Invariant Redundancy and Digital Twins

Invariant Redundancy and Digital Twins Why “Minimal Differentiation” Is Not a Fundamental Invariant — and How Digital Twins Provide a Decisive Test Author: Frédéric Tabary Date: February 2026 DOI: https://doi.org/10.5281/zenodo.18470718 --- Description This white paper addresses a foundational methodological problem in theoretical modeling: the accumulation of invariants that appear intuitively necessary but do not, in fact, restrict the space of admissible worlds. The central question examined is the following: when does a proposed invariant introduce a genuine constraint on admissible worlds, and when is it merely a redundant consequence of more fundamental principles already in place. The paper focuses on the notion of minimal differentiation, understood as the claim that a real system must contain at least one non-zero distinction in order to exist. Although this idea is widespread across physics, information theory, and philosophy, its status as a fundamental invariant is rarely examined explicitly. A strict criterion of invariant independence is introduced: an invariant is fundamental if and only if its removal enlarges the set of admissible coherent worlds. If removing a proposed invariant excludes no additional admissible world, then the invariant is redundant and must be rejected as such. To make this criterion operational, the paper introduces the concept of a digital twin as a stress test for foundational principles. A digital twin is defined as a system-level replica characterized by identical constraints, state variables, and responses to perturbations. Identity of outputs alone is explicitly excluded as a sufficient criterion. Under this framework, minimal differentiation is tested by constructing digital twins with and without this principle. The result is unambiguous: the admissible state space, simulation integrity, and perturbation behavior remain unchanged. Minimal differentiation therefore adds zero discriminative power. The paper concludes that minimal differentiation is not false, but redundant. It does not qualify as a fundamental invariant because it introduces no additional constraint beyond coherence and non-contradictory temporal continuity. Beyond this specific case, the method proposed provides a general tool for cleaning foundational frameworks. By combining strict invariant criteria with digital twins as operational tests, the approach helps distinguish fundamental constraints from emergent regularities and prevents the accumulation of decorative principles. What does not restrict the possible is not an invariant.