Predicting κ in the Temporal-Binding Collapse Theorem

Wave-function collapse has traditionally been modeled as an environment-driven process, independent of how a system is interrogated. In Collapse is Relational, I introduced the Temporal-Binding Collapse Theorem, which showed that collapse rates acquire an additional contribution inversely proportional to the detector’s temporal binding window, \( \tau \), yielding \( \Gamma \)\( \tau \)() = \( \Gamma_E \) + \( \kappa/\tau. \)Reanalyses of ions, spins, qubits, and Bose--Einstein condensates confirmed the predicted linear scaling of \( \Delta \Gamma \) with \( 1/\tau \), but left \( \kappa \)as an empirical, protocol-sensitive parameter. This paper advances that program by introducing a predictive framework for \( \kappa \). Modeling the detector as a temporal filter \( F(\omega;\tau) \)acting on the system’s noise spectrum S(\( \omega \)), I show that \( \kappa \) can be expressed as a spectral-overlap functional. Its sign follows from whether shrinking \( \tau \) admits or suppresses spectral weight (anti-Zeno versus Zeno), and its magnitude reflects the structure of the spectrum and the coupling strength. Worked examples illustrate how this framework accounts for the observed variation of \( \kappa \)across diverse platforms. The contribution is primarily conceptual: it provides the architecture for systematic cross-platform comparison and principled design rules. The next step is to apply this framework to concrete models, derive quantitative predictions, and test them experimentally—laying the foundation for a comparative science of collapse and the longer-term possibility of engineering \( \kappa \) by design.