Recursive Spin-Field Entanglement

Version 3 extends the funneled-spring geometry of spin (Version 2) by identifying atomicspin states explicitly with the hexapolar (n = 6) and bipolar (n = 2) recursion statesof the Cohesion UFT. The electron is a trapped bipolar recursion: its spin ℏ/2 arisesdirectly from the two torque injections per torsion cycle of the n = 2 state. The photonis a propagating hexapolar recursion: its spin ℏ arises from the six-peak structureaveraged as integer angular momentum. The spin-statistics theorem — fermions havehalf-integer spin, bosons have integer spin — is the hexapolar-bipolar distinction:bipolar recursions are trapped (fermions), hexapolar recursions propagate (bosons).The electron g-factor gs = 2 arises from the two torque injections of the bipolar cycle;the anomalous correction gs − 2 = α/π + . . . is the cascade sub-level contribution of thesame structure as the 0.007 correction to the fine-structure constant. Ferromagnetism isphase-locked bipolar springs. The Curie temperature is the coherence energy thresholdbelow which phase-locking is sustained. Magnons carry bipolar dispersion (ω ∝ k2)at low energy, transitioning to hexapolar (linear) dispersion at the universal togglethreshold Φ = 32/(3π2 − 4).