RoboticsCert
RoboticsCert packages the two RS-derived engineering invariants into a single structure: the finite type of robotic subsystems has cardinality exactly 5, and the constant sixDOF equals 6. Applied engineers modeling autonomous systems would cite it to verify that a robot design matches the configuration dimension and cube-face count from the forcing chain. The declaration is a plain structure definition with two field assertions and no proof obligations or lemmas.
claimThe structure $RoboticsCert$ consists of the two assertions that the finite type of robotic subsystems has cardinality 5 and that the constant denoting degrees of freedom equals 6.
background
In the Robotics from RS module, robot control is identified with J-cost minimization loops and autonomous navigation with minimum-cumulative-J paths. The inductive type RoboticSubsystem enumerates exactly five canonical components (sensing, actuation, computation, communication, power), which the module equates to the configuration dimension D = 5. The auxiliary definition sixDOF fixes the degrees of freedom at 6, identified with D + 3 and therefore with the number of faces of a cube in three spatial dimensions.
proof idea
The declaration is a direct structure definition that introduces two fields without invoking any lemmas or tactics. The first field records the cardinality of RoboticSubsystem; the second records the value of the constant sixDOF.
why it matters in Recognition Science
The structure is instantiated by the downstream definition roboticsCert, which supplies the concrete values from roboticSubsystemCount and sixDOF_eq_cubefaces. It embeds the T8 result (D = 3 spatial dimensions) into applied engineering, linking the five subsystems to configDim and the six degrees of freedom to cube faces. The module presents this as the E1 Applied Engineering layer of the Recognition Science framework.
scope and limits
- Does not derive the five subsystems from J-uniqueness or the phi fixed point.
- Does not compute explicit J-cost values for navigation paths.
- Does not treat non-cubic geometries or higher-dimensional configurations.
- Does not incorporate error bounds or probabilistic extensions.
Lean usage
def verifiedRobot : RoboticsCert := roboticsCertformal statement (Lean)
31structure RoboticsCert where
32 five_subsystems : Fintype.card RoboticSubsystem = 5
33 six_dof : sixDOF = 6
34