# L5: J3(Os) FREUDENTHAL DETERMINANT

**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING

## Prompt

J3(Os) FREUDENTHAL DETERMINANT
Using SymPy, implement the Freudenthal cubic norm Det(A) for a general 3x3 Hermitian matrix A over Os. Verify Det is cubic in entries. Compute Det for the diagonal mass matrix diag(m_e,m_mu,m_tau). Show Det maps to the product m_e*m_mu*m_tau up to normalization. #SuperGrokTOE #FreudenthalDet #J3