Color-Neutral Composite Closure: Baryons, Mesons, and Confinement from Rank-Three β-Completion

This paper is Paper 056 in the Anaxiomatic Mechanics / pq-Spacetime stack. It develops the color-neutral composite closure rule for quark-like shards in pq-spacetime. Building on the quark-shard eigenproblem and the rank-three color-comparison algebra, it defines the total traceless exterior completion residue of a composite beta-sector and shows that a freely exterior-closable color sector must satisfy the vanishing condition C_partial(R) = 0. In this framework, color neutrality is not an added postulate but the exterior beta-closure condition for jointly closing confined partial recurrence sectors.

Meson-like closure appears as shard/conjugate-shard cancellation, while baryon-like closure appears as rank-three saturation of the three exterior completion channels. Antibaryon closure follows by conjugation. Configurations with nonzero exterior color-comparison residue fail the free exterior closure test and are therefore confined or beta-transfer suppressed as isolated sectors. Gluon-like modes are identified as internal traceless channel-comparison transitions that preserve total exterior neutrality, making them effective comparison and repair modes of confined shard geometry.

The paper fixes the structural singlet-selection theorem required for the composite QCD track of the pq-spacetime stack. It does not yet compute the Yang-Mills action, running strong coupling, confinement potential, hadron masses, decay rates, or full hadron spectroscopy; those belong to later composite beta-sector dynamics.