Open-Relation Quantum Computation: Complete Operational Constructions, Future-Defined Interfaces, Sequential Completion, and Outcome-Generated Algebras

Open-Relation Quantum Computation (ORQC) is investigated as a contract-first organisation of standard quantum mechanics based on Causal-Relational Closure (CRC): irreversible records need not exhaust relational distinctions accessible to admissible future operations. The computational objects are complete future-response contracts, open relational transitions, and composition rules rather than a prescribed global state-vector history. A reproducible finite-model programme examines coherentrelation composition, noncommuting transformations, contextual completion, future-selected quantum connectivity, delayed operand binding, reusable and generative relational fabrics, and nonlinear outcome-generated computational sectors. A central three-operand example emits two overlapping Boolean-relation records while retaining a five-dimensional coherent branch. Three constrained local generators close exactly to a ten-dimensional Lie algebra isomorphic to so(5); fine-grained operandmeasurement preserves the emitted answer probabilities but destroys future-coherent responses. Additional examples establish exact reference-preserving output instruments under late future choices and successive irreversible records. Negative controls include unsuccessful native fault-tolerance attempts, inefficient sequential contextuality recycling, and adversarial demonstrations of equivalence with optimised conventional quantum circuits. A future-query memory bound and an oracle-accesscounterexample delimit claims of relational compression and coherent black-box control. Known stabilizer, measurement-based, contextuality, teleportation, and constrained-dynamics mechanisms are identified explicitly. The results establish an exploratory, reproducible computational methodology, not new quantum predictions, universal ORQC synthesis, physical quantum advantage, or a certified fault-tolerant implementation.