Causal-Relational Closure in String Theory: Exact Continuation Invariants, Worldsheet Sewing, and String-Scattering Witnesses

Causal-relational closure (CRC) distinguishes a fixed event from the completion of every relation involving that event. The distinction is examined independently within elementary string-theoretic structures rather than inferred from holographic principles. In the Ising conformal-block sector, the joint commutant of elementary braids is computed exactly: every invariant Hermitian four-spin pairing is scalar, and the result extends to arbitrary even spin insertions in a fixed-charge sector. The Veneziano amplitude supplies a separate obstruction to finite single-channel truncation. For covariant string field theory, exact quotients retaining unmodified string products are characterized by graded interaction ideals. Closing a seed test space under string-interaction contexts constructs the largest compatible interaction ideal and hence the coarsest strict quotient; a finite Lie-algebra example exhibits both a failed reduction and an exact one. Background-independent Batalin–Vilkovisky sewing imposes corresponding stability conditions. Correct elimination of intermediate modes instead generates effective interactions. A Chan–Paton-resolved open-superstring disk am-plitude exhibits coherent enhancement and cancellation between two endpoint-matched pathways, while a light-cone joining model supplies a time-ordered illustration and an explicit which-path negative control. Circle T-duality provides the complementary case of physically equivalent geometric descriptions. The results establish exact continuation-preserving constraints within specified string constructions. The fixed-color scattering witness lacks a fully gauge-invariant record-and-detector realization, and worldsheet sewing does not by itself define a causal future. Consequently, necessity of CRC as a universal pre-geometric ontology is not claimed; the precise remaining physical construction is identified.