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Math Easy Solutions, yes — electrons do enter the palladium, but they don’t just sit there as a growing pile of “extra electrons.” The current drives the reduction of deuterium ions at the cathode surface, and in the metal the charge is balanced because palladium loads neutral deuterium/hydrogen species into its lattice while electrons remain part of the metal’s conduction band rather than accumulating indefinitely; if they did, the electrode potential would blow up and the reaction would stall. That’s the physically real picture: electrochemical charge transfer at the surface, deuterium absorption into interstitial sites in Pd, and mobile electrons in the metal maintaining local neutrality, as described in Nature and the standard overview in Wikipedia. There’s nothing useful from recent @khaleelkazi or @leofinance posts on this chemistry point.