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The reference is Algorithm 4.2 on page 40 in this document https://sqisign.org/spec/sqisign-20250707.pdf.

I'm confused by lines 28-33. We have $I_{com,rsp}$ correspond to the isogeny $\varphi_{rsp}^{odd}\circ \varphi_{com}$. If $e'_{rsp} = 0$, then $\varphi_{rsp}=\varphi_{rsp}^{even}\circ \varphi_{rsp}^{odd}$ only has the even-degree component. That means $\varphi_{rsp}^{odd}$ is the identity map on $E_{com}$. In this case, $I_{com, rsp}$ just corresponds to $\varphi_{com}$. What is the point of lines 30-31?

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You are right. Lines 30-31 are redundant, but they don't hurt.

Compare with the corresponding C source (https://github.com/SQISign/the-sqisign/blob/dd133d7aca576c361a270c8e6434832535b42ecc/src/signature/ref/lvlx/sign.c#L593-L602), where we do something less wasteful:

        } else {
            // No 2d isogeny needed, so simulate a "Kani matrix" identity here
            copy_curve(&Eaux2_Echall2.E1, &Ecom_Eaux.E1);
            copy_curve(&Eaux2_Echall2.E2, &Ecom_Eaux.E1);


            reduced_order = sig->two_resp_length;
            ec_dbl_iter_basis(&Eaux2_Echall2.B1, TORSION_EVEN_POWER - reduced_order, &Ecom_Eaux.B1, &Ecom_Eaux.E1);
            ec_dbl_iter_basis(&Eaux2_Echall2.B1, TORSION_EVEN_POWER - reduced_order, &Ecom_Eaux.B1, &Ecom_Eaux.E1);
            copy_basis(&Eaux2_Echall2.B2, &Eaux2_Echall2.B1);
        }
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