Deeper unity of physical transformations and cognitive operators

Determine whether the structural correspondence between the three classes of physical transformations—information-preserving, dissipative, and measurement-like transformations—and DODR’s induction, deduction, and abduction operators reflects a deeper physical-cognitive unity beyond an analogy based on shared information-flow properties.

Background

Proposition 13.1 identifies a one-to-one structural correspondence between physical transformations and DODR cognitive operators according to their information-flow direction. Conservation or reversible processes are associated with full-rank preservation, dissipative processes with rank-deficient information loss, and measurement-like processes with projection or pseudo-inverse behavior.

The paper stresses that this correspondence is a structural analogy and research hypothesis rather than a theorem derived from physical laws. The experiments provide small-scale support for representing physical transformations with trainable matrix operators, but the broader claim of a deeper unity remains unresolved and is not required for the paper’s core algebraic results.