Four-domain validation

Between 2023 and 2026 the Network-Weighted Action prediction has been operationalised and tested in four independent domains, each with its own data, its own pipeline, and its own quantitative observable. The predicted modularity-excess signature appears in every domain.

Physiology

Vertically organising principles unify multi-scale causation; modularity is the architectural substrate. Theoretical anchor of the four-domain programme.

Frasch 2026a, J Physiol, DOI:10.1113/JP290762

Physics

Triple-Action functional recovers Kepler & Hooke laws from noisy data at order-of-magnitude reduced training energy. First demonstration that NWAP is operationally useful as a training objective.

Frasch 2026b, arXiv:2603.16951

Neural architecture

Energy-regularised objective $\mathcal{L}_{\mathrm{CE}} + \lambda E(\theta,x)$ improves training across 2,203 experiments spanning vision, text, neuromorphic, and physiological datasets.

Frasch 2026c, arXiv:2604.24805

Biology

Marine metabolic networks show a robust modularity excess (ΔQ ≈ 0.40 over the bipartite-incidence null) across seven independent samples; recurrent communities map to known functional units.

Frasch 2026d, Tara Oceans, in submission

How the four tests fit together

Each subpage follows the same four-part structure:

Read in order, the four pages tell a single story: NWAP is consistent with the modularity-excess (and energy-cost) signature in every domain where it has been tested. The strongest engineering proof comes from the neural-architecture paper (2,203 controlled experiments where the energy-regularised objective measurably outperforms prediction-error-only baselines), followed by the physics paper (where the Triple-Action functional recovers Kepler's and Hooke's laws at order-of-magnitude reduced training energy). The biology paper is the natural-system population-scale signature in field-collected metagenomic data ($\Delta Q \approx 0.40$ over the gold-standard bipartite null) — strong evidence that the predicted architectural pattern shows up in real ecosystems, but, like all observational data, consistent with rather than discriminating among neighbouring variational principles. The physiology paper ties the four together as the theoretical anchor.