Possible generalizations of the statistics of identical particles, parastatistics, and the corresponding theories of parafields are reviewed. The connection between parastatistics and cases of degeneracy of particles with respect to an internal degree of freedom is discussed, and also the restrictions that are imposed on internal symmetries if they are given a parafield description. In particular, the difference between the hypotheses of ''three-color'' quarks and ''paraquarks'' is discussed.
Parastatistics is an exotic type of exchange statistics beyond fermions and bosons. Paraparticles transform in higher dimensional representations of the exchange symmetry group, analogous to non-Abelian anyons, yet consistently defined in any dimension. Although paraparticles have long been proposed, they were widely believed to be physically equivalent to fermions or bosons. Nevertheless, a recent paper proposed a different theory, called
R-parastatistics, and demonstrated that nontrivial
R-paraparticles can emerge as quasiparticles in condensed matter systems, and are observably distinct from both fermions and bosons. This paper develops the theoretical foundation and several extensions of
R-parastatistics, with particular emphasis on its observable consequences. Central to this paper is a general theory of local observables extending the basic family introduced before. First, we define local observables that distinguish particle types. Second, we formulate local observables at special point defects that probe the internal indices of
R-paraparticles, crucial for observing
R-parastatistics and for the proposed applications in quantum information. Third, we introduce local observables that create or annihilate particle-antiparticle pairs, important for building a relativistic quantum field theory for
R-paraparticles. We further introduce generalized hidden symmetries that act on internal indices of
R-paraparticles while preserving the local observable algebra, providing a basis for proving local indistinguishability and for connecting to a categorical description of
R-paraparticles. This work sets a solid theoretical foundation for understanding the fundamental physical properties of
R-paraparticles and pave the way for finding them in nature.
Within the sealed-records program developed in Part I, we derive the structures of particle statistics and gauge theory as outputs rather than inputs. The results hold at stated scope and are accompanied by machine receipts. First, univalence superselection is derived within the stated record class: the silence of the relative sign is established by exhaustive verification within that class, so the term "derived" carries exactly that scope. The silent-seam axiom then excludes superpositions across the double cover, making the (-1)^F grading central. Second, spin quantization, 2m in Z, follows from the (1,3) signature together with the belt-trick identification, with record anyons confined to genuinely two-dimensional screens. Third, under the named framed-transport premise, namely that exchange is transport of the fiber with its frame, sealed positivity on the exchange collar forces the exchange phase (-1)^{2m}: wrong-statistics sectors carry strictly negative weights, and Pauli exclusion appears as an exact zero. Fourth, parastatistics is excluded at pair-exchange level: the transport commutant on V tensor V is exactly span{1, P}, and the +/-1 options are excluded by the ledger. The full n-strand Doplicher-Haag-Roberts parastatistics question is explicitly scoped. Fifth, the internal symmetry group of the fiber is reconstructed as the commutant of record exchange. Once the ledger forces the statistics, classical Schur-Weyl duality, imported with no novelty claim, delivers the full unitary group of the fiber: U(3) for three-strand fibers, with an implementation check 165 = 165 and the determinant slot included, and U(2) for the weak fiber, with checks 10 = 10 and 20 = 20. This is in the direction of Doplicher-Roberts reconstruction: group as output of statistics. What is delivered here is the global symmetry group; promotion to a local gauge symmetry with connection and dynamics is an additional step, graded as input where Part III uses it. Color receipts include exact Pauli exclusion for color, ||A_4|| = 0, and uniqueness of the baryon singlet. We state the paper's two named premises, framed transport and collar presentability, and the scope of each result. The matter-content selection built on these structures, together with its falsifiable consequences, appears in Part III.