Why All Large-Scale Search Systems Converge: The Russian Dolls Limit

▸ Technical Abstract: We present the Russian Dolls Limit, a theoretical framework explaining why large-scale search systems—from UNESCO's CDS/ISIS (1985) to Meta's FAISS (2017) to Microsoft's SPANN (2021)—converge on architecturally similar solutions despite being developed independently across four decades. We prove this convergence is mathematically optimal under stated constraints: information theory bounds vertical depth, access patterns bound horizontal breadth, and overhead economics establish meta-indexing thresholds. The Architectural Convergence Theorem predicts optimal index structure from three parameters alone: record count, access pattern count, and available memory. ▸ Accessible Explanation: Why do all large search engines end up looking the same inside? Like Russian nesting dolls, they all discover the same layered structure—not because they copy each other, but because mathematics forces their hand. The $4.7 billion information retrieval industry is not innovating architectures—it is rediscovering the same mathematical optimum. ▸ Scientific Significance: This work establishes fundamental limits on information retrieval architecture, analogous to Shannon's channel capacity for communication. Validation against twelve production systems spanning 40 years achieves vertical precision of 91.7% and horizontal recall of 83.3%. The framework unifies database theory, vector search, and distributed systems under a single optimality principle.