Background. Rare diseases (RD; enfermedades poco frecuentes, EPoF, in Chilean policy terminology) collectively affect 3.5-5.9% of the population and are associated with long diagnostic trajectories. Chile lacks a reproducible national operational definition for identifying RD in administrative hospital data. Methods. We conducted a retrospective observational analysis of Chilean GRD-IR events (IR-29301 version) for 2019-2024 released through FONASA Datos Abiertos, covering hospital discharges and major ambulatory surgery reported by 72 public establishments for FONASA-covered persons. The canonical analytical cohort contained 5,779,482 DRG events in 4,027,921 linked patients. We constructed a Chilean Orphanet-ICD-10 homologation and audited it through an agentic human-in-the-loop pipeline, yielding a conservative RD operational catalogue (434 final ICD-10 codes in the KEEP + MAP_TO_SPECIFIC_ORPHA scenario). RD-coded DRG events were labeled as observed inpatient odysseys when at least one prior DRG event existed for the same patient. We quantified prior events, DRG-observed inpatient trajectory time, nonspecific prior diagnoses, DRG weight, and bridge-code associations. Bridge-code enrichment was estimated using patient-level Fisher exact tests with Benjamini-Hochberg false-discovery correction; event-level estimates were retained as sensitivity analyses. Results. The audited conservative catalogue identified 55,284 primary-diagnosis RD-coded DRG events in 45,784 patients and 374,866 RD-coded events in any diagnostic field. We characterized 63,685 observed inpatient odyssey cases in 25,648 unique patients across 371 audited RD ICD-10 codes. Median DRG-observed inpatient trajectory time to RD-coded diagnosis was 241 days, and mean prior events per odyssey was 8.1. Bridge-code analysis identified 616 associations with support >= 10 patients and 390 with q < 0.05; 350 significant associations were no-same-code administrative trajectory signals. These signals varied in interpretation, including clinically plausible precursors, diagnostic refinement, and care-process bridges. The Odyssey Index reordered conditions relative to raw prior-event counts, separating high-volume entities from stronger trajectory signatures. Conclusions. To our knowledge, we provide the first nationwide audited and reproducible characterization of inpatient RD diagnostic odysseys in Latin America using administrative hospital data. The framework supports trajectory surveillance, registry design, quality-control analyses, and prioritization of candidate signals for prospective clinical validation under Chile's Law 21,743. Bridge-code associations should be interpreted as statistically enriched administrative signals, not as validated causal or clinical pathways.