Gray-Structured Transition Decomposition and Sector-Resolved Operator Dynamics on Q5
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2026
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| _version_ | 1866901870977482752 |
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| author | Holdway, Craig Edwin |
| author_facet | Holdway, Craig Edwin |
| contents | <p><em>This paper presents a self-contained structural result on the five-dimensional hypercube Q5. The main result establishes a correspondence between Gray code edge decomposition, operator-induced sector transitions, and scalar commutator dynamics on simultaneous eigensectors. </em></p> <p><em>The construction is purely mathematical, falling within the scope of discrete and combinatorial structures, with an explicit operator-algebraic realization.</em></p> <p><em>This work is independent of the author's concurrent submissions on Q5, each addressing distinct structural results. The present paper focuses specifically on transition decomposition and operator correspondence and does not rely on results from those works.</em></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19319253 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Gray-Structured Transition Decomposition and Sector-Resolved Operator Dynamics on Q5 Holdway, Craig Edwin five-dimensional hypercube Q5 hypercube Penteract hypercube graph Boolean lattice Hamming distance Hamming association scheme H(5,2) Gray code binary reflected Gray code Hamiltonian cycle Gray code Hamiltonian cycle edge decomposition transition decomposition graded operator decomposition sector-resolved operator dynamics Hamming weight grading collective operator scalar commutator relations Heisenberg evolution Ising-type Hamiltonian finite-dimensional operator theory operator algebra B5 symmetry group hyperoctahedral group signed permutation group Coxeter group type B S5 representation theory spectral graph theory distance-regular graph Krawtchouk polynomials parity decomposition 2-adic valuation dyadic structure weight sector decomposition <p><em>This paper presents a self-contained structural result on the five-dimensional hypercube Q5. The main result establishes a correspondence between Gray code edge decomposition, operator-induced sector transitions, and scalar commutator dynamics on simultaneous eigensectors. </em></p> <p><em>The construction is purely mathematical, falling within the scope of discrete and combinatorial structures, with an explicit operator-algebraic realization.</em></p> <p><em>This work is independent of the author's concurrent submissions on Q5, each addressing distinct structural results. The present paper focuses specifically on transition decomposition and operator correspondence and does not rely on results from those works.</em></p> |
| title | Gray-Structured Transition Decomposition and Sector-Resolved Operator Dynamics on Q5 |
| topic | five-dimensional hypercube Q5 hypercube Penteract hypercube graph Boolean lattice Hamming distance Hamming association scheme H(5,2) Gray code binary reflected Gray code Hamiltonian cycle Gray code Hamiltonian cycle edge decomposition transition decomposition graded operator decomposition sector-resolved operator dynamics Hamming weight grading collective operator scalar commutator relations Heisenberg evolution Ising-type Hamiltonian finite-dimensional operator theory operator algebra B5 symmetry group hyperoctahedral group signed permutation group Coxeter group type B S5 representation theory spectral graph theory distance-regular graph Krawtchouk polynomials parity decomposition 2-adic valuation dyadic structure weight sector decomposition |
| url | https://doi.org/10.5281/zenodo.19319253 |