IndisputableMonolith.Cybernetics.FeedbackControlModesFromConfigDim
This module defines feedback control modes derived from configuration dimension in the Recognition Science cybernetics layer. It introduces the core type FeedbackControlMode, a counting function over modes, and certification predicates for valid assignments. The definitions rest on the RS time quantum from the imported Constants module and supply the interface for control-theoretic extensions of the framework.
claimThe module introduces the type $FeedbackControlMode$ indexed by configuration dimension, the function $feedbackControlMode_count : ConfigDim → ℕ$, and the predicate $FeedbackControlModesCert$ that certifies mode validity under RS constraints.
background
Recognition Science extends its forcing chain to cybernetic systems by treating control modes as discrete structures indexed by configuration dimension. The module imports the fundamental RS time quantum τ₀ = 1 tick from Constants, which supplies the native temporal unit for any dynamical control description. Sibling declarations FeedbackControlMode, feedbackControlMode_count, FeedbackControlModesCert, and feedbackControlModesCert together form the definitional core for enumerating and certifying feedback modes.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the definitional base for feedback control within the cybernetics domain of Recognition Science. It feeds parent structures that will derive stability and mode-selection theorems from the phi-ladder and RCL, although no direct used_by edges are recorded yet. The definitions align with the eight-tick octave and D = 3 spatial setting by parameterizing modes through configuration dimension.
scope and limits
- Does not prove existence or uniqueness of any control mode.
- Does not map configuration dimension to explicit physical constants.
- Does not invoke the full T0-T8 forcing chain.
- Does not contain numerical examples or concrete system instances.