What does this research mean for the field?

Passive spectroscopy and current tomography cannot uniquely identify the Hamiltonian of a general Hermitian three-mode ring, but this two-dimensional ambiguity can be exactly resolved by acquiring spectra after the attenuation of two distinct edges. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine whether flux spectra and persistent currents can uniquely identify site energies and couplings in a three-mode synthetic-gauge ring, and identify 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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To determine whether flux spectra and persistent currents can uniquely identify site energies and couplings in a three-mode synthetic-gauge ring, and identify minimal interventions that resolve structural ambiguities.
Formulated an exact polynomial invariant compression mapping five microscopic coordinates to three invariants (Q, D, and T) for the general Hermitian three-mode ring.
Derived closed-form reconstruction equations and optimal experiment design criteria based on calibrated single- and dual-edge attenuations.
Conducted a derivative-free integral closure audit across 20 flux intervals using published superconducting-qubit experimental figures.
Proved that passive spectroscopy and current tomography leave a two-dimensional manifold of indistinguishable Hamiltonians, whereas attenuating two distinct labelled edges yields closed-form global uniqueness.
Demonstrated that complete edge cuts are D-, A-, and E-optimal under equal invariant noise, with an effective displayed current amplitude of 0.7591 of the ideal adiabatic convention.
Public-data audit yielded a central closure RMS of 0.02103 times the hopping scale, a maximum residual of 0.04534, and quadrature error below 8.69×10⁻⁵, consistent with model closure within figure resolution.

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Implication

Theoretical analysis reveals passive measurement ambiguities in three-mode synthetic rings, showing that two controlled edge attenuations uniquely recover microscopic Hamiltonian parameters.

Cite This Study

Mingoo Kim (2026) studied this question.

synapsesocial.com/papers/6aa0091858e84d0ff5b47b1e https://doi.org/10.5281/zenodo.22643651

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Implication

Theoretical analysis reveals passive measurement ambiguities in three-mode synthetic rings, showing that two controlled edge attenuations uniquely recover microscopic Hamiltonian 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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Discussion

Implication

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

Key Points

Discussion

Implication

Cite This Study

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