The Unipolar State

The Cohesion UFT Binary Recursion Toggle established that only two polarity statesare stable for a free funneled-spring recursion under uniform pressure: hexapolar (n = 6)and bipolar (n = 2). This paper identifies a third state accessible when the recursion iscaptured by an asymmetric coherence node: the unipolar state (n = 1). In the free field,n = 1 is excluded because a single-pole spring has no return path. But when a three-bodygravitational system creates a Lagrange point, the return path is provided externally bythe geometry of the system. The unipolar state is tidal locking: the recursion settles intoa single orientation with libration as the torsion oscillation within the coherence node.The stable Lagrange points L4 and L5 are located at exactly 60 = π/3 radians — onehexapolar sector — from the secondary body. This is not coincidental: L4 and L5 arecoherence nodes of the orbital hexapolar recursion, located at two of the six hexapolartorsion maxima positions. The L4/L5 stability condition m2/(m1 + m2) < 1/25 is thecoherence node depth condition Φnode < Φtoggle = 32/(3π2 − 4). Spin-orbit resonances(Mercury’s 3 : 2, the Laplace 4 : 2 : 1) are partial pole collapses — fractional statesbetween bipolar and unipolar stabilised by the cascade ratio r = 3.