The Structure of Arising : Passive Aposteriority and the Posture of Allowing to Hold

This paper, the second in the Extended Imaginary Number Theory series, takes as its subject arising (起こり)—the event in which fine perturbations of imaginary-dimensional origin are captured within cognitive space. Whereas the first paper, "Extended Imaginary Number Theory: Existence as the Dual Structure Z = D + iD" (Muranushi, 2026), described the dual structure of existence itself, the present paper asks under what structure arising comes to hold. This is the core of the inquiry.

Within this framework, the imaginary-dimensional side is described as continuously exerting influence on the real-dimensional side. Within this continuous influence, what stands at the point of origin of upsurge on the real-dimensional side is arising. The accurate capture of arising substantially regulates the precision of the subsequent concretization (具現化). The present paper extracts the structure under which arising comes to hold, thereby providing a structural description of its relation to the precision of concretization.

Intentional grasp—the work by which the subject actively cognizes an object—and arising are not mutually exclusive existential modes; rather, they form a gradation of qualitative texture in relation to the imaginary dimension. The present paper takes this continuum as its premise, phenomenologically describes the situation in which the arising-leaning pole becomes foregrounded, and further organizes its precision along two axes: perspectival scope (視座) and purity (純度).

This paper proceeds throughout as a description from the real-dimensional side. It does not directly describe what occurs in the imaginary dimension but rather aims to extract the structure under which arising comes to hold on the real-dimensional side. The treatment of precision remains a preliminary structural description; its existential and practical development is deferred to a separate work.