DOMAINOLOGY: A Proposed General Science of Domains, Membership, Boundaries, and Reconfiguration

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Domainology (Miền học) is proposed as a general research discipline for systems whose domains, membership relations, boundaries, and feasible couplings are themselves subject to change. Rather than treating a domain as fixed background, the framework makes membership a first-class state relation and separates identity preservation from external adaptation. It defines domain signatures, preservation contracts, Carry-Π boundaries, compatibility and coverage, transdomain trajectories, bridge-domain synthesis, observation-dependent Dark Segments, and a canonical family of seal/open/plan/adapt/handover/validate/commit operators. Domain Membership Operators serve as a reference implementation. Prime-TB Cut and Prime Excalibur are incorporated as an optional factorized algebra for discretized boundary reconfiguration: unique factorization guarantees exact recovery on the integer grid, while no claim is made that nature is intrinsically prime-coded. D-Bench v1.0 provides 1,000 synthetic transition records across five scenarios and five methods. Adaptive paths solve obstacle cases that defeat straight handover; bridge synthesis solves a disconnected-feasibility case that path planning alone cannot; rate governance recovers fast transitions; and PrimeDMO reproduces the reconfiguration behavior with modest quantization overhead. The contribution is therefore a proposed field-level language and research program for studying how systems preserve identity while changing the domains to which they belong.