DNA replication initiation causally sets the added mass for cell division in Escherichia coli

Faithful genome inheritance requires cell division to be precisely coordinated with DNA replication. The classical Cooper-Helmstetter paradigm posited that division occurs at a roughly constant time after replication initiation (initiation-to-division "ID-timer" model). This has since been challenged by conflicting "adder" phenomena, leaving the primary signal for division a fundamental enigma. Here, we resolve these discrepancies by establishing that cell division in Escherichia coli obeys a universal "ID-adder" rule: addition of a defined size increment from replication initiation. This rule is invariant across the physiological range of nutrition-affected growth rates, whereas other versions of the adder phenomenon are emergent properties shaped by inter-cycle correlations. Through population-level perturbations of initiation mass, division machinery, and replication termination, we demonstrate that replication initiation directly and causally sets the division schedule. This principle operates independently of replication termination and division protein levels, providing a robust mechanism for coordinating the genome duplication with the cell division cycle.