Validation
Between 2023 and 2026 the Network-Weighted Action prediction has been operationalised and tested in four independent domains — physiology, physics, neural architecture, and biology — each with its own data, pipeline and observable, and the modularity-excess signature appears in each. In September 2026 the programme added its first controlled physical test, in a nonreciprocal colloidal model. There the mechanism the framework's directed-graph extension assigned to the antisymmetric sector failed on every count, the modularity-excess signature failed with inverted sign, and the structural control held. Both outcomes are reported below.
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/JP290762Physics
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:2603.16951Neural 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:2604.24805Biology
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, arXiv:2605.05254Soft matter — controlled test
A single knob scales the antisymmetric sector of a nonreciprocal colloidal coupling with everything else fixed. Solenoidality, circulation and the modularity-excess signature are refuted; structural control by the antisymmetric ratio is confirmed, non-monotonically. The decomposition survives as an instrument, the mechanism does not.
Frasch 2026e, arXiv submitted 2026-09-09How the tests fit together
Each subpage follows the same four-part structure:
- The claim — what NWAP predicts in this domain.
- Method — how the prediction was operationalised.
- The result — what was actually observed, with effect sizes.
- What this domain adds to the programme — the unique contribution of the test.
Read in order, the first four pages tell a single story: NWAP is consistent with the modularity-excess (and energy-cost) signature in every observational or computational domain where it has been tested. The fifth page is different in kind, and its result is different: it is an intervention with a single control parameter, and the specific mechanism the framework's directed-graph extension assigned to the antisymmetric sector — structure preservation, circulation, a modularity signature — is refuted, while the weaker structural prediction holds. The programme treats that as its most informative result so far, because it is the first that could have failed and did. 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.