Counterfeit Limit Cycle

Canonical definition

Counterfeit Limit Cycle is a structure that displays the phenomenology of sustained oscillation in a coordinate orthogonal to the loop requiring damping, while coupling into that loop with amplifying rather than restoring sign. It is a diagnostic category rather than an architectural commitment: it names a class of misreading in which visible alternation is taken as evidence that a system is self-correcting, when the alternating variable and the variable determining the system's terminus are different variables. A candidate Institutional Buffer qualifies as a genuine restoring node only if three conditions hold jointly, that it introduces a state variable not already in the system, that the variable's feedback closes onto one of the couplings whose product is the Internal Loop Gain, and that the sign of that closure is restoring. A Counterfeit Limit Cycle satisfies the first and fails the other two. The distinguishing observable is not whether alternation occurs but whether the system returns to a prior operating point when it does: a genuine limit cycle is recurrent in the state variables that matter, whereas a Counterfeit Limit Cycle is recurrent in an orthogonal coordinate while those variables advance monotonically. The two are indistinguishable within any single cycle and separable across several. The worked cases are two-party electoral alternation, in which office-holding rotates while the Belief Heterogeneity Buffer is held in Bipolar Convergence, and the rotation of constitutional form across regimes, in which form alternates while network loop gain ratchets through rising Observability.