pith. sign in
theorem

sixDOF_eq_cubefaces

proved
show as:
module
IndisputableMonolith.Physics.RoboticsFromRS
domain
Physics
line
29 · github
papers citing
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plain-language theorem explainer

The equality establishes that the six degrees of freedom in the Recognition Science robotics model equal the integer 6. Roboticists modeling SCARA-style manipulators would cite this to align the DOF count with cube-face geometry from three spatial dimensions. The proof reduces immediately to reflexivity on the constant definition of sixDOF.

Claim. In the Recognition Science model the number of degrees of freedom for a robotic system satisfies $6 = 6$, matching the count of faces on a cube in three spatial dimensions.

background

The RoboticsFromRS module defines five canonical robotic subsystems (sensing, actuation, computation, communication, power) as configDim D = 5. Robot control is realized as a J-cost minimization loop, with autonomous navigation seeking minimum cumulative J paths. The upstream definition sixDOF sets the degrees of freedom to the constant 6, interpreted as D + 3 = cube faces.

proof idea

The proof is a one-line wrapper that applies reflexivity directly to the definition of sixDOF.

why it matters

This equality supplies the six_dof field inside the roboticsCert definition, which certifies alignment between subsystem count and DOF. It connects to the framework derivation of D = 3 spatial dimensions and the cube-face count arising from that geometry. No open questions are addressed.

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