Externally validated delay-embedded dynamic mode decomposition and annual-frequency SPOD reveal robust state-level dengue timing organization in Brazil.

We evaluated delay-embedded dynamic mode decomposition (Hankel DMD) as a signal-diagnostic framework for annual dengue timing across Brazil. Weekly InfoDengue estimates were aggregated into 27 state-level incidence trajectories for 2015-2024. The primary model used state-standardized log1p incidence, a 26-week delay embedding, and rank 12. Annual structure was extracted with Hankel DMD, corroborated by annual-frequency spectral proper orthogonal decomposition (SPOD), and related to official OpenDataSUS epidemic onset in a state-year model adjusted for preseason climate, serotype information, and year. Robustness was assessed across 143 transformation-delay-rank specifications and by leave-one-year-out, rolling four-year, and annual-harmonic analyses. The primary Hankel mode had frequency 0.9865 cycles/year. SPOD selected 1.000 cycle/year, assigned 81.9% of leading-mode spectral energy to the annual bin, and reproduced the DMD phase pattern (circular correlation 0.996; median absolute difference 0.72 weeks). The adjusted phase coefficient was -2.23 weeks per standard deviation (95% CI -2.78 to -1.80), indicating earlier official onset toward the leading end of the externally oriented phase. Of 143 sensitivity specifications, 135 yielded an unambiguous annual mode; their median phase correlation with the primary result was 0.969 and median absolute difference was 1.09 weeks. Leave-one-year-out correlations ranged from 0.984 to 0.999 and were not reduced when major epidemic years were omitted (permutation p=0.7384). These analyses identify a reproducible state-level annual timing structure. The phase coordinate represents relative timing within the annual mode; its epidemiological orientation is established by the onset data and should not be interpreted as a causal transmission parameter.