Multi-Sector Forge ISA: Non-Commutativity of Sector Dequantizations and Annealing-Order-Dependent Computation
Ian Richard C Buckley
PENDING QUALITY AUDIT (2026-08). The file is restricted while this record is reviewed as part of a systematic audit of the author's corpus. It has not yet been assessed. Metadata and DOI remain public, and access can be requested. The Forge ISA operates with a single annealing parameter β. For systems with multiple coupled degrees of freedom, the natural generalisation assigns an independent β_i to each sector. The central result is a non-commutativity theorem: the sector dequantization operators T_∞^c and T_∞^s satisfy [T_∞^c, T_∞^s] = 0 ⟺ I_cs = 0 where I_cs = ⟨H_c H_s⟩ − ⟨H_c⟩⟨H_s⟩ is the off-diagonal Fisher information coupling. When sectors are coupled (I_cs ≠ 0), dequantization order matters: the joint e-geodesic path on the product Fisher manifold outperforms sector-by-sector annealing by ΔE = 0.35 at U = 4t on the half-filled 4-site Hubbard chain (99.3% vs 82.7% of ground state energy). A new Hubbard limit is identified: the spin-frozen limit (β_s → ∞, β_c finite) reduces to a hard-core Bose gas, complementing the known charge-frozen limit (Heisenberg AFM, Anderson 1959). The annealing-order holonomy is the thermodynamic analogue of the Aharonov-Bohm effect, largest near the Mott transition where Fisher curvature peaks. Series: Paper 325 (doi:10.5281/zenodo.20400638) → Paper 419 (doi:10.5281/zenodo.20694527) → Paper 443 (doi:10.5281/zenodo.20752384) → Paper 453 (this paper). Keywords Forge ISA, multi-sector annealing, non-commutativity, Fisher information, Hubbard model, hard-core Bose gas, Mott transition, information geometry, e-geodesic, annealing order, holonomy, Aharonov-Bohm, thermodynamic computation, natural gradient, dequantization
•Jun 20, 2026•0 citations