Adding a 12-month PDO lag did not remove the 2020-2025 mean mismatch in conditional models

We tested whether a 12-month PDO lag repairs a monthly memory and ENSO model for six-year mean PDO. Fits used matched NOAA ERSSTv5 rows from 1951-2019. The observed 2020-2025 mean was -1.995. The added-lag mean path was -0.318, with a central 95% range of -1.028 to 0.434 for simulated means. None of 3,999 draws was as low as the observation. Residual block, training-start and coefficient-variation checks also missed it. Across 35 overlapping earlier windows, added-lag point mean squared error fell by 9.01% and range misses fell from 10 to 8. These descriptive changes do not establish a reliable gain. This result shows a limit of the tested annual-memory extension. It does not rule out physical ocean memory or establish a new climate regime. Known interval selection, revised indices, overlapping windows, conditional ENSO and incomplete slow dynamics limit inference. Code, exact external input paths and hashes, retrieval instructions, all simulated means, a figure and an independent arithmetic audit are preserved. Raw source tables stay outside the publication.

PDO · ENSO · annual memory · six-year mean · conditional simulation · model limits