What does it mean when the reciprocal condition number is equal to 6.85548e-36 and the system is computationally singular resulting in an error in solve.default(crossprod(attr(x, "gradi")[, !fixed]))?

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The reciprocal condition number indicates the sensitivity of the matrix to changes in its elements. A small value for the reciprocal condition number indicates that the matrix is ill-conditioned or close to singular.

In this case, the very small value of the reciprocal condition number (6.85548e-36) suggests that the matrix is very close to being singular, meaning that there might be linearly dependent columns in the matrix. This condition can cause issues when trying to solve the system of equations, resulting in the error message that you received.

To solve this issue, you may need to investigate the matrix further to see if there are any redundant or near-linearly dependent columns. You may also need to consider using a different method for solving the system of equations or consider adding numerical noise to the matrix to help avoid computational singularities.