Kinematic Suppression of Branch Overlaps from Compact Boundary Algebra

This paper examines how the overlap between branch states depends on the size and separation of records on a spherical boundary. Under the stated locality, symmetry, and regularity assumptions, together with a minimal differential-order condition, it derives an inverse-elliptic commutator kernel and connects it to two-dimensional log-correlated Gaussian fields.The analysis gives explicit overlap laws for localized records, records moved across the boundary, and broad records, including the limit in which a record becomes uniform. These results show how branch distinguishability changes with record geometry within the chosen quasi-free state. The derivation requires no environmental coupling or thermodynamic process.