Graph-based NLP and symbolic reasoning models often rely on positional encodings to distinguish tokens, entities, or reasoning states, but the identifiability provided by these encodings remains poorly understood. We analyze a hybrid graph encoding that combines anchor distances with quantized low-frequency spectral energy. Treating the encoding as a deterministic observation map gives an exact image-preimage identity for localization ambiguity and a one-sided information-theoretic converse: if the joint anchor, spectral, and quantization budget is too small, distinct nodes must share the same code, which also lower-bounds task-label ambiguity observable from that code. Experiments on random 3-regular graphs, CLUTRR relation graphs, and Universal Dependencies trees support the predicted scaling. Under matched normalized budgets, Hybrid is best or tied at 74 of 87 attained thresholds, while PE-only UD probes show improved recovery of syntactic-tree geometry. The results therefore position positional encoding as a pre-model, encoding-level necessary-condition diagnostic rather than an achievability guarantee or an end-to-end model claim.