Optomechanical Calibration of the Quantum Precision Holonomy Magnetic Laplacian Physical Units, Held-Out Spectral Tests, and the Quadratic Flux-Gap Law
Paweł Krzysztof Chomiuk
The companion theory paper Quantum Precision Holonomy constructs a magnetic graph Laplacian LU from inverse GNS-Gramian data and proves a quadratic opening law for its lowest eigenvalue. The present paper addresses a narrower physical question: what does the dimensionless operator mean, and how is it assigned physical units in a system where the same operator class is an actual Hamiltonian? We use the programmable nano-optomechanical network of Slim, del Pino, and Verhagen. In the opposed-flux diamond at the special ratio Jc = √ 2J, one antisymmetric apex mode decouples and the remaining three modes are exactly those of an equal-coupling Aharonov– Bohm loop. For the unit-weight magnetic triangle, LU = 2I − AU , and the experimentally realized coupled-mode Hamiltonian satisfies Hphys h = νrefI + jeff(2I − LU ). Thus spectral splittings are linear in differences of eigenvalues of LU ; no particle-mass map is introduced. The independently reported perimeter coupling is J/(2π) = 5.000 kHz, implying jeff = 7.071 067 812 kHz. A one-parameter calibration on ten digitized gaps gives jeff = 6.877 941 342 kHz and hence J/(2π) = 4.863 438 964 kHz, a difference of −2.731%. On nine frozen held-out gaps, MAE = 0.344 229 kHz and RMSE = 0.423 010 kHz. The raster scale is approximately 0.303 kHz per vertical pixel; reported mechanical linewidths are approximately 1 kHz to 7 kHz. The small-flux QPH law becomes ∆νQPH = jeff 9 Φ 2 + O(Φ4 ), with independently calibrated coefficient 0.785 674 201 kHz rad−2 . This is a figure-level held- out consistency test of the downstream map (G, w, U) → LU → physical spectrum. It does not test the upstream derivation of (w, U) from a measured complex GNS Gramian. Keywords: magnetic graph Laplacian; optomechanics; Aharonov–Bohm phase; spectral calibra- tion; held-out test; Quantum Precision Holonomy. Scope. This paper is a self-contained empirical companion to the mathematical QPH paper. It defines every object needed for the calibration, derives the C3 spectral map, freezes one fit parameter and a prospective train/test split, and reports physical units and held-out errors. It does not repeat the full inverse-GNS-Gramian proofs and does not claim that the
•Aug 15, 2026•0 citations