Adaptive Record Consistency in a Schulman-Type Model

Abstract

Adaptive measurements test whether a retrocausal model preserves observable records when experiments are connected by classical feedback. We establish exact and quantitative composition constraints for a finite-width, coplanar Schulman-type source with positive wrapped-Cauchy propagation weights. Raw segment composition admits an explicit adaptive signalling witness. A uniquely determined scalar correction preserves recorded continuations, and a detector with preparation memory implements this correction while retaining the source correlations. For common, independently prepared terminal detectors coupled to the source through arrival angles, exact calibration forces equal-mass antipodal atomic responses. Under setting-only raw feedback, the sharp minimum worst disturbance of an earlier record is ${\epsilon }_{\star }(0)=[2\cosh (2\Gamma ){]}^{-1}$, where $\Gamma$ is the total source-path width. We derive explicit finite-error bounds and prove linear small-error improvement. For four settings at $\Gamma =0.4$, a uniform reduction over arbitrary nonnegative response measures and a continuous polynomial certificate establish ${\epsilon }_{\star }(\delta )={\epsilon }_{\star }(0)-C_{0.4}\delta +O({\delta }^2)$, with $C_{0.4}\simeq 9.351091771057010$. A positive five-atom detector attains this coefficient. The results quantify the compatibility of isolated-source accuracy and adaptive record preservation, and provide precise design conditions for retrocausal apparatus models with explicit preparation, memory, and control.