Pauli Antisymmetry from F2 XOR-Closure: A Discrete-Geometric Derivation of Composite Baryon Statistics

We show that the antisymmetry of composite baryon wavefunctions under exchange—the em- pirical content of Pauli’s exclusion principle for hadrons—can be derived from the F2 XOR-closure structure of a discrete-geometric inner code, without invoking continuum Lorentz invariance, micro- causality, or the spin-statistics theorem. Working on an 8-qubit internal Hilbert space Q3 projected onto a 48-codeword physical subspace, we identify three quark colours that XOR-close to the iden- tity element. We show that the resulting global stabiliser Q promotes baryon creation operators to defect-creating operators with a definite anticommutation algebra. Two consequences follow: (i) baryon parity is a Z2 conserved charge; (ii) the exchange of two baryons produces a phase of−1 from the {X, Z} = 0 algebra of the underlying Pauli operators on the inner code, provided a con- sistent path-ordering convention is established on the macroscopic lattice. The same construction, restricted to the strong-interaction channel Vstrong, gives a tensor decomposition I12 ⊗ AK3 on the 36-dimensional quark sector, where AK3 is the complete-graph-on-three-vertices adjacency matrix. The induced kinetic operator has eigenvalues ±i 2/√3 on colour-singlet states and ±i/√3 on colour- doublet states, energetically favouring colour-singlet bound states by a factor of four. The algebraic claims are verified by exact rational identities in numerical diagonalisation on the projected code- word space. The construction provides a discrete-geometric origin for hadronic Pauli antisymmetry parallel to, but mechanistically independent of, the spin-statistics theorem.