{"_meta":{"battery":"5s","sub_battery":"semantics","version":"v1","task_count":12,"notes":"combinatorics@v1 equivalence-class tests. Equal counts collapse to identical bytes (decimal literal); distinct counts do not. Includes binomial symmetry C(n,k)=C(n,n-k) and Pascal's rule C(n,k) = C(n-1,k-1) + C(n-1,k)."}}
{"id":"5s-sem-comb-001","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"binomial(5,2)","input_b":"10","expected_equivalent":true}
{"id":"5s-sem-comb-002","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"binomial(7,3)","input_b":"binomial(7,4)","expected_equivalent":true}
{"id":"5s-sem-comb-003","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"binomial(7,3)","input_b":"binomial(6,2) + binomial(6,3)","expected_equivalent":true}
{"id":"5s-sem-comb-004","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"factorial(0)","input_b":"1","expected_equivalent":true}
{"id":"5s-sem-comb-005","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"binomial(5,2)","input_b":"factorial(5)/(factorial(2)*factorial(3))","expected_equivalent":true}
{"id":"5s-sem-comb-006","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"catalan(5)","input_b":"binomial(10,5)/(5+1)","expected_equivalent":true}
{"id":"5s-sem-comb-007","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"binomial(0,0)","input_b":"binomial(7,7)","expected_equivalent":true}
{"id":"5s-sem-comb-008","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"binomial(5,7)","input_b":"0","expected_equivalent":true}
{"id":"5s-sem-comb-009","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"factorial(5)","input_b":"factorial(6)","expected_equivalent":false}
{"id":"5s-sem-comb-010","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"binomial(7,2)","input_b":"binomial(8,2)","expected_equivalent":false}
{"id":"5s-sem-comb-011","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"catalan(5)","input_b":"catalan(6)","expected_equivalent":false}
{"id":"5s-sem-comb-012","battery":"5s","sub_battery":"semantics","version":"v1","carrier":"combinatorics","domain":"counting","pi_star_ref":"combinatorics@v1","input_a":"partition(5)","input_b":"partition(7)","expected_equivalent":false}
