Compatibility of Accessibility and Purification: Existence and No-Go Results

Arc V — Gravity & Quantum TheoryPaper 9 Title Compatibility of Accessibility and Purification:Existence and No-Go Results Zenodo DOI 10.5281/zenodo.18234636 Description This paper examines the internal consistency of the finite-accessibility framework when augmented by the purification principle, addressing a critical foundational question: under what conditions can accessibility limitations and purification coexist without contradiction? Building on the axiomatic reconstruction of quantum theory in Paper V.7, the analysis treats purification and accessibility as independent structural constraints and studies their joint realizability. The paper proves several existence results demonstrating that nontrivial operational theories satisfying both principles do exist, while also establishing sharp no-go theorems that rule out broad classes of seemingly plausible models. In particular, the work shows that purification cannot be imposed arbitrarily on accessibility-limited theories. Certain accessibility profiles are incompatible with global purification, leading to unavoidable irreversibility or breakdown of compositional structure. Conversely, when compatibility conditions are satisfied, purification enforces strong constraints on allowable dynamics, correlations, and system composition. These results clarify the logical status of purification within the program: it is neither optional nor universally admissible, but a structurally selective principle that dramatically narrows the space of consistent theories. The paper therefore functions as a consistency checkpoint for the Gravity & Quantum Theory arc, delineating exactly where the program can and cannot be extended. Keywords finite accessibility; purification; no-go theorems; operational quantum theory; axiomatic consistency; irreversibility Notes Arc V — Gravity & Quantum Theory (consistency and constraints) Sharp existence and no-go results for accessibility–purification coexistence Clarifies when quantum reconstruction is structurally possible Constrains admissible accessibility profiles and dynamics Logical bridge between axiomatic reconstruction and non-geometric quantum theory