{"id": "valid_commutator_001", "category": "valid_commutator", "question": "Initialize a Lie superalgebra for two bosonic generators: H_0 and B_field. Evaluate the commutator between H_0 and B_field.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[H_0, B_field]"}}
{"id": "trap_grade_mismatch_028", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for commuting observable S_spin together with a bosonic Hamiltonian P_polar. Evaluate the anticommutator between S_spin and P_polar.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_048", "category": "trap_grade_mismatch", "question": "In the exciton regime, construct bosonic generator S_spin, and a bosonic generator H_int. Request a fermionic anticommutator on S_spin and H_int.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_044", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for two bosonic generators: Q_charge and S_spin. Evaluate the anticommutator between Q_charge and S_spin.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_034", "category": "trap_undeclared", "question": "We study a optical lattice system. Set up generators phi_plasma (bosonic) and psi_down (fermionic). Evaluate the anticommutator between psi_down and psi_ghost.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_022", "category": "trap_undeclared", "question": "For a minimal superconductor toy model, declare generators S_spin (bosonic) and d_quark (fermionic). Finally, anticommute S_spin with psi_ghost.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_015", "category": "trap_undeclared", "question": "Let us model a system where bosonic P_polar alongside fermionic c_annih. Evaluate the anticommutator between c_annih and lambda_fake.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_commutator_030", "category": "valid_commutator", "question": "For a minimal exciton toy model, declare commuting observable A_em, and a commuting observable phi_plasma. Request a commutator bracket on A_em and phi_plasma.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[A_em, phi_plasma]"}}
{"id": "trap_grade_mismatch_031", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for two bosonic generators: H_int and E_field. Request a fermionic anticommutator on H_int and E_field.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_046", "category": "trap_grade_mismatch", "question": "For a minimal heavy-ion collision toy model, declare bosonic generator H_int, and a commuting observable B_field. Request a fermionic anticommutator on H_int and B_field.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_006", "category": "valid_commutator", "question": "Let us model a system where two bosonic generators: S_spin and n_density. Finally, evaluate the commutator of S_spin with n_density.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[S_spin, n_density]"}}
{"id": "valid_commutator_023", "category": "valid_commutator", "question": "Create a Lie superalgebra with bosonic field H_int, and a bosonic field Q_charge. Evaluate the commutator between H_int and Q_charge.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[H_int, Q_charge]"}}
{"id": "valid_commutator_039", "category": "valid_commutator", "question": "Begin with a Lie algebra suited to optical lattice physics: two bosonic generators: B_field and phi_plasma. Finally, evaluate the commutator of B_field with phi_plasma.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[B_field, phi_plasma]"}}
{"id": "valid_commutator_010", "category": "valid_commutator", "question": "We study a QCD system. Set up bosonic field n_density, and a bosonic generator T_stress. Compute the commutator [ n_density, T_stress ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[n_density, T_stress]"}}
{"id": "trap_undeclared_012", "category": "trap_undeclared", "question": "Initialize a Lie superalgebra for bosonic n_density alongside fermionic f_lepton. Compute [ n_density, eta_phantom ] even though eta_phantom was not declared.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_036", "category": "trap_grade_mismatch", "question": "In the plasma regime, construct commuting observable E_field, and a bosonic generator T_stress. Request a fermionic anticommutator on E_field and T_stress.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_002", "category": "trap_undeclared", "question": "For a minimal heavy-ion collision toy model, declare a bosonic generator n_density and a Grassmann generator psi_i. Finally, take the commutator of n_density with the auxiliary field psi_ghost.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_046", "category": "trap_undeclared", "question": "Let us model a system where bosonic H_int alongside fermionic psi_ex. Compute [ psi_ex, psi_ghost ] even though psi_ghost was not declared.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_018", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for two fermionic generators: d_quark and psi_i. Evaluate the commutator between d_quark and psi_i.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_035", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for fermionic fields b_hole and psi_up. Evaluate the anticommutator between b_hole and psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{b_hole, psi_up}"}}
{"id": "valid_anticommutator_041", "category": "valid_anticommutator", "question": "We study a superconductor system. Set up fermionic field psi_e and fermionic creation-like field c_annih. Evaluate the anticommutator between psi_e and c_annih.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_e, c_annih}"}}
{"id": "valid_anticommutator_017", "category": "valid_anticommutator", "question": "Begin with a Lie algebra suited to spin chain physics: fermionic creation-like field f_lepton and fermionic operator psi_up. Request an anticommutator bracket on f_lepton and psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{f_lepton, psi_up}"}}
{"id": "valid_anticommutator_030", "category": "valid_anticommutator", "question": "Let us model a system where two fermionic generators: a_electron and b_hole. Request an anticommutator bracket on a_electron and b_hole.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{a_electron, b_hole}"}}
{"id": "valid_anticommutator_038", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for fermionic fields d_quark and c_annih. Evaluate the anticommutator between d_quark and c_annih.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{d_quark, c_annih}"}}
{"id": "valid_anticommutator_050", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for fermionic field psi_i and Grassmann generator psi_up. Evaluate the anticommutator between psi_i and psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_i, psi_up}"}}
{"id": "valid_commutator_020", "category": "valid_commutator", "question": "Let us model a system where two bosonic generators: S_spin and n_density. Request a commutator bracket on S_spin and n_density.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[S_spin, n_density]"}}
{"id": "trap_undeclared_001", "category": "trap_undeclared", "question": "Begin with a Lie algebra suited to plasma physics: generators phi_plasma (bosonic) and d_quark (fermionic). Compute { d_quark, xi_aux } using the undeclared field xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_020", "category": "trap_grade_mismatch", "question": "Initialize a Lie superalgebra for two bosonic generators: P_polar and B_field. Evaluate the anticommutator between P_polar and B_field.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_016", "category": "trap_grade_mismatch", "question": "We study a exciton system. Set up two bosonic generators: J_current and Q_charge. Request a fermionic anticommutator on J_current and Q_charge.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_032", "category": "trap_undeclared", "question": "Initialize a Lie superalgebra for a bosonic Hamiltonian H_0 and a fermionic creation-like field a_electron. Finally, anticommute H_0 with xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_045", "category": "valid_anticommutator", "question": "Begin with a Lie algebra suited to condensed matter physics: two fermionic generators: psi_up and a_electron. Request an anticommutator bracket on psi_up and a_electron.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_up, a_electron}"}}
{"id": "valid_commutator_022", "category": "valid_commutator", "question": "In the spin chain regime, construct commuting observable J_current, and a commuting observable S_spin. Compute the commutator [ J_current, S_spin ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[J_current, S_spin]"}}
{"id": "trap_grade_mismatch_009", "category": "trap_grade_mismatch", "question": "Let us model a system where fermionic fields b_hole and psi_e. Evaluate the commutator between b_hole and psi_e.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_026", "category": "valid_anticommutator", "question": "In the condensed matter regime, construct fermionic field b_hole and fermionic operator d_quark. Finally, evaluate the anticommutator of b_hole with d_quark.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{b_hole, d_quark}"}}
{"id": "trap_undeclared_025", "category": "trap_undeclared", "question": "We study a condensed matter system. Set up bosonic phi_plasma alongside fermionic psi_up. Compute { psi_up, omega_spur } using the undeclared field omega_spur.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_041", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for two bosonic generators: Q_charge and n_density. Compute { Q_charge, n_density } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_039", "category": "trap_undeclared", "question": "Begin with a Lie algebra suited to optical lattice physics: generators T_stress (bosonic) and psi_down (fermionic). Finally, anticommute T_stress with xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_commutator_018", "category": "valid_commutator", "question": "Define a bosonic field and fermionic operators for bosonic Hamiltonian phi_plasma together with a bosonic generator Q_charge. Evaluate the commutator between phi_plasma and Q_charge.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[phi_plasma, Q_charge]"}}
{"id": "trap_undeclared_013", "category": "trap_undeclared", "question": "Begin with a Lie algebra suited to spin chain physics: generators T_stress (bosonic) and d_creator (fermionic). Compute { d_creator, chi_dark } using the undeclared field chi_dark.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_commutator_029", "category": "valid_commutator", "question": "Let us model a system where commuting observable n_density, and a bosonic Hamiltonian A_em. Evaluate the commutator between n_density and A_em.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[n_density, A_em]"}}
{"id": "trap_grade_mismatch_008", "category": "trap_grade_mismatch", "question": "Begin with a Lie algebra suited to QCD physics: two fermionic generators: b_hole and d_creator. Evaluate the commutator between b_hole and d_creator.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_036", "category": "valid_anticommutator", "question": "For a minimal exciton toy model, declare two fermionic generators: d_quark and c_quark. Finally, evaluate the anticommutator of d_quark with c_quark.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{d_quark, c_quark}"}}
{"id": "valid_commutator_005", "category": "valid_commutator", "question": "Let us model a system where two bosonic generators: H_int and T_stress. Finally, evaluate the commutator of H_int with T_stress.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[H_int, T_stress]"}}
{"id": "trap_undeclared_010", "category": "trap_undeclared", "question": "Let us model a system where bosonic A_em alongside fermionic psi_down. Compute { psi_down, chi_dark } using the undeclared field chi_dark.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_009", "category": "trap_undeclared", "question": "We study a QCD system. Set up bosonic n_density alongside fermionic c_annih. Evaluate the commutator between n_density and xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_003", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for Grassmann generator psi_e and fermionic creation-like field psi_up. Finally, evaluate the anticommutator of psi_e with psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_e, psi_up}"}}
{"id": "valid_anticommutator_047", "category": "valid_anticommutator", "question": "Define a bosonic field and fermionic operators for two fermionic generators: d_creator and psi_i. Evaluate the anticommutator between d_creator and psi_i.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{d_creator, psi_i}"}}
{"id": "valid_commutator_036", "category": "valid_commutator", "question": "In the superconductor regime, construct bosonic field A_em together with a bosonic generator J_current. Compute the commutator [ A_em, J_current ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[A_em, J_current]"}}
{"id": "trap_grade_mismatch_006", "category": "trap_grade_mismatch", "question": "Initialize a Lie superalgebra for two fermionic generators: d_quark and c_quark. Evaluate the commutator between d_quark and c_quark.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_004", "category": "valid_commutator", "question": "In the plasma regime, construct bosonic generator phi_plasma, and a bosonic field T_stress. Finally, evaluate the commutator of phi_plasma with T_stress.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[phi_plasma, T_stress]"}}
{"id": "trap_undeclared_031", "category": "trap_undeclared", "question": "Begin with a Lie algebra suited to plasma physics: bosonic S_spin alongside fermionic f_lepton. Compute { S_spin, eta_phantom } using the undeclared field eta_phantom.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_021", "category": "trap_undeclared", "question": "For a minimal superconductor toy model, declare a commuting observable n_density and a fermionic operator d_quark. Finally, anticommute d_quark with eta_phantom.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_006", "category": "valid_anticommutator", "question": "Create a Lie superalgebra with Grassmann generator a_electron and Grassmann generator psi_up. Request an anticommutator bracket on a_electron and psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{a_electron, psi_up}"}}
{"id": "valid_commutator_026", "category": "valid_commutator", "question": "Let us model a system where commuting observable A_em together with a bosonic generator H_int. Request a commutator bracket on A_em and H_int.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[A_em, H_int]"}}
{"id": "valid_commutator_049", "category": "valid_commutator", "question": "For a minimal plasma toy model, declare bosonic generator J_current, and a bosonic generator A_em. Finally, evaluate the commutator of J_current with A_em.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[J_current, A_em]"}}
{"id": "trap_grade_mismatch_005", "category": "trap_grade_mismatch", "question": "In the condensed matter regime, construct bosonic Hamiltonian H_int together with a bosonic field E_field. Compute { H_int, E_field } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_029", "category": "trap_grade_mismatch", "question": "Let us model a system where fermionic creation-like field a_electron and fermionic operator d_creator. Compute the commutator [ a_electron, d_creator ] for these fermionic fields.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_014", "category": "trap_undeclared", "question": "Define a bosonic field and fermionic operators for a commuting observable E_field and a fermionic field b_hole. Compute { b_hole, psi_ghost } using the undeclared field psi_ghost.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_027", "category": "trap_undeclared", "question": "For a minimal exciton toy model, declare generators n_density (bosonic) and f_lepton (fermionic). Finally, take the commutator of n_density with the auxiliary field xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_commutator_009", "category": "valid_commutator", "question": "We study a optical lattice system. Set up two bosonic generators: A_em and J_current. Compute the commutator [ A_em, J_current ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[A_em, J_current]"}}
{"id": "trap_undeclared_040", "category": "trap_undeclared", "question": "For a minimal condensed matter toy model, declare bosonic T_stress alongside fermionic b_hole. Compute { b_hole, eta_phantom } using the undeclared field eta_phantom.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_019", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for fermionic fields a_electron and psi_up. Request an anticommutator bracket on a_electron and psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{a_electron, psi_up}"}}
{"id": "valid_anticommutator_005", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for two fermionic generators: psi_up and psi_ex. Compute the anticommutator { psi_up, psi_ex }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_up, psi_ex}"}}
{"id": "valid_commutator_002", "category": "valid_commutator", "question": "Create a Lie superalgebra with bosonic Hamiltonian P_polar, and a bosonic Hamiltonian T_stress. Compute the commutator [ P_polar, T_stress ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[P_polar, T_stress]"}}
{"id": "trap_grade_mismatch_010", "category": "trap_grade_mismatch", "question": "For a minimal exciton toy model, declare fermionic fields psi_up and psi_e. Request a bosonic-style commutator on psi_up and psi_e.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_011", "category": "valid_anticommutator", "question": "Let us model a system where fermionic creation-like field d_creator and fermionic field psi_e. Request an anticommutator bracket on d_creator and psi_e.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{d_creator, psi_e}"}}
{"id": "valid_anticommutator_043", "category": "valid_anticommutator", "question": "For a minimal heavy-ion collision toy model, declare two fermionic generators: psi_i and c_annih. Evaluate the anticommutator between psi_i and c_annih.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_i, c_annih}"}}
{"id": "valid_commutator_037", "category": "valid_commutator", "question": "Let us model a system where two bosonic generators: n_density and Q_charge. Evaluate the commutator between n_density and Q_charge.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[n_density, Q_charge]"}}
{"id": "valid_anticommutator_020", "category": "valid_anticommutator", "question": "In the heavy-ion collision regime, construct fermionic fields psi_e and a_electron. Compute the anticommutator { psi_e, a_electron }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_e, a_electron}"}}
{"id": "valid_anticommutator_046", "category": "valid_anticommutator", "question": "Create a Lie superalgebra with two fermionic generators: psi_down and c_annih. Compute the anticommutator { psi_down, c_annih }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_down, c_annih}"}}
{"id": "valid_commutator_046", "category": "valid_commutator", "question": "Define a bosonic field and fermionic operators for commuting observable A_em, and a bosonic Hamiltonian phi_plasma. Finally, evaluate the commutator of A_em with phi_plasma.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[A_em, phi_plasma]"}}
{"id": "valid_commutator_028", "category": "valid_commutator", "question": "Initialize a Lie superalgebra for commuting observable A_em together with a bosonic field S_spin. Compute the commutator [ A_em, S_spin ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[A_em, S_spin]"}}
{"id": "trap_grade_mismatch_040", "category": "trap_grade_mismatch", "question": "In the superconductor regime, construct fermionic fields f_lepton and d_creator. Request a bosonic-style commutator on f_lepton and d_creator.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_009", "category": "valid_anticommutator", "question": "Create a Lie superalgebra with fermionic fields c_quark and psi_ex. Evaluate the anticommutator between c_quark and psi_ex.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{c_quark, psi_ex}"}}
{"id": "trap_grade_mismatch_012", "category": "trap_grade_mismatch", "question": "Create a Lie superalgebra with fermionic fields b_hole and c_annih. Compute the commutator [ b_hole, c_annih ] for these fermionic fields.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_011", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for two bosonic generators: n_density and H_int. Request a fermionic anticommutator on n_density and H_int.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_043", "category": "trap_undeclared", "question": "We study a spin chain system. Set up generators S_spin (bosonic) and psi_e (fermionic). Compute [ S_spin, xi_aux ] even though xi_aux was not declared.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_commutator_003", "category": "valid_commutator", "question": "For a minimal plasma toy model, declare two bosonic generators: E_field and A_em. Finally, evaluate the commutator of E_field with A_em.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[E_field, A_em]"}}
{"id": "valid_anticommutator_031", "category": "valid_anticommutator", "question": "We study a QCD system. Set up fermionic fields a_electron and psi_ex. Finally, evaluate the anticommutator of a_electron with psi_ex.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{a_electron, psi_ex}"}}
{"id": "trap_undeclared_050", "category": "trap_undeclared", "question": "In the condensed matter regime, construct bosonic phi_plasma alongside fermionic d_quark. Compute [ d_quark, xi_aux ] even though xi_aux was not declared.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_034", "category": "valid_anticommutator", "question": "We study a superconductor system. Set up fermionic operator f_lepton and fermionic field d_quark. Compute the anticommutator { f_lepton, d_quark }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{f_lepton, d_quark}"}}
{"id": "trap_undeclared_003", "category": "trap_undeclared", "question": "Define a bosonic field and fermionic operators for bosonic J_current alongside fermionic d_quark. Compute { J_current, psi_ghost } using the undeclared field psi_ghost.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_008", "category": "trap_undeclared", "question": "Create a Lie superalgebra with a commuting observable S_spin and a fermionic operator psi_ex. Evaluate the commutator between S_spin and xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_014", "category": "valid_anticommutator", "question": "We study a heavy-ion collision system. Set up fermionic fields d_quark and c_quark. Request an anticommutator bracket on d_quark and c_quark.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{d_quark, c_quark}"}}
{"id": "valid_anticommutator_040", "category": "valid_anticommutator", "question": "Define a bosonic field and fermionic operators for two fermionic generators: c_quark and f_lepton. Compute the anticommutator { c_quark, f_lepton }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{c_quark, f_lepton}"}}
{"id": "valid_commutator_025", "category": "valid_commutator", "question": "Initialize a Lie superalgebra for bosonic field J_current, and a commuting observable n_density. Request a commutator bracket on J_current and n_density.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[J_current, n_density]"}}
{"id": "trap_grade_mismatch_045", "category": "trap_grade_mismatch", "question": "For a minimal optical lattice toy model, declare two fermionic generators: d_quark and c_quark. Evaluate the commutator between d_quark and c_quark.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_024", "category": "valid_anticommutator", "question": "Let us model a system where fermionic operator f_lepton and fermionic operator c_quark. Compute the anticommutator { f_lepton, c_quark }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{f_lepton, c_quark}"}}
{"id": "trap_grade_mismatch_019", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for fermionic field c_annih and fermionic creation-like field psi_down. Compute the commutator [ c_annih, psi_down ] for these fermionic fields.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_044", "category": "trap_undeclared", "question": "Let us model a system where bosonic H_int alongside fermionic f_lepton. Finally, anticommute H_int with omega_spur.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_049", "category": "valid_anticommutator", "question": "Begin with a Lie algebra suited to superconductor physics: fermionic fields c_annih and d_quark. Compute the anticommutator { c_annih, d_quark }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{c_annih, d_quark}"}}
{"id": "trap_undeclared_026", "category": "trap_undeclared", "question": "Initialize a Lie superalgebra for a commuting observable n_density and a Grassmann generator psi_i. Finally, take the commutator of psi_i with the auxiliary field chi_dark.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_029", "category": "valid_anticommutator", "question": "For a minimal plasma toy model, declare two fermionic generators: f_lepton and psi_up. Finally, evaluate the anticommutator of f_lepton with psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{f_lepton, psi_up}"}}
{"id": "valid_commutator_050", "category": "valid_commutator", "question": "For a minimal optical lattice toy model, declare bosonic generator J_current, and a bosonic Hamiltonian E_field. Finally, evaluate the commutator of J_current with E_field.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[J_current, E_field]"}}
{"id": "valid_commutator_038", "category": "valid_commutator", "question": "We study a exciton system. Set up bosonic field E_field, and a bosonic generator A_em. Compute the commutator [ E_field, A_em ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[E_field, A_em]"}}
{"id": "valid_commutator_007", "category": "valid_commutator", "question": "Let us model a system where bosonic Hamiltonian P_polar together with a bosonic field A_em. Evaluate the commutator between P_polar and A_em.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[P_polar, A_em]"}}
{"id": "valid_commutator_013", "category": "valid_commutator", "question": "We study a condensed matter system. Set up commuting observable S_spin together with a commuting observable E_field. Compute the commutator [ S_spin, E_field ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[S_spin, E_field]"}}
{"id": "trap_grade_mismatch_037", "category": "trap_grade_mismatch", "question": "We study a condensed matter system. Set up Grassmann generator psi_e and Grassmann generator d_creator. Compute the commutator [ psi_e, d_creator ] for these fermionic fields.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_024", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for commuting observable H_int, and a bosonic generator A_em. Compute { H_int, A_em } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_017", "category": "trap_grade_mismatch", "question": "In the spin chain regime, construct fermionic fields d_quark and psi_ex. Evaluate the commutator between d_quark and psi_ex.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_035", "category": "valid_commutator", "question": "Initialize a Lie superalgebra for bosonic Hamiltonian T_stress together with a bosonic Hamiltonian H_int. Finally, evaluate the commutator of T_stress with H_int.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[T_stress, H_int]"}}
{"id": "trap_grade_mismatch_004", "category": "trap_grade_mismatch", "question": "For a minimal condensed matter toy model, declare two bosonic generators: E_field and H_int. Compute { E_field, H_int } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_047", "category": "trap_grade_mismatch", "question": "Begin with a Lie algebra suited to superconductor physics: two fermionic generators: psi_ex and psi_i. Compute the commutator [ psi_ex, psi_i ] for these fermionic fields.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_031", "category": "valid_commutator", "question": "Create a Lie superalgebra with commuting observable phi_plasma together with a bosonic generator T_stress. Finally, evaluate the commutator of phi_plasma with T_stress.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[phi_plasma, T_stress]"}}
{"id": "trap_grade_mismatch_038", "category": "trap_grade_mismatch", "question": "For a minimal spin chain toy model, declare two bosonic generators: T_stress and Q_charge. Compute { T_stress, Q_charge } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_014", "category": "valid_commutator", "question": "Let us model a system where bosonic Hamiltonian E_field, and a bosonic Hamiltonian n_density. Compute the commutator [ E_field, n_density ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[E_field, n_density]"}}
{"id": "valid_anticommutator_022", "category": "valid_anticommutator", "question": "For a minimal QCD toy model, declare fermionic fields psi_e and d_quark. Finally, evaluate the anticommutator of psi_e with d_quark.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_e, d_quark}"}}
{"id": "valid_anticommutator_016", "category": "valid_anticommutator", "question": "For a minimal QCD toy model, declare fermionic field psi_ex and fermionic field c_quark. Request an anticommutator bracket on psi_ex and c_quark.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_ex, c_quark}"}}
{"id": "valid_commutator_048", "category": "valid_commutator", "question": "Begin with a Lie algebra suited to heavy-ion collision physics: bosonic generator A_em, and a bosonic generator S_spin. Compute the commutator [ A_em, S_spin ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[A_em, S_spin]"}}
{"id": "valid_anticommutator_048", "category": "valid_anticommutator", "question": "Begin with a Lie algebra suited to QCD physics: fermionic creation-like field psi_e and Grassmann generator a_electron. Compute the anticommutator { psi_e, a_electron }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_e, a_electron}"}}
{"id": "valid_commutator_017", "category": "valid_commutator", "question": "We study a QCD system. Set up two bosonic generators: n_density and H_0. Finally, evaluate the commutator of n_density with H_0.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[n_density, H_0]"}}
{"id": "valid_anticommutator_002", "category": "valid_anticommutator", "question": "Let us model a system where fermionic fields psi_down and psi_up. Evaluate the anticommutator between psi_down and psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_down, psi_up}"}}
{"id": "valid_commutator_045", "category": "valid_commutator", "question": "Initialize a Lie superalgebra for bosonic field H_0 together with a bosonic Hamiltonian Q_charge. Request a commutator bracket on H_0 and Q_charge.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[H_0, Q_charge]"}}
{"id": "trap_undeclared_018", "category": "trap_undeclared", "question": "Define a bosonic field and fermionic operators for generators P_polar (bosonic) and d_creator (fermionic). Evaluate the anticommutator between d_creator and chi_dark.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_044", "category": "valid_anticommutator", "question": "We study a QCD system. Set up fermionic operator psi_ex and fermionic field psi_down. Request an anticommutator bracket on psi_ex and psi_down.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_ex, psi_down}"}}
{"id": "trap_undeclared_019", "category": "trap_undeclared", "question": "Begin with a Lie algebra suited to heavy-ion collision physics: bosonic P_polar alongside fermionic psi_ex. Compute { P_polar, eta_phantom } using the undeclared field eta_phantom.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_042", "category": "valid_anticommutator", "question": "Begin with a Lie algebra suited to superconductor physics: Grassmann generator b_hole and fermionic field c_annih. Finally, evaluate the anticommutator of b_hole with c_annih.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{b_hole, c_annih}"}}
{"id": "trap_grade_mismatch_027", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for bosonic Hamiltonian n_density, and a bosonic Hamiltonian S_spin. Compute { n_density, S_spin } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_038", "category": "trap_undeclared", "question": "Let us model a system where a bosonic generator S_spin and a fermionic field b_hole. Finally, take the commutator of S_spin with the auxiliary field psi_phonon.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_030", "category": "trap_undeclared", "question": "For a minimal spin chain toy model, declare generators P_polar (bosonic) and c_annih (fermionic). Compute { c_annih, chi_dark } using the undeclared field chi_dark.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_036", "category": "trap_undeclared", "question": "Begin with a Lie algebra suited to spin chain physics: generators E_field (bosonic) and psi_i (fermionic). Evaluate the commutator between E_field and psi_phonon.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_030", "category": "trap_grade_mismatch", "question": "Initialize a Lie superalgebra for bosonic Hamiltonian B_field, and a bosonic generator T_stress. Request a fermionic anticommutator on B_field and T_stress.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_027", "category": "valid_commutator", "question": "Let us model a system where two bosonic generators: S_spin and H_0. Finally, evaluate the commutator of S_spin with H_0.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[S_spin, H_0]"}}
{"id": "valid_anticommutator_010", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for fermionic fields a_electron and d_creator. Compute the anticommutator { a_electron, d_creator }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{a_electron, d_creator}"}}
{"id": "valid_anticommutator_012", "category": "valid_anticommutator", "question": "Let us model a system where fermionic fields psi_up and c_quark. Finally, evaluate the anticommutator of psi_up with c_quark.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_up, c_quark}"}}
{"id": "trap_undeclared_041", "category": "trap_undeclared", "question": "In the spin chain regime, construct a bosonic field Q_charge and a fermionic creation-like field d_creator. Evaluate the anticommutator between Q_charge and xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_007", "category": "valid_anticommutator", "question": "Begin with a Lie algebra suited to optical lattice physics: two fermionic generators: b_hole and c_annih. Compute the anticommutator { b_hole, c_annih }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{b_hole, c_annih}"}}
{"id": "valid_commutator_041", "category": "valid_commutator", "question": "Initialize a Lie superalgebra for bosonic generator S_spin together with a commuting observable Q_charge. Evaluate the commutator between S_spin and Q_charge.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[S_spin, Q_charge]"}}
{"id": "valid_commutator_016", "category": "valid_commutator", "question": "We study a plasma system. Set up bosonic generator J_current together with a bosonic Hamiltonian H_int. Request a commutator bracket on J_current and H_int.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[J_current, H_int]"}}
{"id": "trap_grade_mismatch_039", "category": "trap_grade_mismatch", "question": "We study a optical lattice system. Set up two bosonic generators: S_spin and T_stress. Evaluate the anticommutator between S_spin and T_stress.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_017", "category": "trap_undeclared", "question": "Create a Lie superalgebra with bosonic H_0 alongside fermionic psi_e. Finally, take the commutator of psi_e with the auxiliary field omega_spur.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_027", "category": "valid_anticommutator", "question": "We study a exciton system. Set up two fermionic generators: psi_down and psi_e. Compute the anticommutator { psi_down, psi_e }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_down, psi_e}"}}
{"id": "trap_undeclared_004", "category": "trap_undeclared", "question": "For a minimal heavy-ion collision toy model, declare generators H_int (bosonic) and b_hole (fermionic). Compute { H_int, omega_spur } using the undeclared field omega_spur.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_013", "category": "valid_anticommutator", "question": "For a minimal heavy-ion collision toy model, declare two fermionic generators: psi_down and psi_up. Request an anticommutator bracket on psi_down and psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_down, psi_up}"}}
{"id": "trap_undeclared_024", "category": "trap_undeclared", "question": "In the plasma regime, construct bosonic B_field alongside fermionic b_hole. Evaluate the anticommutator between b_hole and psi_ghost.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_007", "category": "trap_grade_mismatch", "question": "Begin with a Lie algebra suited to QCD physics: two fermionic generators: psi_down and c_annih. Compute the commutator [ psi_down, c_annih ] for these fermionic fields.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_025", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for two fermionic generators: psi_down and psi_ex. Evaluate the anticommutator between psi_down and psi_ex.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_down, psi_ex}"}}
{"id": "trap_undeclared_028", "category": "trap_undeclared", "question": "Begin with a Lie algebra suited to optical lattice physics: a bosonic generator P_polar and a fermionic creation-like field c_quark. Evaluate the commutator between P_polar and psi_phonon.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_047", "category": "trap_undeclared", "question": "Create a Lie superalgebra with generators S_spin (bosonic) and f_lepton (fermionic). Compute { S_spin, psi_phonon } using the undeclared field psi_phonon.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_007", "category": "trap_undeclared", "question": "Define a bosonic field and fermionic operators for generators H_0 (bosonic) and c_quark (fermionic). Finally, take the commutator of c_quark with the auxiliary field xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_004", "category": "valid_anticommutator", "question": "We study a optical lattice system. Set up fermionic fields d_creator and psi_i. Request an anticommutator bracket on d_creator and psi_i.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{d_creator, psi_i}"}}
{"id": "valid_anticommutator_018", "category": "valid_anticommutator", "question": "For a minimal spin chain toy model, declare fermionic fields psi_down and psi_e. Finally, evaluate the anticommutator of psi_down with psi_e.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_down, psi_e}"}}
{"id": "valid_commutator_012", "category": "valid_commutator", "question": "For a minimal condensed matter toy model, declare commuting observable J_current together with a bosonic field n_density. Compute the commutator [ J_current, n_density ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[J_current, n_density]"}}
{"id": "trap_grade_mismatch_013", "category": "trap_grade_mismatch", "question": "For a minimal spin chain toy model, declare bosonic Hamiltonian J_current, and a bosonic generator P_polar. Compute { J_current, P_polar } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_008", "category": "valid_commutator", "question": "We study a condensed matter system. Set up commuting observable H_int, and a bosonic generator T_stress. Finally, evaluate the commutator of H_int with T_stress.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[H_int, T_stress]"}}
{"id": "valid_commutator_011", "category": "valid_commutator", "question": "We study a plasma system. Set up two bosonic generators: Q_charge and T_stress. Finally, evaluate the commutator of Q_charge with T_stress.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[Q_charge, T_stress]"}}
{"id": "trap_undeclared_045", "category": "trap_undeclared", "question": "We study a superconductor system. Set up a bosonic generator H_0 and a Grassmann generator psi_ex. Finally, anticommute H_0 with xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_anticommutator_037", "category": "valid_anticommutator", "question": "In the heavy-ion collision regime, construct fermionic fields psi_up and c_annih. Request an anticommutator bracket on psi_up and c_annih.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_up, c_annih}"}}
{"id": "trap_grade_mismatch_003", "category": "trap_grade_mismatch", "question": "In the plasma regime, construct fermionic fields psi_down and b_hole. Evaluate the commutator between psi_down and b_hole.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_022", "category": "trap_grade_mismatch", "question": "Define a bosonic field and fermionic operators for two bosonic generators: P_polar and phi_plasma. Compute { P_polar, phi_plasma } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_049", "category": "trap_undeclared", "question": "We study a superconductor system. Set up bosonic J_current alongside fermionic d_creator. Compute [ J_current, nu_shadow ] even though nu_shadow was not declared.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_002", "category": "trap_grade_mismatch", "question": "For a minimal optical lattice toy model, declare commuting observable S_spin, and a bosonic generator J_current. Compute { S_spin, J_current } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_044", "category": "valid_commutator", "question": "Define a bosonic field and fermionic operators for commuting observable Q_charge, and a bosonic field P_polar. Finally, evaluate the commutator of Q_charge with P_polar.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[Q_charge, P_polar]"}}
{"id": "trap_grade_mismatch_026", "category": "trap_grade_mismatch", "question": "Let us model a system where bosonic field J_current, and a bosonic field Q_charge. Compute { J_current, Q_charge } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_024", "category": "valid_commutator", "question": "Create a Lie superalgebra with two bosonic generators: A_em and H_int. Compute the commutator [ A_em, H_int ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[A_em, H_int]"}}
{"id": "trap_undeclared_037", "category": "trap_undeclared", "question": "Begin with a Lie algebra suited to plasma physics: bosonic S_spin alongside fermionic d_creator. Evaluate the commutator between d_creator and xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_021", "category": "trap_grade_mismatch", "question": "Begin with a Lie algebra suited to superconductor physics: commuting observable A_em together with a commuting observable Q_charge. Compute { A_em, Q_charge } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_033", "category": "trap_grade_mismatch", "question": "In the plasma regime, construct bosonic Hamiltonian Q_charge, and a bosonic generator A_em. Evaluate the anticommutator between Q_charge and A_em.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_021", "category": "valid_anticommutator", "question": "Create a Lie superalgebra with fermionic operator a_electron and fermionic creation-like field psi_down. Request an anticommutator bracket on a_electron and psi_down.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{a_electron, psi_down}"}}
{"id": "trap_grade_mismatch_032", "category": "trap_grade_mismatch", "question": "For a minimal plasma toy model, declare commuting observable H_0 together with a bosonic generator J_current. Request a fermionic anticommutator on H_0 and J_current.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_001", "category": "valid_anticommutator", "question": "Create a Lie superalgebra with fermionic fields psi_down and d_quark. Finally, evaluate the anticommutator of psi_down with d_quark.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_down, d_quark}"}}
{"id": "valid_anticommutator_015", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for fermionic fields c_annih and d_quark. Evaluate the anticommutator between c_annih and d_quark.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{c_annih, d_quark}"}}
{"id": "valid_commutator_021", "category": "valid_commutator", "question": "For a minimal QCD toy model, declare two bosonic generators: B_field and E_field. Finally, evaluate the commutator of B_field with E_field.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[B_field, E_field]"}}
{"id": "valid_anticommutator_023", "category": "valid_anticommutator", "question": "For a minimal optical lattice toy model, declare fermionic fields a_electron and d_quark. Evaluate the anticommutator between a_electron and d_quark.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{a_electron, d_quark}"}}
{"id": "trap_grade_mismatch_023", "category": "trap_grade_mismatch", "question": "Let us model a system where bosonic generator E_field, and a bosonic Hamiltonian H_int. Compute { E_field, H_int } for these bosonic generators.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_050", "category": "trap_grade_mismatch", "question": "In the optical lattice regime, construct fermionic fields psi_up and psi_ex. Compute the commutator [ psi_up, psi_ex ] for these fermionic fields.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_008", "category": "valid_anticommutator", "question": "In the exciton regime, construct two fermionic generators: d_quark and psi_up. Finally, evaluate the anticommutator of d_quark with psi_up.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{d_quark, psi_up}"}}
{"id": "valid_anticommutator_033", "category": "valid_anticommutator", "question": "In the optical lattice regime, construct fermionic field psi_e and fermionic creation-like field b_hole. Finally, evaluate the anticommutator of psi_e with b_hole.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_e, b_hole}"}}
{"id": "valid_commutator_042", "category": "valid_commutator", "question": "We study a exciton system. Set up bosonic Hamiltonian J_current together with a bosonic Hamiltonian T_stress. Compute the commutator [ J_current, T_stress ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[J_current, T_stress]"}}
{"id": "valid_commutator_043", "category": "valid_commutator", "question": "For a minimal superconductor toy model, declare bosonic Hamiltonian phi_plasma, and a bosonic Hamiltonian n_density. Compute the commutator [ phi_plasma, n_density ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[phi_plasma, n_density]"}}
{"id": "valid_anticommutator_028", "category": "valid_anticommutator", "question": "Initialize a Lie superalgebra for two fermionic generators: psi_down and d_creator. Evaluate the anticommutator between psi_down and d_creator.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{psi_down, d_creator}"}}
{"id": "valid_commutator_040", "category": "valid_commutator", "question": "Let us model a system where bosonic Hamiltonian phi_plasma together with a bosonic field B_field. Finally, evaluate the commutator of phi_plasma with B_field.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[phi_plasma, B_field]"}}
{"id": "trap_grade_mismatch_049", "category": "trap_grade_mismatch", "question": "In the QCD regime, construct bosonic field H_int together with a bosonic field A_em. Evaluate the anticommutator between H_int and A_em.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_commutator_032", "category": "valid_commutator", "question": "Begin with a Lie algebra suited to spin chain physics: bosonic field S_spin together with a bosonic field E_field. Compute the commutator [ S_spin, E_field ].", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[S_spin, E_field]"}}
{"id": "valid_commutator_015", "category": "valid_commutator", "question": "For a minimal spin chain toy model, declare two bosonic generators: P_polar and H_int. Finally, evaluate the commutator of P_polar with H_int.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[P_polar, H_int]"}}
{"id": "trap_undeclared_029", "category": "trap_undeclared", "question": "Initialize a Lie superalgebra for bosonic n_density alongside fermionic psi_i. Finally, anticommute psi_i with psi_phonon.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_011", "category": "trap_undeclared", "question": "Define a bosonic field and fermionic operators for bosonic P_polar alongside fermionic psi_down. Finally, anticommute psi_down with nu_shadow.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "valid_commutator_034", "category": "valid_commutator", "question": "Let us model a system where two bosonic generators: H_0 and E_field. Evaluate the commutator between H_0 and E_field.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[H_0, E_field]"}}
{"id": "valid_commutator_047", "category": "valid_commutator", "question": "We study a spin chain system. Set up bosonic field J_current together with a bosonic Hamiltonian A_em. Evaluate the commutator between J_current and A_em.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[J_current, A_em]"}}
{"id": "trap_grade_mismatch_001", "category": "trap_grade_mismatch", "question": "In the condensed matter regime, construct fermionic fields c_annih and psi_e. Evaluate the commutator between c_annih and psi_e.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_014", "category": "trap_grade_mismatch", "question": "For a minimal exciton toy model, declare fermionic field c_annih and Grassmann generator d_creator. Request a bosonic-style commutator on c_annih and d_creator.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_042", "category": "trap_undeclared", "question": "Define a bosonic field and fermionic operators for generators H_int (bosonic) and c_annih (fermionic). Finally, take the commutator of H_int with the auxiliary field omega_spur.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_042", "category": "trap_grade_mismatch", "question": "Create a Lie superalgebra with Grassmann generator d_creator and fermionic field a_electron. Evaluate the commutator between d_creator and a_electron.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_039", "category": "valid_anticommutator", "question": "Begin with a Lie algebra suited to QCD physics: Grassmann generator c_quark and Grassmann generator c_annih. Compute the anticommutator { c_quark, c_annih }.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{c_quark, c_annih}"}}
{"id": "trap_undeclared_033", "category": "trap_undeclared", "question": "Define a bosonic field and fermionic operators for generators H_0 (bosonic) and f_lepton (fermionic). Evaluate the anticommutator between H_0 and eta_phantom.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_025", "category": "trap_grade_mismatch", "question": "For a minimal plasma toy model, declare bosonic Hamiltonian A_em, and a bosonic generator T_stress. Evaluate the anticommutator between A_em and T_stress.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_undeclared_020", "category": "trap_undeclared", "question": "Let us model a system where generators J_current (bosonic) and psi_up (fermionic). Compute { psi_up, chi_dark } using the undeclared field chi_dark.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_016", "category": "trap_undeclared", "question": "Initialize a Lie superalgebra for a bosonic Hamiltonian A_em and a fermionic creation-like field d_creator. Finally, take the commutator of A_em with the auxiliary field xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_043", "category": "trap_grade_mismatch", "question": "Create a Lie superalgebra with fermionic fields c_quark and d_creator. Request a bosonic-style commutator on c_quark and d_creator.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_015", "category": "trap_grade_mismatch", "question": "In the QCD regime, construct two fermionic generators: d_creator and c_annih. Request a bosonic-style commutator on d_creator and c_annih.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "valid_anticommutator_032", "category": "valid_anticommutator", "question": "We study a optical lattice system. Set up fermionic fields c_quark and psi_i. Request an anticommutator bracket on c_quark and psi_i.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "{c_quark, psi_i}"}}
{"id": "valid_commutator_033", "category": "valid_commutator", "question": "Create a Lie superalgebra with bosonic generator P_polar, and a bosonic Hamiltonian E_field. Request a commutator bracket on P_polar and E_field.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[P_polar, E_field]"}}
{"id": "valid_commutator_019", "category": "valid_commutator", "question": "Initialize a Lie superalgebra for two bosonic generators: Q_charge and B_field. Evaluate the commutator between Q_charge and B_field.", "scoring_rubric": {"objective_satisfied": true, "quaestro_locked": true, "exit_reason": "objective_satisfied", "min_segments": 2, "quaestro_last_result_contains": "[Q_charge, B_field]"}}
{"id": "trap_undeclared_048", "category": "trap_undeclared", "question": "Begin with a Lie algebra suited to heavy-ion collision physics: a commuting observable J_current and a Grassmann generator a_electron. Evaluate the commutator between J_current and nu_shadow.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_005", "category": "trap_undeclared", "question": "For a minimal spin chain toy model, declare a bosonic Hamiltonian S_spin and a fermionic creation-like field b_hole. Evaluate the commutator between b_hole and xi_aux.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_006", "category": "trap_undeclared", "question": "For a minimal spin chain toy model, declare generators E_field (bosonic) and psi_e (fermionic). Compute { psi_e, nu_shadow } using the undeclared field nu_shadow.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_035", "category": "trap_undeclared", "question": "Initialize a Lie superalgebra for a bosonic generator phi_plasma and a fermionic operator psi_e. Finally, take the commutator of psi_e with the auxiliary field omega_spur.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_undeclared_023", "category": "trap_undeclared", "question": "Initialize a Lie superalgebra for generators B_field (bosonic) and c_quark (fermionic). Finally, anticommute B_field with omega_spur.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_UNDECLARED_GENERATOR"]}}
{"id": "trap_grade_mismatch_035", "category": "trap_grade_mismatch", "question": "Let us model a system where bosonic generator n_density, and a bosonic field H_0. Evaluate the anticommutator between n_density and H_0.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}
{"id": "trap_grade_mismatch_034", "category": "trap_grade_mismatch", "question": "In the optical lattice regime, construct two bosonic generators: phi_plasma and J_current. Evaluate the anticommutator between phi_plasma and J_current.", "scoring_rubric": {"objective_satisfied": false, "quaestro_locked": false, "exit_reason": "unverified_stall", "min_segments": 2, "trap_codes": ["QUAE_GRADE_MISMATCH"]}}