Pauli Antisymmetry from F2 XOR-Closure: A Discrete-Geometric Derivation of Composite Baryon Statistics
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| Language: | English |
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2026
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| _version_ | 1866901747118637056 |
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| author | Elliman, David |
| author_facet | Elliman, David |
| contents | <p class="p1">We show that the antisymmetry of composite baryon wavefunctions under exchange—the em-</p> <p class="p1">pirical content of Pauli’s exclusion principle for hadrons—can be derived from the F<span class="s1">2 </span>XOR-closure</p> <p class="p1">structure of a discrete-geometric inner code, without invoking continuum Lorentz invariance, micro-</p> <p class="p1">causality, or the spin-statistics theorem. Working on an 8-qubit internal Hilbert space Q<span class="s1">3 </span>projected</p> <p class="p1">onto a 48-codeword physical subspace, we identify three quark colours that XOR-close to the iden-</p> <p class="p1">tity element. We show that the resulting global stabiliser Q promotes baryon creation operators</p> <p class="p1">to defect-creating operators with a definite anticommutation algebra. Two consequences follow: (i)</p> <p class="p1">baryon parity is a Z<span class="s1">2 </span>conserved charge; (ii) the exchange of two baryons produces a phase of−1</p> <p class="p1">from the {X, Z} = 0 algebra of the underlying Pauli operators on the inner code, provided a con-</p> <p class="p1">sistent path-ordering convention is established on the macroscopic lattice. The same construction,</p> <p class="p1">restricted to the strong-interaction channel V<span class="s1">strong</span>, gives a tensor decomposition I<span class="s1">12 </span>⊗ A<span class="s1">K</span><span class="s2">3 </span>on the</p> <p class="p1">36-dimensional quark sector, where A<span class="s1">K</span><span class="s2">3 </span>is the complete-graph-on-three-vertices adjacency matrix.</p> <p class="p1">The induced kinetic operator has eigenvalues ±i 2/√3 on colour-singlet states and ±i/√3 on colour-</p> <p class="p1">doublet states, energetically favouring colour-singlet bound states by a factor of four. The algebraic</p> <p class="p1">claims are verified by exact rational identities in numerical diagonalisation on the projected code-</p> <p class="p1">word space. The construction provides a discrete-geometric origin for hadronic Pauli antisymmetry</p> <p class="p1">parallel to, but mechanistically independent of, the spin-statistics theorem.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20129742 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Pauli Antisymmetry from F2 XOR-Closure: A Discrete-Geometric Derivation of Composite Baryon Statistics Elliman, David Pauli exclusion principle Spin statistics theorem Discrete gauge theory Z2 Guage symmetry F2 XOR Closure Composite Fermion Statistics Baryon parity Jordan-Wigner transformation Quark Colour Algebra <p class="p1">We show that the antisymmetry of composite baryon wavefunctions under exchange—the em-</p> <p class="p1">pirical content of Pauli’s exclusion principle for hadrons—can be derived from the F<span class="s1">2 </span>XOR-closure</p> <p class="p1">structure of a discrete-geometric inner code, without invoking continuum Lorentz invariance, micro-</p> <p class="p1">causality, or the spin-statistics theorem. Working on an 8-qubit internal Hilbert space Q<span class="s1">3 </span>projected</p> <p class="p1">onto a 48-codeword physical subspace, we identify three quark colours that XOR-close to the iden-</p> <p class="p1">tity element. We show that the resulting global stabiliser Q promotes baryon creation operators</p> <p class="p1">to defect-creating operators with a definite anticommutation algebra. Two consequences follow: (i)</p> <p class="p1">baryon parity is a Z<span class="s1">2 </span>conserved charge; (ii) the exchange of two baryons produces a phase of−1</p> <p class="p1">from the {X, Z} = 0 algebra of the underlying Pauli operators on the inner code, provided a con-</p> <p class="p1">sistent path-ordering convention is established on the macroscopic lattice. The same construction,</p> <p class="p1">restricted to the strong-interaction channel V<span class="s1">strong</span>, gives a tensor decomposition I<span class="s1">12 </span>⊗ A<span class="s1">K</span><span class="s2">3 </span>on the</p> <p class="p1">36-dimensional quark sector, where A<span class="s1">K</span><span class="s2">3 </span>is the complete-graph-on-three-vertices adjacency matrix.</p> <p class="p1">The induced kinetic operator has eigenvalues ±i 2/√3 on colour-singlet states and ±i/√3 on colour-</p> <p class="p1">doublet states, energetically favouring colour-singlet bound states by a factor of four. The algebraic</p> <p class="p1">claims are verified by exact rational identities in numerical diagonalisation on the projected code-</p> <p class="p1">word space. The construction provides a discrete-geometric origin for hadronic Pauli antisymmetry</p> <p class="p1">parallel to, but mechanistically independent of, the spin-statistics theorem.</p> |
| title | Pauli Antisymmetry from F2 XOR-Closure: A Discrete-Geometric Derivation of Composite Baryon Statistics |
| topic | Pauli exclusion principle Spin statistics theorem Discrete gauge theory Z2 Guage symmetry F2 XOR Closure Composite Fermion Statistics Baryon parity Jordan-Wigner transformation Quark Colour Algebra |
| url | https://doi.org/10.5281/zenodo.20129742 |