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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.20001818 |
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Table of Contents:
- <p>Abstract</p> <p>We investigate how survival conditioning alters Koopman operator representations in XOR-based causal dynamics using weighted Extended Dynamic Mode Decomposition (EDMD).</p> <p>We show that survival conditioning induces a deformation of the underlying probability measure without modifying the dynamics. This deformation systematically breaks operator normality: both Henrici’s departure and the numerical abscissa increase monotonically with conditioning strength. These non-normality measures are strongly correlated with imaginary spectral broadening (r ≈ 0.85–0.89).</p> <p>Pseudospectral analysis reveals resolvent amplification and spectral bulging under conditioning. A null model that preserves marginal distributions but destroys temporal correlations removes these effects, indicating that the phenomenon arises from causal temporal structure.</p> <p>At the operator level, the mechanism is traced to non-commutation of weighted covariance operators, yielding a non-self-adjoint Koopman operator. The results establish a structural link between measure deformation, operator non-normality, and spectral deformation.</p> <p>This work provides a reproducible empirical foundation for a general operator-theoretic principle: probabilistic conditioning can induce non-normal Koopman dynamics through measure deformation.</p>