Konno Continuous Inner Product Algebra (KCIPA) A Mathematical Foundation for Closed Surface Theory

Description Konno Continuous Inner Product Algebra (KCIPA) is proposed as the mathematical foundation of Closed Surface Theory. KCIPA extends the conventional inner product into a recursive continuous algebra acting on ordered vector sequences, producing alternating vector and scalar states. Within this framework, physical space is represented as a Complex Closed-Surface Space, composed of tangent and normal structures associated with finite closed surfaces. The theory distinguishes mathematical zero from physical zero, interprets the imaginary component as an orthogonal normal-field operator, and provides a unified geometric description of matter, fields, and motion. KCIPA offers an alternative algebraic framework for describing relativistic geometry and the geometric structure of physical reality.