[Hydrodynamical]

The numerical experiments duplicate dynamics, objectives and training, while shared figure directories can silently replace outputs. This refactor provides an installable graphon_control package with one numerical core and separate experiment and plotting modules. Existing root commands and numerical imports remain available.

The implementation follows the October 20 manuscript's Appendix 5: W = wbar/N, receiver-to-sender orientation, the beta kernel penalty, Euler/Maruyama noise scaling, and measured receiver variation. The generic trainer's former beta/2 convention is deliberately changed to beta; retaining the former regularization strength requires halving that configuration value. Paper experiment defaults and raw checkpoint names are preserved. Optional bounded scores expose a density-cap mechanism without changing default experiments or claiming an enforced BV budget.

Runs now reserve new directories, save configuration/environment/code provenance and separate evaluation seeds, and refuse overwrite collisions. Saved arrays support --replot without retraining. Figure collection uses an explicit manifest; noisy comparisons and archived sweeps validate their inputs. The README stays brief and links to numerical and development guides.

Validation:

• 182 CPU tests passed; 2 accelerator tests skipped because CUDA/MPS are unavailable locally.
• Both 20-update smoke runs generated metrics, checkpoints, PDFs and GIFs; representative figures were visually checked.
• Archive/replot, legacy checkpoint reload, invalid settings, collision refusal, gradients and analytic numerical invariants are covered by tests.
• Short pre-refactor E1/E2 replays preserve final model parameters and trajectories exactly; one E2 loss differs by 2.98e-8 from reduction order.
• Editable install and wheel build/import verified outside the source checkout.
• GitHub Actions runs the tests and numerical smoke checks on CPU.

The manuscript and reference PDFs are not included or modified. This is a draft for review; main is unchanged.