Branch Indexical Theorem proves a conditional no-go for observable single-history selection at the post-decoherence pointer level. A branch indexical law is a single-history selection structure that marks one selected branch by an inaccessible label while leaving the unitary dynamics unchanged. The Branch Indexical Theorem (BIT) identifies a quiescent class of such laws and shows that every member is operationally silent on the post-decoherence pointer algebra. The result is intentionally narrow. It does not derive the Born rule, solve the measurement problem, choose an ontology, or introduce a new empirical prediction. It classifies what follows once a single-history selection structure preserves the unitary flow, respects the post-decoherence pointer basis, reproduces Born weights, and induces a linear physical ensemble map on the pointer marginal. Within that class, no pointer-algebra measurement distinguishes the selection law from standard unitary quantum mechanics supplemented by an inaccessible dummy label. The selected-history fact may remain as ontology, but it carries no operational signature at the pointer level. The boundary analysis shows where observable variants must pay: by leaving the quiescent class or by modifying the unitary dynamics. The paper gives representative witness channels for these exits and separates silent ontology from falsifiable dynamical deformation. BIT is therefore a demarcation theorem. Quiescent single-history selection is operationally inert; empirically visible single-history selection must come from extra structure outside the quiescent class.
Claudio Irrgang (Thu,) studied this question.