Abstract
Decentralized coordination assumes agents can exchange state fast enough to act on it. When communication delay approaches the coordination timescale, that assumption fails — but where it fails, and whether the failure depends on the coordination algorithm, has not been mapped directly. We treat delay as a controlled axis and measure a normalized coordination quality $Q \in [0,1]$ over a grid of coordination primitive $\times$ delay $\times$ swarm size $\times$ task, using a simplified 3-D kinematic simulator in which each agent acts on a delayed view of its peers while its own physics advances on true state. Across two peer-derived-target tasks — mutual rendezvous and consensus — three otherwise-distinct primitives (gossip-consensus, flocking, and CRDT-intent) collapse together from $Q \approx 1$ at zero delay through a boundary near $10$–$20$ integration steps, reaching a floor by delay $40$. A no-communication reference holds that floor, delay-independent. The overlap of the three primitives is the central result: within this regime the collapse is primitive-independent — delay, not the algorithm, sets where coordination breaks — and it is invariant across swarm sizes $N \in {500, 2000}$. We then test the mechanism directly: varying the intrinsic convergence rate through the gossip consensus gain $\alpha$, the collapse onset $d_c$ scales inversely with $\alpha$ ($d_c,\alpha \approx 2.8$ across a factor of four in gain and two swarm speeds), and beyond onset every gain relaxes onto a single gain-independent master curve — so the boundary is set by the ratio of delay to the swarm's own coordination timescale, now measured rather than inferred. We anchor the substrate to an external result by reproducing the Vicsek order–disorder transition ($\psi: 1.00 \to 0.63$ across the noise range) before trusting its coordination measurements. All figures regenerate from committed experiment records ($900$-cell phase grid plus a $520$-cell intrinsic-timescale grid, $5$ seeds each; $0$ NaN, $0$ agent faults). We scope the claim precisely: this is a simulation-based algorithmic result about coordination primitives under delay, not physical-device validation.