Missed Symbols Become False Connections: Quantifying Detection-to-Graph Error Propagation in P&ID Digitization

Pipeline P&ID digitization detects symbols, traces lines, then builds a connectivity graph. We use an interpretable pipeline as a measurement instrument to quantify how symbol-detection errors propagate into connectivity on real drawings (PID2Graph OPEN100). Missing symbols damage connectivity precision far more than recall (0.86 to 0.57 at a 20% miss while recall holds near 0.81, over 5 seeds), because an undetected symbol's ink merges separate wires into a false connection; we confirm this with a real leave-drawings-out detector. A supporting study on procedurally generated (synthetic) sheets shows fine-grained valve subtypes are never confused and all error is recall on small valves, with a sharp data-efficiency threshold near 20 to 50 sheets, and that an open-vocabulary detector fails zero-shot. Detection recall, not classification, is the bottleneck, and its failure mode is false edges. Connectivity results are on real drawings. the valve sheets are synthetic and not presented as real.