What does this research mean for the field?

Passive spectroscopy and current tomography cannot uniquely determine the microscopic parameters of a general Hermitian three-mode ring, but the Hamiltonian can be globally identified by acquiring spectra after attenuating two distinct edges. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine whether flux-dependent spectra and persistent currents can uniquely identify site energies and couplings in Hermitian three-mode rings, and to establish minimal interventions that resolve structural ambiguities.

September 8, 2026Open Access

Spectral–Current Nonidentifiability and Globally Identifying Interventions in Flux Trimers: Exact Invariant Compression, Calibrated Edge Attenuation, and a Public-Data Closure Audit

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MKMingoo Kim

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Implication

Theoretical analysis uncovers intrinsic Hamiltonian nonidentifiability in Hermitian flux trimers, demonstrating that two distinct edge interventions uniquely recover microscopic parameters.

Key Points

To determine whether flux-dependent spectra and persistent currents can uniquely identify site energies and couplings in Hermitian three-mode rings, and to establish minimal interventions that resolve structural ambiguities.
Formulated an exact invariant compression mapping phase-resolved eigenvalues and conjugate currents of three-mode rings to three polynomial invariants (Q, D, and T).
Derived closed-form reconstruction equations under single and dual labelled edge-attenuation interventions with delta-method covariance propagation and experimental design optimality criteria.
Conducted a derivative-free integral closure audit on published superconducting-qubit experimental figures (Roushan et al., 2017) across 20 flux intervals.
Passive spectroscopy and current tomography leave a two-dimensional manifold of indistinguishable Hamiltonians, and a single-edge cut still leaves a fourfold ambiguity among positive-hopping Hamiltonians.
Spectra acquired following attenuation of two distinct edges provide unique, closed-form recovery of all site offsets and positive hoppings, with a symmetric-point determinant of −4(1−ρ₁²)²(1−ρ₃²)².
The public experimental data audit yielded a central closure RMS of 0.02103 of the hopping scale, a maximum residual of 0.04534, and an effective displayed current amplitude of 0.7591 relative to the ideal adiabatic convention.

Cite This Study

Mingoo Kim (2026) studied this question.

synapsesocial.com/papers/6a9fd7d558e84d0ff5b46f14 https://doi.org/10.5281/zenodo.22643650

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Implication

Theoretical analysis uncovers intrinsic Hamiltonian nonidentifiability in Hermitian flux trimers, demonstrating that two distinct edge interventions uniquely recover microscopic parameters.

Spectral–Current Nonidentifiability and Globally Identifying Interventions in Flux Trimers: Exact Invariant Compression, Calibrated Edge Attenuation, and a Public-Data Closure Audit

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Cite This Study

Spectral–Current Nonidentifiability and Globally Identifying Interventions in Flux Trimers: Exact Invariant Compression, Calibrated Edge Attenuation, and a Public-Data Closure Audit

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Implication

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