RTLI Two-Boundary Inference and Constraint Topology: A Diagnostic Tool for Structured Physical Systems

This work introduces Two-Boundary Inference (TBI) as a unifying diagnostic framework for analyzing physical systems whose observed states are shaped by selection between initial and final boundary conditions. Instead of reconstructing forward trajectories, TBI extracts information from the topology of the constraint surface that couples boundaries, revealing structure that standard modeling treats as scatter or degeneracy. Across exoplanet orbital architectures, galaxy halo-mass inference, and the cosmic microwave background, we identify a common pattern: strong variance compression without collapse, relational encoding of information, and asymmetric null spaces that indicate the direction of selection. Quantitative diagnostics—including Compression-Without-Collapse (CWC), null-space asymmetry, and coherence thresholds—transform residuals and model disagreement into interpretable signals of constraint softness, stability margins, and proximity to phase boundaries. In exoplanet systems, a statistically testable exterior bias of near-resonant period ratios reflects post-capture divergent evolution rather than fine-tuning. In galaxy dynamics, disagreement among NFW, Einasto, and DC14 halo models is shown to encode baryon–halo coupling regimes and constraint sensitivity, not merely fitting uncertainty. In the CMB, extreme but structured variance suppression illustrates maximal constraint satisfaction with preserved relational memory. TBI is presented as a methodological tool, not a new physical theory. Its value lies in reframing degeneracy and scatter as information about constraint topology, enabling cross-domain comparison, falsifiable predictions, and principled analysis of complex systems—including potential applications to long-term stability and memory in AI systems.