From Nothingness to Matter: Relational Capacity, Cyclic Confinement, and Timelike Existence in Entanglement–Algebraic Spacetime

This paper is archived as a speculative research work.Why does a universe of relationships require matter? Entanglement–Algebraic Spacetime (EAS) approaches the origin of physical existence through the requirements of relationship: distinguishable participants, contrast, continuing identity, admissible connection, ordered variation, and an enduring physical framework in which variation can register as change. Scalar Fields (SFs) supply relational capacity; conjugate scalar content activates distinction; reciprocal phase-qualified associations and second-order ordering (SOO) organize its succession. Scalar-binary-bit (SBB) carriage preserves a relationship while its participating roles change. These are algebraic conditions for relationship and succession. The physical realization of change requires an additional condition: time-like participation. Free SBB organization admits a null, light-like interface; a null worldline carries no proper-time interval of its own. Qualified collisions permit conserved SBB relationships to enter a continuing cyclic shell. At the certified conditional physical interface, that bounded shell admits a stable positive-mass particle representation, with time-like duration and inertial response. Matter thereby becomes both a consequence of relational organization and the enduring physical participant through which succession, difference, and interaction can be registered as change. Source-distinct, noncyclic conditioned exteriors extend the same system to mediated relationships across relational depth. The certified EAS matter-formation theorem stack and its integrated MF7 construction demonstrate the compatibility of these organizational processes through explicit source-conserving witnesses. The resulting scientific account presents matter as the time-like enabling structure within one economical system for the physical manifestation of relationships.