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If the correlation holds in all models, measuring it would calibrate the matrix elements.","posed_since":"2018","precise":"Shell-model calculations show a near-linear correlation between the ground-state double Gamow-Teller matrix element $M^{\\mathrm{DGT}}$ and $M^{0\\nu}$ (Shimizu, Menendez and Yako, PRL 120, 142502, 2018). Determine whether the correlation holds across many-body methods and with two-body currents, and extract M^{DGT} from heavy-ion double-charge-exchange reactions (NUMEN at LNS Catania, RCNP Osaka). Answer: yes or no for model independence, with calibration slope and uncertainty.","problem_ref":null,"references":"","settled_by":"Ab initio and QRPA calculations of $M^{\\mathrm{DGT}}$ and $M^{0\\nu}$ across ten or more nuclei, plus a reaction-theory-controlled extraction of $M^{\\mathrm{DGT}}$ from double-charge-exchange data.","status_note":"","title":"Can double Gamow-Teller transitions calibrate the matrix 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