P-104: The Geometric Origin of Decimal Quantum Computing — From Planck Micro-element Coherent Subgraphs to the Native d=10 Qudit

Abstract:The quantum bit (qubit) is conventionally regarded as the fundamental unit of quantum computing. However, recent years have seen significant progress in exploiting high-dimensional quantum dits (qudits), particularly decimal qudits (d=10), across multiple experimental platforms including ion traps, photonic chips, and neutral atoms. A fundamental theoretical question then arises: is the choice of the optimal computational dimension a matter of engineering convenience, or a manifestation of deeper physical laws? Mainstream quantum theory cannot answer this question — the number 10 is merely explained as the "coincidental" nuclear spin I=9/2 of 87Sr. Starting from Space Ontology, we provide the first axiomatic theory of dimension selection for quantum computing. Based on the core postulate that "space is the only entity," we rigorously prove the theorem of the optimal coherent subgraph of micro-elements: the minimal non-trivial sub-structure of fully connected coherent micro-elements that satisfies phase-winding closure and chiral self-consistency has vertex number d=10. This number is not an engineering choice, but a physical necessity uniquely determined by the RG freezing history of the effective dimension D_eff of the cosmic background. Our argument converges to the same conclusion from two independent paths. Path I (graph-energy path): starting from the micro-element Hamiltonian, we derive the partition function of coherent subgraphs, proving that the survival probability P_surv(d) ∝ e^(−d²/2) · Θ(D_eff − d), and combined with energy minimisation, establishes the uniqueness of d^* = 10. Path II (RG dimension freezing path): based on the rigorously proven RG dimension freezing theorem, the effective dimension of the universe is forced to freeze to D_super = 10 at the string scale, and through the dimension anchoring principle directly locks d=10. We map this K_10 coherent subgraph to a native decimal qudit state space, and prove that its topological protection mechanism originates from the closed-loop phase winding of the 10 micro-elements. Systematic comparison with mainstream qubit and engineered qudit schemes shows that our native d=10 qudit exhibits fundamental intrinsic quantum advantages: (1) a dimensionality peak in decoherence time — T_2(d) exhibits a maximum at d=10; (2) instinctive entanglement of two-qudit gates — two d=10 qudits can spontaneously establish entanglement through spatial coherent coupling. This paper is part of the second series (Applications and Verifications) of Space Ontology, building upon the foundational framework established in the first series (17 papers total).