Agent traces are fundamentally sequences of events, but developers need to visualize their causal structure as execution trees. Building these trees requires more than timestamp sorting, as events can arrive out of order, siblings may run concurrently, and spans can be incomplete or retried. A minimum event contract ensures stable trace and span identities, with start events establishing parentage and end events defining outcomes. Timestamps alone are insufficient for correct parentage, necessitating explicit assembly of start and end events into spans.A span assembler manages state, buffering end events until their corresponding starts arrive and reporting diagnostics for issues like missing starts or duplicate events. It explicitly represents assembled spans and handles potential future issues with unbounded streams by suggesting size limits and expiration policies. Building a forest of execution trees allows for handling multiple roots and orphaned spans gracefully, preventing crashes and ensuring all information is presented. Validating parent links for cycles is crucial before rendering to avoid infinite recursion.Orphaned spans, those without a clear parent, should be displayed separately to avoid obscuring instrumentation gaps. Siblings are sorted by start time for stable display but do not imply causality, as parallel children can overlap significantly. A useful UI combines a tree view, showing parentage and retries, with a timeline view, illustrating overlap and latency. Summing span durations overstates trace time due to included child durations and overlapping parallel work.Instead, trace wall time, span duration, self time, and critical path are more accurate metrics. Retries and fallbacks should be modeled as children of the operation, allowing the parent to succeed even if children fail. Partial traces must be preserved, rendering incomplete spans distinctly with a reason for their incompleteness, avoiding invented durations or statuses. Comparing trees involves invariant properties like span kinds, parent-child relationships, and terminal statuses, rather than exact snapshots. The event store should remain append-friendly, with events indexed by trace ID and sensitive data excluded by default. Validation ensures the integrity of the trace, separating validation errors from actual agent errors. The core shift is from treating event arrival order as execution to assembling lifecycle events into trustworthy structural trees for better inspection.