Figure 1: Persistence Diagram – Alt Text

Figure 1: Topological Persistence Analysis of Agent System Behavior

A two-dimensional scatter plot showing topological feature persistence. The x-axis represents "Birth" time/scale (0.0 to 1.0), and the y-axis represents "Death" time/scale (0.0 to 1.0). Forty orange X markers are scattered across the plot space, each representing a topological feature (connected component or loop) that appears at birth time and disappears at death time. A diagonal orange reference line runs from (0,0) to (1,1); features close to this diagonal are short-lived noise, while features farther from the diagonal (higher death values for given birth values) represent persistent, significant topological structures.

Interpretation: Points far above the diagonal indicate topological features with long lifetimes—stable agent clusters (β₀) or recurring feedback loops (β₁) in the system. These persistent features reveal emergent organizational patterns in the multi-agent swarm that transcend individual agent behaviors. The diagram quantifies system coherence: more high-persistence features correlate with stronger emergent coordination and consciousness-like self-organization.

Connection to Document Theory: This visualization operationalizes Section 1.1's discussion of Topological Data Analysis. The β₀ features (connected components) track how agent clusters form and dissolve, while β₁ features (loops) capture recursive information flows. High persistence indicates the "Stand Alone Complex" emergence described in Section 2.1—coordination without central control.

Technical Note: Generated from synthetic data using matplotlib. In production deployment with agisa_sac, this diagram would be computed from actual Pub/Sub message topology using persistent homology algorithms (e.g., GUDHI, Ripser).

Color Accessibility: Orange markers maintain >4.5:1 contrast ratio with white background per WCAG 2.1 AA standards.