Neural text representations often lack structural guarantees for syntactic variations, relying instead on statistical interpolation to recognize paraphrases. We introduce the Pāṇinian Intermediate Representation (PIR), a deterministic compiler that maps English sentences to role-tagged canonical sequences using Universal Dependency parses. Unlike heuristic methods such as stopword removal, the PIR compiler is deterministic: given a correct dependency parse, syntactically equivalent paraphrases compile to identical strings. On a 200-pair diagnostic suite of templated syntactic alternations spanning active/passive voice, dative shift, and topicalization, the compiler produces identical strings for 196 pairs; all four failures are structurally typed and traced to known parser limitations. Stopword removal produces identical strings for 0 of 200 pairs. To bridge the performance gap in downstream tasks, we propose Hybrid PIR, which selectively restores lexical content through a deduplication mechanism. Hybrid PIR achieves similarity performance comparable to stopword removal (0.8130 vs. 0.8154 average ρ; bootstrap 95% CI on the difference includes zero) at 43.8% token compression, while providing structural guarantees that surface-level methods cannot. On retrieval benchmarks, Hybrid PIR reaches 80% of the English baseline nDCG@10 on BEIR SciFact and 86% of MRR@10 on MS MARCO QA at 39.0% compression. A three-variant representation ablation validates our deduplication design: removing this mechanism degrades retrieval performance by 3.5 points and turns the compression benefit negative (-3.0%). In a QQP-validation duplicate-detection use case (40,430 pairs), Hybrid PIR reaches precision 0.861 with no tuning, matching a tuned embedding threshold and validating the intended deployment as an offline canonicalization tool for deduplication and index construction.