What question did this study set out to answer?

To explore the structural conditions required for non-trivial persistence under real transformations and identify the role of selectivity.

March 4, 2026Open Access

The Architecture of Persistence – La Profilée And The Law of Asymmetry as Structural Core

Key Points

To explore the structural conditions required for non-trivial persistence under real transformations and identify the role of selectivity.
Analyzed structural architecture in relation to transformations and identity.
Examined the implications of complete transitivity on persistence.
Developed arguments based on theoretical assertions regarding transformations and state spaces.
Complete transitivity is shown to be incompatible with persistence.
Selectivity in transformation is necessary for structural asymmetry.
Orbit structures represent a preorder of reachability, highlighting constraints on transformation sequences.

Abstract

This paper consolidates the minimal structural architecture of non-trivial persistence under real transformation. Assuming (i) a non-empty state space, (ii) admissible transformations containing at least one real transformation, and (iii) the meaningful assertion of non-trivial invariant identity, it is shown that complete transitivity of the transformation structure is incompatible with persistence. From this incompatibility follows a necessary structural asymmetry: transformation must act selectively. This selectivity induces orbit structure, a preorder of reachability (structural time), and a constraint on admissible transformation sequences. The argument is strictly conditional and does not claim a global ontology. It establishes only the structural conditions under which non-trivial identity under real transformation can coherently persist.

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