Better Reconstruction, Worse Transfer: Probing Representation Geometry in Cross-Reynolds Generalisation

Neural PDE surrogates degrade sharply when the governing physical parameter shifts. How the degradation distributes across the components of the pipeline has not been measured, so improvement effort is allocated by intuition. We address this on a zero-shot cross-Reynolds task in forced 2D Navier-Stokes, using a retrieval predictor as a diagnostic instrument, not because it is competitive, but because it is decomposable: its encoder, database, selection rule and autoregressive loop permit nested diagnostic substitutions. In seed 42, these give a 16.2% encode-decode reference, a 5.7-point reference-to-refreshed-oracle gap and a 14.0-point state-refresh gap; neither contrast distinguishes error injection from dynamical amplification. Holding representation and output path fixed, retrieved increments transfer better than the two tested learned-transition implementations, though by smaller margins than the equal-width PCA-ConvAE contrast; this does not make the increment mechanism irrelevant. Representation interventions then decouple reconstruction from transfer. A random projection of equal width yields 99.42% error, level with its own 99.27% reconstruction reference error, so reducing dimension is not by itself sufficient. A linear encoder of equal width reconstructs the target regime better (10.99% against 16.20%) yet transfers worse (41.93% against 38.30%, paired CI [3.26, 4.00]), a reversal that holds for all three autoencoder training seeds, so reconstruction fidelity does not determine transfer ordering. Widening that linear family from 64 to 512 improves the reconstruction reference error 3.16-fold while leaving transfer error unimproved, so capacity does not determine it either. Tested nonorthogonal invertible linear reparameterisations preserve reconstruction to numerical tolerance but increase mean deployment error by up to 4.75 points, showing that transfer depends on the retrieval coordinate frame even when reconstruction is held fixed. On the physical-output route, a fourth encoder trained with no reconstruction objective transfers 11.92 points worse (paired CI [11.30, 12.54]) while passing its encoder collapse diagnostics, so a non-reconstruction objective is not by itself sufficient either. Eight further candidates have mixed outcomes, including beneficial database expansion, a nonsignificant curvature-proxy association and an untested phase-alignment control. The established result is a decoupling between reconstruction fidelity and deployment ordering; organisation is a suggested explanation still to be identified. All claims are scoped to this benchmark and a tenfold parameter shift. We do not present a method: no tested diagnostic variant beats its canonical baseline.