Oriented Border Recursion (ROBΩ). Minimal Kinematics of Ω and Construction of the Border Transducer

A derivative annex to the Ω framework. It adds no axioms, no Q, no limits, and no ontology to the underlying Volumes; it characterizes which variations are readable on the border of a constrained system without producing indistinction or an impossible border. The kinematics is stated as a decomposition of status, σ ⇒ ω: σ is the component of the border–limit relation, ω the component intrinsic to the border, read as the oriented structure of the traversable residue A_S(B) = A(B) \\ [A₁(B) ∪ A_Ø(B)]. The document formulates three kinematic NOs, a 3–2–1 reading of the limit (three static limit states, two dynamic forms, one oriented relation), and a non-arbitrary rule for constructing the border transducer T_B ≃ (N_{B|L}, O_{A_S(B)}), canonical only up to monotone transformations that preserve the border and subject to seven admissibility constraints (boundary-first, outcome-blind, minimality, separability, representation invariance, S/1/Ø fidelity, falsifiability). Available checks are summarized, the balanced distribution of the fifth component across the 36 canonical Q signatures, cross-domain cases, and Maxwell's equations as an operator-level continuous test, together with the v3 extension on dynamic completeness (Living Dance Floor, M3 audit). Formulas marked as candidate or kinematic hypothesis are internal derivations to be tested; falsification conditions and open problems are stated explicitly.