Supplementary Lecture: Limit Applications of the Dynamic Causality Model

This paper serves as a supplementary lecture to *Temporal Asynchrony and Individual Independence* (Revised Edition, Amendment V1), extending the **Dynamic Causal Propagation Model** to its limiting cases. Building on two foundational premises established in the parent work — (1) that causal influence propagates at a finite velocity (one second per second, forward in time), and (2) that the world possesses no metacognitive faculty and merely outputs whatever input it receives — this paper systematically derives the consequences of applying these premises to iterated time travel and self-homicide scenarios. Under the finite-velocity model, the "simple circular loop" presupposed in much science fiction cannot obtain. In its place, the paper demonstrates the emergence of an **Intermittent Loop**: a three-phase pulse structure consisting of an On-phase, Off-phase, and Restoration-phase. Analysis of the self-homicide paradox reveals that what is eliminated is not the time traveler but a distinct physical entity belonging to that temporal coordinate, thereby dissolving the apparent contradiction without additional postulates. The paper further demonstrates that encounters between multiple instances of the same individual within a single spacetime are processed by the world as nothing more than multiple co-present physical data sets, generating no logical inconsistency. The logic of return travel is treated under the same framework: the influences of departure and arrival propagate independently; the time traveler's present is shielded from the advancing causal wave while their past is not; and repeated time travel produces cumulative divergence from the original state. Throughout, the world recognizes none of this as anomalous — it outputs only the present state. All conclusions derived herein require no supplementary assumptions; they follow by pure deduction from the two foundational premises. What appears as a time paradox is, invariably, nothing more than a succession of local state transitions, which the world continues to output, indifferently.