carry Born weights, and how those weights can guide expectation when all outcome components persist. This article develops perspectival quantum monism, in which the universal quantum state and its unitary structure are fundamental, branches are emergent record structures rather than countable primitive entities, and empirical descriptions depend on a system-environment cut and a grain of description. The quantitative question is addressed by the Descriptive Born-weight uniqueness theorem. In finite complex dimension at least three, positivity, normalization, coherence under refinement, and null support uniquelyimply the Born weight for every cell of every finite orthogonal decomposition. The complete proof chain has been mechanized in Lean 4 without project-specific axioms. A separate formalization of a Riedel-type result shows that, in a finite local record model, redundancy and a non-pair-covering condition yield a unique orthogonal joint-branch decomposition. A further Lean construction gives a strictly unitary circuit generating exact or noisy two-branch states with redundant records while preserving amplitudes and squared norms. These results support, but do not prove, covariance across all physically admissible descriptions. The semantic-normative question is treated separately through observer internality, self-location relative to accessible records, and comparison with deterministic classical probability. The article does not derive the bridge from measure to rational credence. It argues instead that Everettian theory requires no independent numerical Born postulate once the stated structuralassumptions are accepted.