Foundations of Structural Distinguishability (FSD)

Foundations of Structural Distinguishability (FSD) develops a minimal and fully structural account of distinguishability in terms of automorphism groups and orbit decompositions. Given a nonempty set equipped with additional structure, structural distinguishability is defined via separation into distinct orbits under the natural action of its automorphism group. The central result establishes that distinguishability exists if and only if the automorphism group acts non-transitively. Equivalently, nontrivial invariant descriptions exist precisely in the non-transitive case. The framework is purely structural and independent of dynamics, probability, topology, or physical interpretation. Extended results classify all invariant descriptions via lattice structure, establish the universal property of the orbit quotient, quantify distinguishability in finite cases, and analyze symmetry reduction under structural refinement. The work provides a minimal and self-contained foundation for structural differentiation grounded entirely in symmetry and group action Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/