What question did this study set out to answer?

To establish when declared operational regimes are behaviorally equivalent, determine what state distinctions can be safely forgotten, and characterize the boundary of behavioral change under question refinement.

August 14, 2026Open Access

Regime Equivalence and Refinement: Transport, Normal Forms, and the Boundary of Declared Change

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To establish when declared operational regimes are behaviorally equivalent, determine what state distinctions can be safely forgotten, and characterize the boundary of behavioral change under question refinement.
Separated static verdict equivalence from contextual behavioral equivalence within a total many-sorted algebraic and coreflective framework.
Constructed relative normal forms via congruence interiors and established an antitone Galois connection between promised question families and safe congruences.
Evaluated decidability in the finite fragment using terminating partition refinement algorithms and constructed minimal countermodels to test invariant claims.
Demonstrated that two regimes share behavioral specification equivalence if and only if their relative normal forms are isomorphic or admit a common reduced safe quotient.
Proved contextual equivalence is computable via terminating partition refinement in finite presentations, while separation depth is presentation-relative rather than a behavioral invariant.
Showed that safe regime compression requires both behavioral sufficiency and structural admissibility, formalizing an order anti-isomorphism between promised queries and safely forgotten distinctions.

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Implication

Theoretical analysis characterizes behavioral equivalence and normal forms across declared regimes, showing how systems safely compress distinctions under refined problem specifications.

Cite This Study

Devin Bostick (2026) studied this question.

synapsesocial.com/papers/6a7ec754b70b84ec8b91391f https://doi.org/10.5281/zenodo.21897736

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Implication

Theoretical analysis characterizes behavioral equivalence and normal forms across declared regimes, showing how systems safely compress distinctions under refined problem specifications.

Regime Equivalence and Refinement: Transport, Normal Forms, and the Boundary of Declared Change

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Implication

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Regime Equivalence and Refinement: Transport, Normal Forms, and the Boundary of Declared Change

Key Points

Discussion

Implication

Cite This Study

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