{"id":"dual-proof-composition-prevents-explosion","text":"Composition's scalability advantage over inheritance is supported by quantitative evidence from two independent pattern categories: Decorator demonstrates that n independent embellishments require up to 2^n subclasses via inheritance but only n+1 classes via composition, while Bridge shows that M abstraction kinds × N implementation platforms require M×N classes without the pattern but only M+N with it. Together, these examples suggest that composition's superiority in managing combinatorial complexity holds across both structural decoration and abstraction-implementation separation, grounded in concrete class-count reductions rather than theoretical argument alone.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["decorator-proves-composition-scalability","bridge-eliminates-class-explosion"],"outlist":[],"label":"Two independent quantitative proofs of composition's advantage across different GoF categories"}],"dependents":["composition-quadruply-evidenced","prototype-eliminates-hierarchy-explosion-via-composition-shift"],"metadata":{"source_type":"derived","review_result":"invalid","repair_action":"softened"},"created_at":"2026-06-17T23:12:23+00:00","updated_at":"2026-06-18T06:40:35+00:00","reviewed_at":"2026-06-18T06:15:08+00:00","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"dual-proof-composition-prevents-explosion","truth_value":"IN","reason":"SL justification valid","antecedents":["decorator-proves-composition-scalability","bridge-eliminates-class-explosion"],"label":"Two independent quantitative proofs of composition's advantage across different GoF categories"},{"node":"decorator-proves-composition-scalability","truth_value":"IN","reason":"SL justification valid","antecedents":["decorator-avoids-inheritance-explosion","composition-superiority-for-reuse"],"label":"Decorator's avoidance of class explosion quantifies composition's advantage as exponential, not just qualitative"},{"node":"decorator-avoids-inheritance-explosion","truth_value":"IN","reason":"premise"},{"node":"composition-superiority-for-reuse","truth_value":"IN","reason":"SL justification valid","antecedents":["favor-composition-over-inheritance","inheritance-breaks-encapsulation","inheritance-compile-time-composition-run-time","delegation-composition-as-powerful-as-inheritance"],"label":"Four independent arguments converge on composition's superiority over inheritance"},{"node":"favor-composition-over-inheritance","truth_value":"IN","reason":"premise"},{"node":"inheritance-breaks-encapsulation","truth_value":"IN","reason":"premise"},{"node":"inheritance-compile-time-composition-run-time","truth_value":"IN","reason":"premise"},{"node":"delegation-composition-as-powerful-as-inheritance","truth_value":"IN","reason":"premise"},{"node":"bridge-eliminates-class-explosion","truth_value":"IN","reason":"premise"}]}}