Update design: Serialize and allow referencing split indices for reproducibility

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We are updating the training split design to improve reproducibility and support referencing existing splits for new runs.

## Previous Approach
Splits for train, validation, and test sets were determined on-the-fly based on the provided percentages (or counts), and a random seed was used to achieve reproducibility. However, this could create challenges if new runs needed to reuse exactly the same splits.

## Updated Requirements
- Whenever train/validate/test splits are computed, serialize the sample indices used for each split to the results directory for that run.
- Serialization format should be stable and easily reloadable (e.g., JSON, CSV, or similar), and must record enough information to reconstruct the exact splits.
- On a new training run, the user can reference (point to) a results directory from a prior run in order to reuse those split indices, ensuring true reproducibility between runs.
- If using a referenced index file, the system must verify compatibility (e.g., same dataset, or raise errors if there's a mismatch) and use only the selected indices from those files when creating the splits for the new run.

## Additional Details
- The split indices must be created per data directory/group as needed, and must allow for the complementary/reproducible split logic described previously (i.e., summed split fractions not exceeding 1.0 for a given directory).
- When referencing indices from a previous run, ensure that the splits (train, validate, test) remain complementary and non-overlapping.
- Continue to support both the single-directory and multi-directory split logic from the original proposal.

## Examples / Usage
- After a training run, the results directory might contain:
- `train_indices.json`
- `validate_indices.json`
- `test_indices.json`
- New runs can point to these files to use the exact same data partitions.

All other combination, validation, and "left join" logic from the original design still applies, but now with reproducible split indices as an optional override for future reproducibility.

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*This update reflects feedback from offline discussion requesting more deterministic and externally referenceable split logic for data handling.*

The issue names no files, tests, or entry points; begin by locating the existing single-directory and multi-directory split computation and results-directory handling. Define the serialization and reference-input interfaces, then verify dataset compatibility, complementary non-overlapping splits, and reproducibility for both supported layouts.

Written by the indexing model from the issue text.