= Solution
\b[The intended ordinary-carbide comparison is energetic: the smaller, more strongly polarizing $\mathrm{Mg^{2+}}$ can stabilize a different balance of lattice energy and carbon-anion bonding from the larger $\mathrm{Ca^{2+}}$.] Stabilization of the highly charged $\mathrm{C_3^{4-}}$ group competes with acetylide formation; electron counting alone does not require the same carbide stoichiometries for both metals. Ionic size and charge density provide a qualitative explanation, not a complete phase-stability calculation.
The literal claim that calcium has only one carbide is too broad. Primary calculations and high-pressure synthesis have established additional calcium carbides, including $\mathrm{Ca_2C_3}$ and $\mathrm{Ca_2C}$; known calcium-carbide chemistry also includes $\mathrm{CaC_6}$. Thus the conventional comparison must be limited to the familiar salt-like compounds and conditions intended here, rather than treated as a prohibition on other calcium–carbon compositions.<Investigation of exotic stable calcium carbides using theory and experiment by Yan-Ling Li and others>[2015, abstract, Ca2C3 section and experimental synthesis]{ref}
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