Fisher-information-inspired collective feedback in Kuramoto--XY Hamiltonians: exact small-system structure and a hardware falsification

This preprint introduces and characterises a collective Fisher-information-inspired magnetisation-feedback term for Kuramoto--XY quantum simulations. The model augments a heterogeneous XY Hamiltonian with a diagonal term proportional to minus lambda times total magnetisation squared, normalised by qubit count, creating explicit magnetisation-sector energy shifts while preserving ideal XY magnetisation conservation. Artefact-generated exact diagonalisation on n = 4, 6, and 8 qubits shows systematic changes in ground energy, spectral width, and spectral gap as the feedback strength varies. The manuscript also reports adjacent-gap statistics, low-energy bipartition entropy trends, and a small n = 4 VQE benchmark comparing a K_ij-informed ansatz against generic TwoLocal and EfficientSU2 baselines. The record archives the source, bibliography, and PDF for a hardware-falsifiable modelling contribution. Claims are limited to the stated exact diagonalisation grid, VQE benchmark configuration, and associated committed artefacts.