# Altermagnetism and superconductivity Separate magnetic symmetry, pairing-model constraints and proximity experiments, with specimen-specific evidence and explicit limits. ## Scope Altermagnetism describes compensated collinear magnetic order whose opposite-spin sectors are related by crystal operations such as rotations. It can produce momentum-dependent spin splitting without requiring spin–orbit coupling. Cancellation of the total magnetic moment does not imply degeneracy of opposite spins at every momentum. Nor does the absence of a uniform moment remove every constraint on superconducting pairing. The magnetic symmetry, the occupied bands and the proposed superconducting state must be specified separately. [R1](#ref-source-ea3e0a10f6917658) [R2](#ref-source-7258aa669504806d) Three questions should remain distinct: whether a specimen has altermagnetic order, whether it becomes intrinsically superconducting, and whether superconducting electrodes induce correlations in a hybrid device. Evidence for one does not establish the others. A 2026 In–CrSb–In experiment provides a concrete proximity platform, so a blanket statement that experimental altermagnet–superconductor systems do not exist is outdated. That device does not establish intrinsic bulk superconductivity in CrSb. [R3](#ref-source-26b1bd116249a6d3) [R4](#ref-source-807f7414e83e5e4c) ## Mathematical assumptions A useful symmetry relation is $E_\uparrow(\mathbf k)=E_\downarrow(R\mathbf k)$ for an appropriate crystal operation $R$. It need not imply $E_\uparrow(\mathbf k)=E_\downarrow(\mathbf k)$. In a simple even-parity texture, $\delta(\mathbf k)=d(\cos k_x-\cos k_y)$ changes sign under a right-angle rotation and vanishes along diagonal directions. This illustrates a possible angular pattern, rather than identifying a material or determining its superconducting gap. [R1](#ref-source-ea3e0a10f6917658) [R2](#ref-source-7258aa669504806d) The Chakraborty–Black-Schaffer construction retains two low-energy states with opposite spins on different sublattices. Its onsite singlet restriction depends on those projected states: opposite spins on the same site are absent from that retained space. A two-component band Hamiltonian must therefore preserve what its components represent. Reading its Pauli matrices as ordinary spin while discarding sublattice information changes the pairing problem. The result should not be promoted to an unconditional ban covering every multiband or strongly hybridized material. [R2](#ref-source-7258aa669504806d) An independent local calculation illustrates the projection explicitly. For spin $\sigma=\pm1$, take $h_\sigma=(\delta+\sigma M)\tau_z+t\tau_x$, with $M>0$, real hybridization $t$ and sublattice Pauli matrices $\tau$. Let $u_\sigma$ be the normalized lower-band eigenvector. An imposed unit onsite singlet has projected magnitude $P=|u_\uparrow^T u_\downarrow|$. When $t=0$ and $|\delta|0$, real hybridization $t$ and sublattice Pauli matrices $\tau$. Let $u_\sigma$ be the normalized lower-band eigenvector. An imposed unit onsite singlet has projected magnitude $P=|u_\uparrow^T u_\downarrow|$. When $t=0$ and $|\delta|