fix: add clear error for unsatisfiable ACIR AssertZero opcode (#22417)

## Summary
When an ACIR `AssertZero` opcode has no variables but a non-zero
constant, the circuit is fundamentally unsatisfiable (`nonzero == 0` can
never hold). Previously this hit a generic assertion about empty gates
with no indication of the real problem.

Added an early check in `assert_zero_to_quad_constraints` that detects
this case and produces a clear error: "circuit is unsatisfiable. An
AssertZero opcode contains no variables but has a non-zero constant,
which can never equal zero."

## Test plan
- All 60 existing quad/big-quad constraint tests pass
- Built and ran `dsl_tests` successfully

ClaudeBox log: https://claudebox.work/s/bcd66a8253a37704?run=1

Author: AztecBot

barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_format.test.cpp

@@ -36,8 +36,7 @@ TYPED_TEST(AcirFormatTests, ExpressionWithOnlyConstantTermFails)
         .return_values = {},
     };
 
-    EXPECT_THROW_WITH_MESSAGE(circuit_serde_to_acir_format(circuit),
-                              "split_into_mul_quad_gates: resulted in zero gates.");
+    EXPECT_THROW_WITH_MESSAGE(circuit_serde_to_acir_format(circuit), "circuit is unsatisfiable");
 }
 
 TYPED_TEST(AcirFormatTests, ExpressionWithCancellingCoefficientsFails)

barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_to_constraint_buf.cpp

@@ -571,6 +571,17 @@ void assert_zero_to_quad_constraints(Acir::Opcode::AssertZero const& arg, AcirFo
     };
 
     auto linear_terms = process_linear_terms(arg.value);
+
+    // Check for unsatisfiable constraint: no variables but a non-zero constant means the circuit requires
+    // `constant == 0` which can never be satisfied.
+    if (arg.value.mul_terms.empty() && linear_terms.empty()) {
+        fr constant = from_buffer_with_bound_checks(arg.value.q_c);
+        BB_ASSERT_EQ(constant,
+                     fr::zero(),
+                     "circuit is unsatisfiable. An AssertZero opcode contains no variables but has a non-zero "
+                     "constant, which can never equal zero.");
+    }
+
     bool is_single_gate = is_single_arithmetic_gate(arg.value, linear_terms);
     std::vector<mul_quad_<fr>> mul_quads = split_into_mul_quad_gates(arg.value, linear_terms);
 

barretenberg/cpp/src/barretenberg/dsl/acir_format/arithmetic_constraints.test.cpp

@@ -385,3 +385,26 @@ TYPED_TEST(BigQuadOpcodeGateCountTest, OpcodeGateCount)
 
     EXPECT_EQ(program.constraints.gates_per_opcode, std::vector<size_t>({ BIG_QUAD<TypeParam> }));
 }
+
+TEST(AssertZeroConstraintTest, UnsatisfiableCircuitWithNonZeroConstantOnly)
+{
+    // An AssertZero opcode with no variables and a non-zero constant is fundamentally unsatisfiable:
+    // it asserts `nonzero_constant == 0` which can never hold.
+    Acir::Expression expr{ .q_c = bb::fr::one().to_buffer() };
+    Acir::Opcode::AssertZero assert_zero{ .value = expr };
+    AcirFormat af;
+    EXPECT_THROW_WITH_MESSAGE(
+        assert_zero_to_quad_constraints(assert_zero, af, 0),
+        "circuit is unsatisfiable. An AssertZero opcode contains no variables but has a non-zero constant");
+}
+
+TEST(AssertZeroConstraintTest, SatisfiableCircuitWithZeroConstantOnly)
+{
+    // An AssertZero opcode with no variables and a zero constant is trivially satisfiable (0 == 0),
+    // but should still be rejected since it produces a zero gate.
+    Acir::Expression expr{ .q_c = bb::fr::zero().to_buffer() };
+    Acir::Opcode::AssertZero assert_zero{ .value = expr };
+    AcirFormat af;
+    EXPECT_THROW_WITH_MESSAGE(assert_zero_to_quad_constraints(assert_zero, af, 0),
+                              "split_into_mul_quad_gates: resulted in zero gates");
+}