Legometric mechanics of laws

This work introduces a foundational theoretical framework in which physical laws are no longer treated as fixed axioms, but as dynamical entities that evolve, interact, and stabilize within a structured space of possibilities. Rather than describing the evolution of states under immutable rules, the framework shifts the level of description to the laws themselves.At the core of the proposal is the idea that each effective physical theory can be represented as a point in a continuous “space of laws.” In this space, laws possess inertia, can undergo selection, and may transition between regimes, much like physical systems do in ordinary spacetime. The persistence and viability of a law are determined by its ability to sustain structured, coherent dynamics over long timescales, rather than by external assumptions or fine-tuning.A geometric structure is introduced on this space of laws, allowing distances to be interpreted as meaningful differences in physical behavior. Laws that produce similar dynamics are geometrically close, while radically different physical regimes are separated by critical boundaries. The evolution of laws follows a variational principle that balances resistance to change with a form of ontological selection pressure, favoring laws that maintain stability, coherence, and informational persistence.Within this framework, familiar processes such as inertial motion, dissipation, renormalization flows, evolutionary selection, and learning dynamics appear as special cases of a more general mechanics acting at the level of laws. Transitions between distinct kinds of physics are interpreted as phase transitions in the space of laws, where degrees of freedom, causal structure, or stability properties can abruptly change.The central conclusion is that physics itself emerges as a stable phase of a deeper dynamical process. Laws are not fundamental givens, but the outcome of an underlying geometric and ontological selection. This perspective provides a unified language for understanding why particular laws exist, how new effective theories may arise, and how radically different physical regimes can coexist within a single coherent framework.