Scientific foundation models are built to reuse representations across datasets and acquisition protocols, yet their representations degrade under distribution shift. We trace one source of this failure to selective state-space models (SSMs). Their memory depends on the step Delta and the state matrix A only through their product, so data do not identify the physical timescale of memory, and under a shift the resulting memory no longer matches the signal's timescales. We call this failure memory-timescale misalignment. To resolve it, the split between Delta and A must be tied to physical units. We therefore propose Physically-Anchored Latent-timescale Mamba (PALM), which disentangles A from Delta by anchoring both to acquisition units: Delta through spectrum-estimated knee frequencies and A through a physical memory range. We evaluate PALM against parameter-matched baselines in two domains, under temporal-context truncation, low-resource transfer, and brain-state shift on fMRI and under held-out-station forecasting on Weather-5K. Under fMRI context truncation with run-level spectral calibration, PALM keeps its latent timescales in physical units and retains 11% higher representation similarity than Mamba2. At geographically isolated weather stations never seen during training, PALM achieves the lowest error on every variable and horizon, 15.2% below the best baseline on average, and outperforms zero-shot forecasting foundation models. Across both domains, the gains come from where the backbone places memory in physical time rather than from model size. We therefore argue that physically anchored latent timescales are a design requirement for scientific foundation models that must transfer across acquisition conditions.
What makes a pretraining corpus transferable? We describe a corpus by three properties: its structure, its dimensionality, and the distribution shape of each unit's values. We propose the Transfer-Invariance Principle: the same property can be irrelevant to transfer under one input transform and decisive under another, so the model's input transform, not the data modality, decides which properties can matter. To test it we build TransferForge, a generator that places a synthetic population at any prescribed structure, dimensionality, and distribution shape. KernelSynth, the synthetic prior of Chronos, cannot, because it draws independent series. When the model standardizes each input window (PatchTST on UCR), the distribution shape is inert and the structural setting governs. Synthetic pretraining then matches a real corpus of the same size and exceeds it once scaled. When the model encodes calcium fluorescence signals without normalization (POYO Plus), the shape becomes a governing constraint, and a shape-matched synthetic corpus replaces real pretraining with zero real neural activity. Flipping only the input normalization, with the model and data fixed, changes the effect of a shape manipulation by a factor of 5.3, so the pipeline, not the modality, sets the switch. The principle yields a recipe that chooses what to synthesize before any training. Pretraining data then becomes something to manufacture for the model, most valuably where real data is scarce, expensive, or private.