Invariant Compression (IC): A Method for Structural Context Transfer Across Heterogeneous LLMs

This preprint introduces Invariant Compression (IC), a method for transferring structured context across large language models (LLMs) without shared memory. IC transforms interaction into invariant representations (Brick, Seed, Transferable Core) that preserve structural constraints while minimizing token overhead. These artifacts are probed across independent models using Reverse Brick analysis, enabling reconstruction, constraint extraction, and iterative refinement. Empirical observations show that models do not merely reconstruct content, but decompose invariant structures into applicability domains, degradation conditions, and missing boundary definitions. These gaps mark points where reconstruction shifts from invariant-based reasoning to prior-driven completion. The work introduces the concept of regime-conditioned invariants, where invariant stability depends on competing completion pressures rather than binary preservation. IC is positioned as a structural transfer mechanism, complementary to governance frameworks such as Domain Beacons, which define operational scope. Together, they address key failure modes in agentic systems: structural drift and unauthorized action. This work is conceptual and qualitative, based on cross-model testing without shared state. Cross-model agreement is treated as a signal, not as proof. This work was developed through iterative, structured interaction with multiple large language models as part of the methodological process. This version includes an author-provided Ukrainian translation of the preprint for broader accessibility. The Ukrainian version includes minor clarifications and refinements of the method.