Structural Spin as Quantised Recurrence Density: Primitive Winding, Exchange Holonomy and 3+1D Local Constraints - Paper 11

Structural Spin as Quantised Recurrence Density: Primitive Winding, Exchange Holonomy and 3+1D Local Constraints - Paper 11 Abstract Building on the U(1) persistence sector established in Paper 9 and the composite excitation sector introduced in Paper 10, this paper formalises structural spin as quantised recurrence density within the Finite Reversible Closure (FRC) framework. Primitive admissibility constrains driver-level winding to integer values via π₁(U(1)) ≅ ℤ. Fractional spin cannot originate at the primitive level without introducing additional covering structure. In the emergent isotropic infrared regime, rotations act through configuration-space holonomy. In 3+1D local relativistic regimes, exchange topology restricts phases to ±1. We further prove that a residual ℤ₂ parity fibre arises generically from gauge-invariant composite structure as a projective-frame ambiguity. This yields a necessary rotation–exchange identification at the composite level without introducing new primitive degrees of freedom. Introduction The Finite Reversible Closure (FRC) programme develops a strictly local, finite-dimensional, constraint-defined substrate in which structure emerges through admissible reversible update. Paper 9 established minimal persistent cyclic recurrence and demonstrated U(1) universality in the infrared. Paper 10 constructed the first gauge-invariant composite excitation and showed that it survives correlator-matching coarse-graining. Paper 11 addresses the structural status of spin;- What is spin in a recurrence-based ontology and how does half-integer behaviour arise without inserting covering groups by assumption? We show that;- Primitive loop winding is integer-quantised via π₁(U(1)) No half-integer spin exists at the driver level without introducing additional primitives Exchange phases arise in configuration space rather than primitive recurrence In 3+1D relativistic regimes, exchange phases reduce to ±1 A residual ℤ₂ parity fibre arises generically from gauge-invariant composite structure via projective frame ambiguity This establishes a rotation–exchange equivalence at the composite level while preserving strict integer quantisation at the primitive level.