roboticsCert
plain-language theorem explainer
The definition assembles a RoboticsCert record by populating the subsystem cardinality field with the result of a decision procedure and the degrees-of-freedom field by reflexivity. Roboticists and applied physicists modeling control loops from the J-cost framework would cite it to confirm that the five canonical subsystems and six-DOF architecture match the RS-derived counts. The construction is a direct record literal that invokes the two upstream theorems without additional reasoning steps.
Claim. Let RoboticsCert be the structure whose fields require that the cardinality of RoboticSubsystem equals 5 and that sixDOF equals 6. Then roboticsCert is the record satisfying both equalities.
background
Recognition Science treats robot control as a J-cost minimization loop, where J(x) = (x + x^{-1})/2 - 1 arises from the forcing chain. The module states that the five canonical subsystems (sensing, actuation, computation, communication, power) equal the configuration dimension D = 5, while six degrees of freedom equal the number of faces of a cube in three spatial dimensions. RoboticsCert is the structure packaging these two numerical constraints as a single certificate.
proof idea
The definition is a one-line record constructor that supplies the five_subsystems field directly from the theorem roboticSubsystemCount and the six_dof field directly from the theorem sixDOF_eq_cubefaces.
why it matters
This definition completes the E1 Applied Engineering section by exhibiting an explicit certificate that the RS subsystem count and cube-face degree count align with standard robotic architecture. It links the abstract J-cost loop to concrete 5 + 6 structure without new axioms or hypotheses. No downstream results depend on it, leaving open its embedding into larger control-theory developments inside the framework.
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