{ "evaluation_id": "EVAL-20260402-181953", "question_id": "REASON-028", "question_text": "(1) Explain P vs NP to a smart non-technical person using only analogies and examples. (2) Why do most computer scientists believe P ≠ NP? (3) If someone proved P = NP tomorrow, what would the practical consequences be? (Be specific about cryptography, optimization, and AI.) (4) Would P = NP mean all problems are easy to solve? Why or why not?", "category": "reasoning", "timestamp": "2026-04-02T18:19:53.825Z", "display_date": "Apr 02, 2026", "winner": { "name": "GPT-5.4", "provider": "openrouter", "score": 9.12 }, "avg_score": 8.171, "matrix_size": 88, "models_used": [ { "id": "gpt_5_4", "name": "GPT-5.4", "provider": "openrouter" }, { "id": "grok_420", "name": "Grok 4.20", "provider": "openrouter" }, { "id": "deepseek_v4", "name": "DeepSeek V4", "provider": "openrouter" }, { "id": "claude_opus_46", "name": "Claude Opus 4.6", "provider": "openrouter" }, { "id": "claude_sonnet_46", "name": "Claude Sonnet 4.6", "provider": "openrouter" }, { "id": "mimo_v2_flash", "name": "MiMo-V2-Flash", "provider": "Xiaomi" }, { "id": "gpt_oss_120b", "name": "GPT-OSS-120B", "provider": "OpenAI" }, { "id": "gemini_25_flash", "name": "Gemini 2.5 Flash", "provider": "openrouter" }, { "id": "minimax_m25", "name": "MiniMax M2.5", "provider": "openrouter" }, { "id": "gemini_31_pro", "name": "Gemini 3.1 Pro", "provider": "openrouter" } ], "rankings": { "gpt_5_4": { "display_name": "GPT-5.4", "provider": "openrouter", "average_score": 9.12, "score_count": 9, "min_score": 8.8, "max_score": 10, "rank": 1 }, "grok_420": { "display_name": "Grok 4.20", "provider": "openrouter", "average_score": 8.89, "score_count": 9, "min_score": 7.35, "max_score": 9.55, "rank": 2 }, "mimo_v2_flash": { "display_name": "MiMo-V2-Flash", "provider": "Xiaomi", "average_score": 8.46, "score_count": 9, "min_score": 7.35, "max_score": 9.45, "rank": 3 }, "claude_opus_46": { "display_name": "Claude Opus 4.6", "provider": "openrouter", "average_score": 8.07, "score_count": 9, "min_score": 6.1, "max_score": 9, "rank": 4 }, "gemini_25_flash": { "display_name": "Gemini 2.5 Flash", "provider": "openrouter", "average_score": 8.07, "score_count": 9, "min_score": 6.2, "max_score": 9, "rank": 5 }, "gpt_oss_120b": { "display_name": "GPT-OSS-120B", "provider": "OpenAI", "average_score": 8.06, "score_count": 8, "min_score": 5.2, "max_score": 9.45, "rank": 6 }, "claude_sonnet_46": { "display_name": "Claude Sonnet 4.6", "provider": "openrouter", "average_score": 7.99, "score_count": 9, "min_score": 6.05, "max_score": 9.2, "rank": 7 }, "minimax_m25": { "display_name": "MiniMax M2.5", "provider": "openrouter", "average_score": 7.94, "score_count": 9, "min_score": 6.7, "max_score": 8.8, "rank": 8 }, "deepseek_v4": { "display_name": "DeepSeek V4", "provider": "openrouter", "average_score": 7.9, "score_count": 9, "min_score": 6.55, "max_score": 9, "rank": 9 }, "gemini_31_pro": { "display_name": "Gemini 3.1 Pro", "provider": "openrouter", "average_score": 7.21, "score_count": 8, "min_score": 4.85, "max_score": 8.6, "rank": 10 } }, "judgments": [ { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 8.8, "brief_justification": "Accurate, thorough, well-structured explanation with nuanced practical implications and clear analogies." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 8.65, "brief_justification": "Accurate, thorough coverage of all parts with clear analogies and realistic implications; offers solid insight and practical relevance." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 8.15, "brief_justification": "" }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 7, "brief_justification": "The response provides excellent, accurate, and deep answers to the first two questions, but it cuts off mid-sentence in Part 3, completely missing the required sections on optimization, AI, and the entirety of question 4." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 10, "brief_justification": "The response perfectly addresses all parts of the prompt with highly accurate, accessible analogies, deep technical nuances explained simply, and excellent formatting." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9.55, "brief_justification": "" }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 7.2, "brief_justification": "The response provides excellent, accurate, and clear explanations with great analogies for the first two questions. However, it cuts off mid-sentence during the third question, completely missing the required sections on optimization, AI, and the fourth question." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 7.35, "brief_justification": "" }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 7.2, "brief_justification": "" }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.25, "brief_justification": "The response is highly accurate, clear, and provides excellent analogies and depth. However, it is cut off at the very end, which negatively impacts its completeness." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 8.75, "brief_justification": "The response is highly clear and covers all prompts well, but contains a technical inaccuracy by stating that factoring is believed to be NP-hard (it is generally believed to be NP-intermediate)." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 8.45, "brief_justification": "Clear, accurate, and insightful with good practical implications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 8.8, "brief_justification": "The response is highly accurate, thorough, and insightful, covering all aspects of the question with clear analogies and detailed explanations. It provides practical implications and maintains a high level of clarity throughout." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9, "brief_justification": "Comprehensive, clear, and insightful with practical implications well-explained." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9, "brief_justification": "Comprehensive, clear, and insightful with practical implications well-explained." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9, "brief_justification": "Highly accurate, thorough, and clear with deep insights and practical implications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9, "brief_justification": "Comprehensive, clear, and insightful explanation with practical implications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 8.8, "brief_justification": "Accurate, thorough, and clear with insightful analysis and practical implications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9, "brief_justification": "Comprehensive, clear, and insightful explanation with practical implications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 8.45, "brief_justification": "Accurate, well-structured, and insightful with practical implications clearly explained." }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 6.3, "brief_justification": "The response is well-written and uses excellent analogies for part 1. However, it is clearly incomplete - the response cuts off mid-sentence in part 3, never finishing the cryptography section, never addressing optimization or AI consequences, and never reaching part 4 at all. The technical content that is present is mostly accurate, though the characterization of NP could be more precise (NP problems are those verifiable in polynomial time by a nondeterministic Turing machine, not just 'hard to" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 6.75, "brief_justification": "The response is well-structured and clearly written, but contains several correctness issues. (1) The jigsaw analogy conflates P with 'easy to verify' rather than 'easy to solve' - the description of P problems is muddled. (2) Factoring large numbers is not known to be NP-hard/NP-complete; it's in NP but not proven NP-complete, so saying 'factoring is hard (NP)' is misleading. RSA doesn't directly rely on P≠NP but on the hardness of specific problems. (3) The claim that P=NP would make ML traini" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9, "brief_justification": "Exceptionally clear and well-structured response that uses excellent analogies throughout. Correctly explains P, NP, and the P vs NP question. The reasons for believing P ≠ NP are accurate and well-articulated (experience, NP-completeness equivalence, barrier results, intuition). The consequences section is specific and nuanced—correctly distinguishing between constructive and non-constructive proofs, addressing cryptography (public-key vs symmetric), optimization, and AI with appropriate caveat" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9.2, "brief_justification": "Excellent response that is accurate, comprehensive, and exceptionally well-structured. The analogies in part 1 are varied and effective. Part 2 correctly captures the intuition without overclaiming. Part 3 is specific and nuanced, correctly noting that AES/symmetric crypto would survive while public-key infrastructure would collapse, and appropriately tempering the AI claims. Part 4 correctly identifies that P=NP doesn't make all problems easy, citing undecidable problems and problems outside NP" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 8.3, "brief_justification": "The response is exceptionally well-written, accurate, and deeply insightful across Parts 1, 2, and the beginning of Part 3. The analogies are excellent and the reasoning for P ≠ NP belief is thorough and nuanced. However, the response is clearly truncated mid-sentence in Part 3 (cryptography section incomplete, optimization and AI sections missing entirely, and Part 4 is absent). This significantly impacts completeness and usefulness since two of the four explicitly asked questions are not answe" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.3, "brief_justification": "" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 8, "brief_justification": "The response is well-structured, accurate, and uses excellent analogies for explaining P vs NP. The reasons for believing P ≠ NP are thorough and technically sound, covering oracle results, natural proofs barrier, and empirical evidence. The cryptography section is detailed and specific. However, the response appears to be cut off mid-sentence in section 3(b), leaving the optimization and AI consequences incomplete, and section 4 (whether P=NP means all problems are easy) is entirely missing. Th" }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 7.1, "brief_justification": "Accurate analogies and solid reasons for P≠NP, clear structure, good depth, but the answer cuts off before fully covering practical consequences and the final question, reducing completeness and practical usefulness." }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 7.35, "brief_justification": "The response is well-structured and clearly written with excellent analogies for a non-technical audience. However, there are some correctness issues: the P problems analogy ('finding is as easy as checking') conflates P with NP rather than properly defining P as problems solvable in polynomial time. The claim that P=NP would mean optimization problems become 'easy' overstates things - a polynomial algorithm could still have impractically large exponents. The response also cuts off mid-sentence " }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 6.75, "brief_justification": "The response is well-structured and clearly written, but has notable correctness issues. Factoring is not known to be NP-hard (it's in NP but not proven NP-complete), and the claim that 'most encryption would break' conflates NP-completeness with specific hardness assumptions. The explanation of why P≠NP is believed is superficial—it omits important reasons like oracle separations, circuit complexity barriers, and the structural consequences (polynomial hierarchy collapse). The jigsaw puzzle ana" }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 4.85, "brief_justification": "The response explains the basic intuition of P vs NP with accessible analogies and is fairly clear, but it is incomplete because section 3 is cut off and section 4 is entirely missing. It also overstates several points, especially about cryptography and 'overnight' consequences, and the 'creativity' argument is more rhetorical than rigorous." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 6.55, "brief_justification": "Clear and mostly accurate, with good high-level coverage and accessible analogies. However, it contains notable inaccuracies and overstatements: the P vs NP analogy blurs verification vs solving, factoring is not known to be NP-complete, cryptography would not automatically 'collapse' from P=NP alone in the simple way stated, and claims about AI/optimization becoming trivial or perfect are overstated. It does correctly note that P=NP would not make all problems easy and mentions polynomial-time " }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 6.1, "brief_justification": "Clear and engaging with good analogies and some solid complexity-theory context, but the response is incomplete because Part 3 is cut off and Parts 3-4 are not fully answered. It also overstates some claims, especially around cryptography and broad consequences of P=NP." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 7.35, "brief_justification": "Clear and engaging, with strong coverage of the requested parts, but it has important technical inaccuracies: it conflates P with 'easy to verify' rather than 'easy to solve,' overstates some consequences of P=NP, and incorrectly suggests lattice/hash-based public-key systems may remain secure under P=NP. Good practical framing overall." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 6.05, "brief_justification": "Clear and engaging explanation with good intuition and some nuanced points, but the response is incomplete/truncated and contains notable inaccuracies, especially around cryptography and examples of NP-complete problems." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 7.5, "brief_justification": "Clear, well-structured, and broadly informative, but it contains notable inaccuracies and overstatements: P is mischaracterized as 'find as fast as verify,' cryptography does not rely entirely on P≠NP and would not necessarily collapse overnight from P=NP alone, factoring is not known NP-complete, protein folding claims are too strong, and calling the Halting Problem NP-hard is problematic in the standard sense. Still, it covers all requested parts with practical examples and good accessibility." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 5.2, "brief_justification": "Clear structure and some solid intuition, but the answer is incomplete/truncated and contains notable inaccuracies, especially around complexity claims and cryptography implications." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 6.2, "brief_justification": "Clear analogies and generally accurate basics, but the response is incomplete because it is cut off, and it overstates practical consequences—especially cryptography and AI—without important caveats about polynomial degree, constants, and the fact that P=NP would not automatically break all cryptosystems or make all AI tasks easy." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 6.7, "brief_justification": "Clear and accessible, with decent coverage of the requested parts. However, it contains important inaccuracies: factoring and discrete log are not known to be NP-hard, and claiming most encryption would break from P=NP is too strong without caveats. The AI consequences are somewhat overstated. Good explanation of why P=NP would not make all problems easy, but overall depth and factual precision are only moderate." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 7.45, "brief_justification": "The response is clear, uses good analogies, and is mostly accurate. It covers parts 1 and 2 well with insight, but part 3 is incomplete (cuts off mid-sentence) and lacks specificity on optimization and AI as requested. Part 4 is entirely missing, reducing completeness. Depth is solid on intuition but could explore more formal reasons." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 8.25, "brief_justification": "The response is factually accurate, uses good analogies, covers all four questions clearly and engagingly. Depth is solid but could explore more nuance on why P≠NP (e.g., formal barriers). Practical consequences are specific and realistic." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 8.85, "brief_justification": "The response is factually accurate, logically sound, and covers all four parts thoroughly with clear analogies, strong evidence for P ≠ NP, specific practical impacts, and a precise explanation of why not all problems become easy. Depth is excellent via barriers, oracle results, and caveats on polynomial degree. Minor deduction on usefulness as the cryptography section is truncated mid-sentence." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9, "brief_justification": "The response is factually accurate, uses excellent analogies for P vs NP, covers all four parts thoroughly with clear structure, provides insightful explanations on beliefs and consequences, and is highly practical. Minor deduction for slightly incomplete final section on problems harder than NP." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 8.6, "brief_justification": "The response is factually accurate, uses excellent analogies for non-technical explanation, covers all four questions thoroughly with good depth on reasons and consequences, and is clearly structured and highly useful." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.8, "brief_justification": "The response is factually accurate, uses effective analogies, covers all four parts thoroughly with good explanations and examples, and provides insightful practical details while being clearly structured." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 8.6, "brief_justification": "The response is factually accurate, uses effective analogies, covers all four questions thoroughly with good structure and insightful details on barriers, crypto impacts, and limitations. Minor cutoff in optimization table slightly reduces completeness but does not affect core accuracy." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.6, "brief_justification": "The response is factually accurate, uses effective analogies for non-technical explanation, covers all four parts thoroughly with good structure and insightful details on implications, though the final section is slightly truncated." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 8.25, "brief_justification": "The response accurately explains P vs NP with good analogies, covers all four questions, and is clearly structured. Minor issues: the jigsaw analogy is slightly imprecise (NP is about verifying a proposed solution, not just checking a completed puzzle), and it overstates that most crypto relies on NP-hardness (it's typically based on problems in NP but not known to be NP-complete). Depth is solid but could explore more nuance on why P≠NP is believed." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 6.45, "brief_justification": "The response is well-written and uses excellent analogies for parts 1 and 2, with clear structure and accessible language. However, the response is clearly truncated mid-sentence in part 3, cutting off before completing the cryptography section and entirely omitting the optimization, AI, and part 4 sections. This severely impacts completeness and usefulness scores. The content that is present is mostly accurate, though the 'philosophy of creativity' argument for P≠NP, while intuitive, is somewha" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 7.55, "brief_justification": "The response is well-structured and accessible, with good analogies and practical examples. However, there are some inaccuracies: protein folding is not NP-hard in the classical sense, and the claim that 'encryption assumes factoring is NP' is misleading (factoring is in NP but not known to be NP-complete). The depth on why P≠NP is believed is shallow—missing oracle results, natural proofs barrier, algebrization, and the structural arguments. The P=NP consequences section is solid but somewhat s" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9, "brief_justification": "Exceptional response covering all four parts with accurate technical content, excellent analogies, and sophisticated depth (oracle results, Natural Proofs barrier, polynomial hierarchy collapse). The response is cut off mid-sentence in Part 3, preventing full evaluation of the cryptography cascade and the AI/optimization sections, which reduces completeness. The nuance about polynomial exponents mattering practically is particularly insightful. Overall one of the strongest explanations of P vs N" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9, "brief_justification": "Exceptionally clear and well-structured response that uses effective analogies throughout. Correctly explains P vs NP, gives solid reasoning for why P≠NP is believed, and provides specific practical consequences across cryptography, optimization, and AI. The nuance about proof vs practical algorithm is excellent. Minor issue: the response appears slightly truncated at the end of section 4, cutting off mid-thought about problems harder than NP. Otherwise nearly exemplary." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9, "brief_justification": "Excellent response across all four questions. The analogies are well-chosen and genuinely illuminating for non-technical readers. The cryptography consequences are accurate and specific. The P≠NP reasoning is solid. The final section correctly notes polynomial degree caveats and undecidable problems. Minor gaps: doesn't mention that a constructive P=NP proof might have impractically large constants/exponents even for NP problems it solves, and the AI section could note that learning theory has i" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.3, "brief_justification": "Excellent structure and accessible analogies throughout. The jigsaw and maze analogies work well for part 1. Part 2 covers the main intuitions though the 'reduction' explanation is slightly muddled (NP-completeness/reduction is about showing problems are equally hard, not about collapsing them). Part 3 is strong and specific about cryptography, optimization, and AI. Part 4 correctly notes undecidable problems and complexity classes beyond NP, though the claim that P contains problems 'where you " }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 8.6, "brief_justification": "The response is highly accurate, well-structured, and uses excellent analogies for a non-technical audience. It covers cryptography, optimization, and AI implications with good specificity. The response appears to be cut off at the end (circuit design section incomplete), which reduces completeness. The relativized worlds and natural proofs barriers show genuine depth. The table format enhances clarity and practical usefulness throughout." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.15, "brief_justification": "Excellent analogies and clear structure throughout. The party/treasure hunt analogy effectively communicates P vs NP. The cryptography and optimization sections are specific and accurate. The AI section is solid but slightly overstates certainty (P=NP doesn't guarantee fast neural network training directly). The response is cut off mid-sentence in section 4, which is a significant flaw reducing completeness. The explanation of why P≠NP is believed (NP-completeness argument) is well-handled. Mino" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 7.55, "brief_justification": "The response is well-structured and clearly written for a non-technical audience. However, there are some inaccuracies: factoring and discrete logarithm are not known to be NP-hard (they're in NP but not proven NP-complete), and the explanation of why P≠NP is believed is shallow—it misses the deeper mathematical intuitions like circuit complexity, natural proofs barriers, and the structural arguments. The analogy for P vs NP is decent but imprecise (P problems aren't just 'simple mazes'—they're " }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 8.6, "brief_justification": "Accurate analogies, clear structure, and specific consequences; response cut off but covers key points." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 9, "brief_justification": "Accurate, thorough, and well-structured with practical examples and clear explanations." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9, "brief_justification": "Comprehensive, accurate, and well-structured response with strong analogies, detailed reasoning, and specific practical implications." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9, "brief_justification": "Accurate, thorough, and well-structured with strong analogies and practical implications." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9, "brief_justification": "Accurate, thorough, and well-structured with strong analogies and specific examples; minor room for deeper nuance on polynomial bounds." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 8.45, "brief_justification": "Accurate analogies, thorough coverage, clear structure, insightful analysis, and practical implications." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 8.6, "brief_justification": "Accurate, thorough, and well-structured with strong analogies and specific consequences." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.6, "brief_justification": "Accurate, thorough, and well-structured with strong analogies and specific examples; minor incompleteness in the final answer." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 8.6, "brief_justification": "Accurate analogies, thorough coverage, clear structure, insightful analysis, and practical implications explained well." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 8.25, "brief_justification": "Accurate analogies and explanations, covers all requested points, clear structure, offers insightful nuance about limits of P=NP, and provides practical implications." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 7.25, "brief_justification": "Accurate analogies and solid reasons for P≠NP, but the answer cuts off before fully covering AI implications and ends abruptly, reducing completeness and practical usefulness." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.65, "brief_justification": "Accurate analogies and explanations, covers all requested points, clear structure, offers insightful reasons and practical impacts, though some statements simplify cryptographic assumptions." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.4, "brief_justification": "Accurate analogies and coverage of all sub‑questions, well‑structured and clear. Minor oversimplifications about cryptographic assumptions keep correctness from being perfect." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 7.6, "brief_justification": "Clear, well-structured answer covering all parts, but contains minor factual errors about cryptography and NP-hardness, limiting full correctness and depth." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 8.45, "brief_justification": "The response provides a clear and accurate explanation of P vs NP using effective analogies. It covers the core reasons for the belief P != NP and offers specific, well-reasoned consequences for cryptography, optimization, and AI, though the AI section is cut off. The explanation of 'all problems' is also well-handled." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 8.8, "brief_justification": "The response effectively uses analogies to explain P vs NP, covers the main reasons for P != NP belief, and provides specific, well-thought-out consequences for cryptography, optimization, and AI if P = NP. It also correctly addresses the nuance that P = NP doesn't make all problems easy." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9, "brief_justification": "The response provides an excellent, comprehensive, and well-structured explanation of P vs NP. The analogies are effective, the reasons for belief in P ≠ NP are thoroughly covered, and the practical consequences are detailed and specific across various domains. The distinction between theoretical and practical polynomial time is also well-made." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9.45, "brief_justification": "The response provides an exceptionally clear and accurate explanation of P vs NP using effective analogies. It thoroughly addresses all parts of the question with good depth, particularly regarding the practical consequences and nuances of P=NP." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9.45, "brief_justification": "The response is exceptionally clear, using effective analogies to explain complex concepts. It provides a comprehensive and accurate overview of P vs NP, the reasons for the P != NP belief, and detailed practical consequences, while also correctly addressing common misconceptions." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9.2, "brief_justification": "The response provides an exceptionally clear and comprehensive explanation of P vs NP, using effective analogies. It thoroughly addresses all parts of the prompt with good depth and practical insights." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.45, "brief_justification": "The response provides an excellent, clear, and comprehensive explanation of P vs NP using effective analogies. It thoroughly addresses all parts of the prompt, including the practical consequences and common misconceptions, demonstrating strong depth and usefulness." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.45, "brief_justification": "The response is exceptionally clear, using effective analogies to explain complex concepts. It provides a comprehensive overview of P vs NP, the reasons for the P ≠ NP belief, and detailed practical consequences, especially in cryptography and optimization. The structure is logical and easy to follow." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 8.8, "brief_justification": "The response provides a clear and accurate explanation of P vs NP using effective analogies. It thoroughly addresses all parts of the prompt, including the reasons for P != NP belief, practical consequences, and the nuance that P=NP doesn't make all problems 'easy'." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 7.1, "brief_justification": "Clear explanations with good analogies for P vs NP. However, the response is abruptly cut off mid-sentence and never completes the discussion of optimization and AI consequences, making it incomplete." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 7.8, "brief_justification": "Clear and accurate explanation with excellent analogies. Covers all four parts of the question well, with good structure and accessibility for non-technical readers. Some room for more depth, but substantive and practical." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 7.75, "brief_justification": "Excellent analogies and deep explanation of why P≠NP is believed. However, the response is cut off mid-sentence, leaving optimization, AI, and a complete answer to whether P=NP means all problems are easy (beyond the brief mention) unaddressed." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 8.8, "brief_justification": "Excellent response that thoroughly covers all four parts of the question with accurate, well-structured explanations. Uses effective analogies (jigsaw puzzles, locksmiths, Sudoku) to make concepts accessible. Provides nuanced discussion of practical consequences including the important distinction between theoretical and practical efficiency, and correctly notes that not all problems would become easy even with P=NP." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 8.8, "brief_justification": "Excellent response covering all four parts with clear analogies (dinner party, Sudoku, needle in haystack), accurate technical explanations, and specific practical consequences. Slightly less deep on theoretical nuances but highly informative and well-structured." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 7.9, "brief_justification": "Excellent explanations with good analogies and depth, but response is truncated and cuts off mid-sentence, leaving parts of the question unanswered." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.8, "brief_justification": "Excellent response that thoroughly addresses all four parts of the question with clear analogies (jigsaw puzzle, maze), accurate technical explanations, and specific practical consequences for cryptography, optimization, and AI. Shows good depth by discussing complexity classes beyond NP and addresses the common misconception about all problems becoming easy. Slight deduction in depth for not exploring edge cases or theoretical nuances more deeply." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.05, "brief_justification": "Excellent explanation with clear analogies (treasure hunt, jigsaw puzzle) that make P vs NP accessible. Technically accurate coverage of cryptography, optimization, and AI consequences. However, the response is cut off mid-sentence in part 4, losing significant completeness. The NP-Complete explanation adds good depth, and the structure is very clear." } ], "meta": { "source": "The Multivac (app.themultivac.com)", "methodology": "10x10 blind peer matrix evaluation", "criteria": "correctness, completeness, clarity, depth, usefulness", "self_judgments": "excluded from rankings", "license": "Open data — cite as: The Multivac (2026)" } }