When Does a Quantum Branch Become an Outcome?

This work investigates which outcome-like behaviors can arise in closed, momentum-accounted quantum models before any additional irreversible state-selection mechanism is introduced. A hierarchy of conservative controls is developed using a finite-mass beam splitter, explicit record degrees of freedom, conditioned and unconditioned branch histories, nonlinear two-mode many-body dynamics, many-mode record sectors, and recoil-dependent visibility and distinguishability.

The analysis shows that several behaviors commonly associated with measurement-like dynamics can be reproduced within the closed models considered here. A finite-mass splitter supports explicit entanglement between recoil and field apparatus while preserving the total momentum ledger. Record formation suppresses reduced-state coherence and produces strongly branch-polarized conditioned histories, while the unconditioned state retains both alternatives.

A separate many-body status analysis shows that collective nonlinear dynamics can generate genuine self-trapping and long-lived population imbalance, while the interaction studied becomes branch-independent in the single-excitation sector through J_z² = I/4. Increasing record complexity can also strongly suppress finite-window recoherence through effective spectral participation and phase structure without introducing nonunitary dynamics.

Finally, the finite apparatus degree of freedom that carries recoil is connected directly to branch-state overlap, interference visibility, and optimal path distinguishability, providing a common quantitative description of momentum exchange and which-path information.

The results do not constitute a solution to the quantum measurement problem, a derivation of a unique measurement outcome or the Born rule, or a no-go theorem for modified quantum dynamics. Rather, they establish a reproducible control hierarchy: outcome-like behavior should first be tested against closed standard models capable of reproducing the same observable signature before it is interpreted as evidence for an additional irreversible state-selection mechanism.

Data and reproducibility: Numerical data, source code, diagnostic outputs, and publication figures supporting the computational controls are available in the associated Zenodo reproducibility archive.