The Nucleon Projection Theorem: Spin-12 , Exterior Charge, and the uud/udd β-Sectors

This is Paper 069 in the Anaxiomatic Mechanics / pq-Spacetime stack. It defines the nucleon projection inside the finite three-shard β-baryon sector of pq-spacetime. Starting from the complete rank-three color-neutral baryon domain, the nucleon subspace is selected by simultaneous projection onto first-generation u/d shard content, exterior color neutrality, conserved exterior charge, and total spin-1/2 recurrence holonomy.

The result identifies two distinguished closed β-sectors: the proton-like uud sector with exterior charge +1, and the neutron-like udd sector with exterior charge 0. Fractional shard charges are treated as partial exterior-neutrality defects, meaningful only inside jointly closing color-neutral composites rather than as freely isolatable particle charges.

The theorem introduces no new force law, fitted potential, baryon mass input, hyperfine parameter, or independent color/charge knob. It is a projection-level result: it fixes the structural nucleon domains on which later recurrence-energy and mass-spectrum calculations must act. A possible spin-3/2 label is treated only as a formal non-nucleon total-holonomy projection of the baryon domain and is not assumed to be physically realized here.

This paper is part of the Anaxiomatic Mechanics / pq-Spacetime Stack and continues the β-QCD sequence by passing from complete baryon closure to the specific uud/udd nucleon sectors.