What question did this study set out to answer?

To establish a transport rule that relates equivalence classes across variations for persistence maintenance.

February 6, 2026Open Access

Admissible Spectral Comparison Across Configurations — Analytic continuation as an admissibility rule

Key Points

To establish a transport rule that relates equivalence classes across variations for persistence maintenance.
Analyzed minimal consistency requirements for transport persistence under variation.
Explored local equivalence of descriptions for single comparisons.
Assessed the effects of path-dependency on re-combined evaluations.
Identified that local equivalence fails under recomposition due to path-dependency.
Demonstrated that consistency necessitates a transport rule for maintaining persistence.
Transportation serves as a structural necessity independent of traditional principles like time or symmetry.

Abstract

Minimal Consistency Requirements for Transport Persistence under composed variation requires that comparisons remain representative-independent when local evaluations are recombined. Local equivalence of descriptions suffices for single comparisons but fails under recomposition once loss is path-dependent. Consistency then forces the existence of a transport rule relating equivalence classes across variation. Transport is derived here as a structural necessity of persistence bookkeeping, introduced prior to and independent of time, dynamics, geometry, or symmetry principles.

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