Kasei-Theory V: The First Phase of Structural Impossibility［可性論 V］

This work fixes a structural account of impossibility that departs from standard modal, epistemic, and metaphysical treatments. Rather than construing impossibility as negation, external limitation, contradiction, or failure of access, it is defined here as a non-return configuration within ongoing operational systems: a condition in which the formal path back to a prior differentiating state becomes closed while processing continues. The analysis is restricted to what is termed the first phase of structural impossibility. At this level, impossibility remains structurally describable, yet irreducible to causal explanation, epistemic deficit, exceptional case, or transcendence. The study fixes three simultaneous conditions under which such configurations stabilize: the presupposition of division, the internal circulation of updates, and the formal closure of return-path structures. When these conditions coincide, impossibility is fixed not as an event, contradiction, or modal boundary, but as a configuration internal to the system. By distinguishing structural impossibility from the unknown, from exception, and from transcendence, this work reframes modality in configurational rather than propositional or possible-world terms. The present volume confines itself to what remains structurally articulable within this first phase. Structural impossibility is not a boundary of the possible; it is the internal configuration in which the possible no longer returns to itself.