Exploring how scale-free physical laws may relate to agentic generality through the Network-Weighted Action Principle (NWAP) and Domain-Complete Intelligence (DCI).
Biological architectures, physical systems, and machine intelligence models may be described by a common variational quantity.
In classical variational physics, Action describes cumulative system pathway efficiency over a stretch of time, rather than a brief static snapshot. By applying this to network-weighted systems, SNW suggests that biological growth, neural learning, and cognitive agents tend to self-organize along a trajectory of "least resistance" — seeking to extremise (minimize) their structural cost of existence.
The thermodynamics of execution (metabolic ATP in physiology, electrical wattage in GPUs). Constrained directly to ensure long-term survivability.
The network's capacity to model environment structures and reduce uncertainty. Because it carries a negative sign (−I), minimizing overall action forces this to be maximised.
A tuning scale representation of evolutionary or environmental pressure. Defines how heavily connectivity economy is prioritized over raw computation capacity.
Physical constraints of maintaining links (axon lengths in cortical layouts, physical piping in metabolism). Minimized to protect scaling limits.
Temporal path integral progression. The integration (∫...dt) tracks the cumulative historical state transitions of the network.
To minimize overall Action (SNW), the network is structurally forced to compress energy (E) and connection lengths (C) while maximizing its information processing capacity (I). Modularity is the mathematical equilibrium of this struggle.
The mathematical signature of NWAP is modularity excess (Q over null models). Watch the network partition itself as we increase optimization pressure to minimize physical wire costs.
When connection cost is ignored, network architecture is chaotic. When connection costs are heavily penalized, nodes group into dense local clusters with thin inter-module pipelines—the architecture of robust, rapid local decision-making.
Living systems cannot survive in pure rigid order, nor can they handle pure thermal chaos. NWAP specifies a narrow, mathematically precise phase-transition zone.
By avoiding the extremes of pure energy minimisation (crystallisation) and pure information maximisation (entropic noise), our action functional selects for the exact golden ratio that permits structural self-preservation and responsive behavioral evolution.
Rigorously tested modularity-excess and energy-efficiency signatures in independent domains. Click a domain title to explore the scientific paper.
Frasch 2026a, J Physiol
Establishes vertically organising principles as keys to unify multi-scale causation. Shows modularity acts as the core biological substrate.
Frasch 2026b, arXiv:2603.16951
Recovers classical Kepler and Hooke laws from messy, noisy sensor data at an order-of-magnitude reduction in active training energy.
Frasch 2026c, arXiv:2604.24805
Proves energy-regularised objective constraints improve structural convergence and efficiency across 2,203 deep-learning experiments.
Frasch 2026d, arXiv:2605.05254
Demonstrates marine metabolic networks possess a robust modularity excess (ΔQ ≈ 0.40) over null models; communities map directly to known functions.
Grounded in NWAP, we propose DCI as a candidate bridge connecting fluid reasoning (ARC-AGI Level 2) with general agentic AI.
Unlike current monolithic artificial architectures optimized purely for prediction error, DCI operates via an Object-Meta Reflexivity Loop. This aligns the object execution domain directly with the high-level variational action functional.
"Meaning"—the successful reduction of uncertainty through physical action—takes a similar shape across structural scales.
Integrate multi-author LaTeX positioning notes and explore the mathematical and python benchmarks within the open-source DCI workspace.
The project is ready to compile with standard TeX Live setups, using specialized mathematical notation macros defined in the preamble to keep research outputs consistent across authors.
Archived on Zenodo: doi.org/10.5281/zenodo.21364866