{"_meta":{"battery":"5s","sub_battery":"semantics","version":"v1","task_count":13,"notes":"algebra-symbolic@v1 equivalence-class tests. Polynomial identity collapses; exponential identity collapses (sp.expand handles exp(a+b)=exp(a)exp(b) by default). Trigonometric identity (sin(x)**2+cos(x)**2=1) does NOT collapse at Phase 1 — algebra-symbolic-simplified@v1 (planned Phase-1b) wraps sp.simplify for that surface at unbounded CPU cost."}}
{"id":"5s-sem-algebra-001","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"(x+1)**2","input_b":"x**2 + 2*x + 1","expected_equivalent":true}
{"id":"5s-sem-algebra-002","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"(x+1)**2","input_b":"x*x + 2*x + 1","expected_equivalent":true}
{"id":"5s-sem-algebra-003","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"(a+b)*(a-b)","input_b":"a**2 - b**2","expected_equivalent":true}
{"id":"5s-sem-algebra-004","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"2*x + 3*x","input_b":"5*x","expected_equivalent":true}
{"id":"5s-sem-algebra-005","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"x*(x+1)","input_b":"x**2 + x","expected_equivalent":true}
{"id":"5s-sem-algebra-006","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"(x-1)*(x-2)","input_b":"x**2 - 3*x + 2","expected_equivalent":true}
{"id":"5s-sem-algebra-007","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"a + b","input_b":"b + a","expected_equivalent":true}
{"id":"5s-sem-algebra-008","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"a*b","input_b":"b*a","expected_equivalent":true}
{"id":"5s-sem-algebra-009","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"x**2","input_b":"x**3","expected_equivalent":false}
{"id":"5s-sem-algebra-010","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"x + 1","input_b":"x","expected_equivalent":false}
{"id":"5s-sem-algebra-011","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"a*b","input_b":"a + b","expected_equivalent":false}
{"id":"5s-sem-algebra-012","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"sin(x)**2 + cos(x)**2","input_b":"1","expected_equivalent":false}
{"id":"5s-sem-algebra-013","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"symbolic_algebra","domain":"polynomial","pi_star_ref":"algebra-symbolic@v1","input_a":"exp(a+b)","input_b":"exp(a)*exp(b)","expected_equivalent":true}
