Parity-Projected Cumulant Response of Four-Sector Affinity under Sector-Specific Exponential Tilting

Paper 6 studies how the relationship between four groups changes when each group is affected in a different way. The method separates the change into different statistical levels such as the mean, variance, and higher-order effects. This is useful because sometimes the average effect is zero, but an important effect can still appear through the variance or other higher-order structure. The paper gives a systematic way to identify which level is producing the change. Paper6_Parity_Projected_Cumulan… It also shows when different effects cancel each other exactly. This can help explain situations where strong patterns are visible in separate groups, but disappear after all groups are combined. The quantum-switch example in the paper demonstrates this type of exact cancellation. Paper6_Parity_Projected_Cumulan… The main formulas are exact within their stated mathematical conditions, and the method does not require a small-change approximation for the main finite-coupling identity. Paper6_Supporting_Information_v… Main benefits of Paper 6: identifies whether a response comes from the mean, variance, or higher-order statistical structure; continues the analysis even when the first-order or average effect is zero; shows when group effects cancel after pooling; provides exact mathematical formulas and clear diagnostic steps; includes a Gaussian example and a quantum-switch consistency example; can be reproduced using QDL Research Suite v1.5.0. Paper6_Supporting_Information_v… The computational companion is QDL Research Suite v1.5.0, published at DOI 10.5281/zenodo.23026104.