Mathematical Form of Physical Law as Invariant-Form Compression: Invariant, Equivariant, and Covariant Law Forms in Finite Distinction Systems

Yining Wu · 2026-05-19

Interprets the mathematical form of physical law as invariant-form compression in finite distinction systems. Physical laws are not raw microstate enumerations but compressed invariant, equivariant, or covariant relations that survive finite capacity, perturbation, coordinate change, coarse-graining, and boundary-maintenance constraints. Reframes Wigner's puzzle: mathematics is effective because the portable part of physics is the part compressible into invariant-form structures. Includes RG fixed-point analogy, search-cost asymmetry, constants as operational scales, and Physical AI implications (generalization gap, OOD stability, latent constraint preservation).

@misc{wu2026fdsx5,
  author = {Yining Wu},
  title = {Mathematical Form of Physical Law as Invariant-Form Compression: Invariant, Equivariant, and Covariant Law Forms in Finite Distinction Systems},
  year = {2026},
  doi = {10.5281/zenodo.20278236},
}