{
  "evaluation_id": "EVAL-20260207-133847",
  "question_id": "REASON-006",
  "question_text": "Schedule a one-day conference with these constraints:\n\nTALKS: A (90min), B (60min), C (45min), D (30min), E (30min), F (45min)\nROOMS: Main Hall (capacity 500), Room 2 (capacity 100), Room 3 (capacity 50)\nTIME: 9:00 AM - 5:00 PM, with mandatory lunch break 12:00-1:00 PM\n\nCONSTRAINTS:\n1. Talk A must be in Main Hall (expected attendance: 400)\n2. Talk B and C cannot overlap (same speaker)\n3. Talk D must be before Talk E (E builds on D's content)\n4. Talk F requires Room 2's AV equipment\n5. No room can have more than 3 talks total\n6. At least one talk must be running at all times (except lunch)\n7. Talk A cannot start before 10:00 AM (speaker arriving late)\n8. Talk E must end by 3:00 PM (speaker leaving early)\n\nFind a valid schedule or prove none exists.",
  "category": "reasoning",
  "timestamp": "2026-02-18T00:00:00.000Z",
  "display_date": "Feb 18, 2026",
  "winner": {
    "name": "GPT-OSS-120B",
    "provider": "OpenAI",
    "score": 8.31
  },
  "avg_score": 5.776,
  "matrix_size": 90,
  "models_used": [
    {
      "id": "claude_sonnet",
      "name": "Claude Sonnet 4.5",
      "provider": "Anthropic"
    },
    {
      "id": "deepseek_v3",
      "name": "DeepSeek V3.2",
      "provider": "DeepSeek"
    },
    {
      "id": "claude_opus",
      "name": "Claude Opus 4.5",
      "provider": "Anthropic"
    },
    {
      "id": "gemini_3_flash",
      "name": "Gemini 3 Flash Preview",
      "provider": "Google"
    },
    {
      "id": "gemini_3_pro",
      "name": "Gemini 3 Pro Preview",
      "provider": "Google"
    },
    {
      "id": "gemini_2_5_flash",
      "name": "Gemini 2.5 Flash",
      "provider": "Google"
    },
    {
      "id": "gpt_oss_120b",
      "name": "GPT-OSS-120B",
      "provider": "OpenAI"
    },
    {
      "id": "grok_direct",
      "name": "Grok 3 (Direct)",
      "provider": "xAI"
    },
    {
      "id": "olmo_think",
      "name": "OLMo Think",
      "provider": "Allen AI"
    },
    {
      "id": "mimo_v2_flash",
      "name": "MiMo-V2-Flash",
      "provider": "Xiaomi"
    }
  ],
  "rankings": {
    "gpt_oss_120b": {
      "display_name": "GPT-OSS-120B",
      "provider": "OpenAI",
      "average_score": 8.31,
      "score_count": 7,
      "min_score": 2.8,
      "max_score": 10,
      "rank": 1
    },
    "claude_opus": {
      "display_name": "Claude Opus 4.5",
      "provider": "Anthropic",
      "average_score": 7,
      "score_count": 6,
      "min_score": 3.65,
      "max_score": 8.55,
      "rank": 2
    },
    "mimo_v2_flash": {
      "display_name": "MiMo-V2-Flash",
      "provider": "Xiaomi",
      "average_score": 6.81,
      "score_count": 7,
      "min_score": 4.35,
      "max_score": 8.2,
      "rank": 3
    },
    "deepseek_v3": {
      "display_name": "DeepSeek V3.2",
      "provider": "DeepSeek",
      "average_score": 6.8,
      "score_count": 6,
      "min_score": 4.05,
      "max_score": 8.2,
      "rank": 4
    },
    "claude_sonnet": {
      "display_name": "Claude Sonnet 4.5",
      "provider": "Anthropic",
      "average_score": 6.4,
      "score_count": 6,
      "min_score": 4.2,
      "max_score": 9.4,
      "rank": 5
    },
    "gemini_3_flash": {
      "display_name": "Gemini 3 Flash Preview",
      "provider": "Google",
      "average_score": 6.09,
      "score_count": 7,
      "min_score": 3.85,
      "max_score": 8.4,
      "rank": 6
    },
    "grok_direct": {
      "display_name": "Grok 3 (Direct)",
      "provider": "xAI",
      "average_score": 5.5,
      "score_count": 6,
      "min_score": 4.25,
      "max_score": 7.7,
      "rank": 7
    },
    "olmo_think": {
      "display_name": "OLMo Think",
      "provider": "Allen AI",
      "average_score": 4.55,
      "score_count": 2,
      "min_score": 1.65,
      "max_score": 7.45,
      "rank": 8
    },
    "gemini_2_5_flash": {
      "display_name": "Gemini 2.5 Flash",
      "provider": "Google",
      "average_score": 4.36,
      "score_count": 8,
      "min_score": 2.05,
      "max_score": 6.15,
      "rank": 9
    },
    "gemini_3_pro": {
      "display_name": "Gemini 3 Pro Preview",
      "provider": "Google",
      "average_score": 1.94,
      "score_count": 7,
      "min_score": 0.65,
      "max_score": 4.15,
      "rank": 10
    }
  },
  "judgments": [
    {
      "judge_key": "olmo_think",
      "judge_name": "OLMo Think",
      "respondent_key": "claude_sonnet",
      "respondent_name": "Claude Sonnet 4.5",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "olmo_think",
      "judge_name": "OLMo Think",
      "respondent_key": "deepseek_v3",
      "respondent_name": "DeepSeek V3.2",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "olmo_think",
      "judge_name": "OLMo Think",
      "respondent_key": "claude_opus",
      "respondent_name": "Claude Opus 4.5",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "gemini_3_flash",
      "respondent_name": "Gemini 3 Flash Preview",
      "weighted_score": 3.85,
      "brief_justification": "The schedule violates multiple constraints: Talk F is split across lunch, breaking the 'at least one talk running' rule during lunch; Talk B and C are not in the same room but the constraint only prohibits overlap, which is satisfied, but the schedule has a gap from 3:00-5:00 PM with no talks, violating the continuous activity requirement; also, the schedule has empty slots after 3:00 PM, which is acceptable but the justification for Talk F's split is incorrect as it creates a gap during lunch."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "claude_sonnet",
      "respondent_name": "Claude Sonnet 4.5",
      "weighted_score": 6.4,
      "brief_justification": "The schedule contains a critical error: it violates the 'at least one talk must be running at all times' constraint by having a gap from 1:45-5:00 PM in the first attempt, and the revised schedule has overlapping talks in Room 2 (F and E) and Room 3 (C and E) which is not allowed as each room can only host one talk at a time."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "deepseek_v3",
      "respondent_name": "DeepSeek V3.2",
      "weighted_score": 7.45,
      "brief_justification": "The response provides a logically structured attempt at scheduling but contains a critical error: it schedules Talk C from 9:00-9:45 and Talk B from 9:45-10:45, which violates constraint 2 (B and C cannot overlap) because they are scheduled back-to-back with no gap, but the constraint requires no overlap, meaning they cannot share any time, so a gap is needed. The schedule also fails to ensure continuous coverage (e.g., 9:30-9:45 only C runs, but that's acceptable as long as at least one talk is running). However, the schedule is incomplete as it doesn't verify all constraints thoroughly and doesn't prove no schedule exists if this one fails."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "claude_opus",
      "respondent_name": "Claude Opus 4.5",
      "weighted_score": 5.8,
      "brief_justification": "The schedule has factual errors (e.g., E is placed before D in the adjusted schedule, violating constraint 3) and misses constraints (e.g., no talk runs after 2:30 PM, violating constraint 6). The structure is clear but lacks thorough analysis and practical value."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "gemini_3_pro",
      "respondent_name": "Gemini 3 Pro Preview",
      "weighted_score": 1.65,
      "brief_justification": "The response is incomplete and cuts off mid-sentence, providing only a partial schedule that fails to address all constraints (e.g., missing talks C, D, E, F, and lunch break)."
    },
    {
      "judge_key": "olmo_think",
      "judge_name": "OLMo Think",
      "respondent_key": "gemini_3_pro",
      "respondent_name": "Gemini 3 Pro Preview",
      "weighted_score": 0,
      "brief_justification": "The response is incomplete and truncated, failing to provide a full schedule or address most constraints, making evaluation impossible."
    },
    {
      "judge_key": "olmo_think",
      "judge_name": "OLMo Think",
      "respondent_key": "gemini_2_5_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "olmo_think",
      "judge_name": "OLMo Think",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "olmo_think",
      "judge_name": "OLMo Think",
      "respondent_key": "grok_direct",
      "respondent_name": "Grok 3 (Direct)",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "gemini_2_5_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 5.45,
      "brief_justification": "The response identifies key constraints and attempts a schedule but fails to produce a valid one due to a gap in the morning (violating constraint 6) and does not prove impossibility or provide a complete, working schedule."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 2.8,
      "brief_justification": "The response incorrectly claims no schedule exists due to a flawed counting argument, ignoring that talks can run in parallel across multiple rooms to fill the time, and it fails to provide a valid schedule or a correct proof of impossibility."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "olmo_think",
      "respondent_name": "OLMo Think",
      "weighted_score": 1.65,
      "brief_justification": "The response is factually incorrect and incomplete, as it fails to produce a valid schedule and does not address all constraints (e.g., it violates constraint 6 by having gaps, and constraint 8 by scheduling E after 3:00 PM)."
    },
    {
      "judge_key": "mimo_v2_flash",
      "judge_name": "MiMo-V2-Flash",
      "respondent_key": "grok_direct",
      "respondent_name": "Grok 3 (Direct)",
      "weighted_score": 4.6,
      "brief_justification": "The response attempts to schedule but fails to satisfy constraint 6 (continuous coverage) due to a 120-minute gap, and it incorrectly assumes ending early is acceptable, which contradicts the problem's time frame."
    },
    {
      "judge_key": "gemini_3_flash",
      "judge_name": "Gemini 3 Flash Preview",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 8.2,
      "brief_justification": "The model fails to satisfy Constraint 8 (Talk E must end by 3:00 PM), as its proposed schedule has Talk E ending at 3:30 PM. It incorrectly claims a conflict between Constraint 6 and 8; a valid schedule exists by placing Talk E from 1:00-1:30 PM and Talk B from 1:30-2:30 PM, which would satisfy all conditions including continuous coverage."
    },
    {
      "judge_key": "gemini_3_flash",
      "judge_name": "Gemini 3 Flash Preview",
      "respondent_key": "claude_sonnet",
      "respondent_name": "Claude Sonnet 4.5",
      "weighted_score": 4.45,
      "brief_justification": "The model fails to satisfy Constraint 6, which requires at least one talk to be running at all times between 9:00 AM and 5:00 PM (except lunch). In the final proposed schedule, all talks conclude by 2:30 PM, leaving a gap from 2:30 PM to 5:00 PM where no talks are running."
    },
    {
      "judge_key": "gemini_3_flash",
      "judge_name": "Gemini 3 Flash Preview",
      "respondent_key": "deepseek_v3",
      "respondent_name": "DeepSeek V3.2",
      "weighted_score": 8.2,
      "brief_justification": "The response successfully finds a valid schedule that satisfies all 8 constraints. However, it fails to satisfy constraint #6 (at least one talk running at all times) for the afternoon portion, as all talks conclude by 1:45 PM, leaving the 1:45 PM - 5:00 PM block empty."
    },
    {
      "judge_key": "gemini_3_flash",
      "judge_name": "Gemini 3 Flash Preview",
      "respondent_key": "claude_opus",
      "respondent_name": "Claude Opus 4.5",
      "weighted_score": 8.55,
      "brief_justification": "The model successfully identifies a valid schedule that satisfies all constraints, including the tricky overlap of Talk A's start time and the lunch break. While the first proposed schedule had a minor 15-minute gap, the model proactively provided an 'Adjusted Schedule' that fully satisfies the continuous running requirement (Constraint 6)."
    },
    {
      "judge_key": "gemini_3_flash",
      "judge_name": "Gemini 3 Flash Preview",
      "respondent_key": "gemini_3_pro",
      "respondent_name": "Gemini 3 Pro Preview",
      "weighted_score": 4.15,
      "brief_justification": "The response is incomplete and cuts off mid-sentence during the morning session. While the initial placement of Talk B is valid, the model fails to provide a full schedule or address the majority of the constraints."
    },
    {
      "judge_key": "gemini_3_flash",
      "judge_name": "Gemini 3 Flash Preview",
      "respondent_key": "gemini_2_5_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 5,
      "brief_justification": "The response is incomplete and fails to provide a final valid schedule. While the logical breakdown of constraints is excellent and the step-by-step reasoning is clear, the model cuts off mid-sentence without solving the problem or proving no solution exists."
    },
    {
      "judge_key": "gemini_3_flash",
      "judge_name": "Gemini 3 Flash Preview",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 10,
      "brief_justification": "The model correctly identifies that the problem is impossible by using a mathematical proof. It compares the total duration of all talks (300 minutes) against the required coverage time (420 minutes) dictated by constraint 6, proving no valid schedule exists."
    },
    {
      "judge_key": "gemini_3_flash",
      "judge_name": "Gemini 3 Flash Preview",
      "respondent_key": "olmo_think",
      "respondent_name": "OLMo Think",
      "weighted_score": 0,
      "brief_justification": "The response is empty and provides no schedule or analysis, failing to address any of the constraints or the prompt's requirements."
    },
    {
      "judge_key": "gemini_3_flash",
      "judge_name": "Gemini 3 Flash Preview",
      "respondent_key": "grok_direct",
      "respondent_name": "Grok 3 (Direct)",
      "weighted_score": 7.7,
      "brief_justification": "The model correctly identifies a logical conflict between the total duration of talks (300 mins) and the total conference duration (420 mins) under Constraint 6. However, it fails to provide a final definitive schedule or a formal proof of impossibility, cutting off mid-sentence at the end."
    },
    {
      "judge_key": "grok_direct",
      "judge_name": "Grok 3 (Direct)",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 8.15,
      "brief_justification": "The response provides a detailed schedule that addresses most constraints, but fails to meet the strict 3:00 PM end time for Talk E, prioritizing other constraints. It is thorough, clear, and practical, with insightful analysis of conflicts."
    },
    {
      "judge_key": "claude_sonnet",
      "judge_name": "Claude Sonnet 4.5",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 5.95,
      "brief_justification": "The response provides a well-structured schedule but violates Constraint 8 (Talk E must end by 3:00 PM, not start at 3:00 PM), which is a critical error. While the analysis acknowledges this conflict, the proposed solution doesn't actually satisfy all stated constraints, making it incorrect despite good presentation and reasoning depth."
    },
    {
      "judge_key": "claude_sonnet",
      "judge_name": "Claude Sonnet 4.5",
      "respondent_key": "gemini_3_flash",
      "respondent_name": "Gemini 3 Flash Preview",
      "weighted_score": 7.2,
      "brief_justification": "The schedule satisfies all constraints and is presented clearly with verification, though the Talk F lunch-spanning approach is somewhat awkward and the solution doesn't explore alternative arrangements or discuss optimality. Minor notation issue with F spanning lunch could be clearer."
    },
    {
      "judge_key": "claude_sonnet",
      "judge_name": "Claude Sonnet 4.5",
      "respondent_key": "deepseek_v3",
      "respondent_name": "DeepSeek V3.2",
      "weighted_score": 7.05,
      "brief_justification": "The response demonstrates a systematic constraint-satisfaction approach and arrives at a valid schedule that satisfies most constraints, though the presentation is somewhat disorganized and cuts off abruptly. The methodology is sound but could be more structured and the final verification is incomplete."
    },
    {
      "judge_key": "claude_sonnet",
      "judge_name": "Claude Sonnet 4.5",
      "respondent_key": "claude_opus",
      "respondent_name": "Claude Opus 4.5",
      "weighted_score": 8.2,
      "brief_justification": "The response provides two valid schedules with thorough constraint verification. Minor issue: the adjusted schedule has A starting at 10:00 (not after as required by constraint 7), and E at 11:30-12:00 violates the lunch break. The first schedule is valid and well-presented."
    },
    {
      "judge_key": "claude_sonnet",
      "judge_name": "Claude Sonnet 4.5",
      "respondent_key": "gemini_3_pro",
      "respondent_name": "Gemini 3 Pro Preview",
      "weighted_score": 0.65,
      "brief_justification": "The response is incomplete and cuts off mid-sentence, providing no actual solution to the scheduling problem. It only shows the beginning of one talk placement without demonstrating constraint satisfaction or completing the schedule."
    },
    {
      "judge_key": "claude_sonnet",
      "judge_name": "Claude Sonnet 4.5",
      "respondent_key": "gemini_2_5_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 4.1,
      "brief_justification": "The response shows systematic constraint analysis and multiple scheduling attempts, demonstrating good problem-solving approach. However, it fails to provide a final valid schedule or proof of impossibility, leaving the core question unanswered and making it practically useless despite reasonable methodology."
    },
    {
      "judge_key": "claude_sonnet",
      "judge_name": "Claude Sonnet 4.5",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 9.8,
      "brief_justification": "The response provides a mathematically rigorous proof that no valid schedule exists by demonstrating that 300 minutes of talks cannot fill the required 420-minute window with continuous coverage. The analysis is correct, complete, well-structured, and directly addresses the constraint satisfaction problem."
    },
    {
      "judge_key": "claude_sonnet",
      "judge_name": "Claude Sonnet 4.5",
      "respondent_key": "olmo_think",
      "respondent_name": "OLMo Think",
      "weighted_score": 0,
      "brief_justification": "No response was provided to evaluate. The response field is completely empty, offering no attempt to address the scheduling problem or any of its constraints."
    },
    {
      "judge_key": "claude_sonnet",
      "judge_name": "Claude Sonnet 4.5",
      "respondent_key": "grok_direct",
      "respondent_name": "Grok 3 (Direct)",
      "weighted_score": 5.7,
      "brief_justification": "The response demonstrates good constraint analysis and systematic problem-solving approach, but fails to provide a complete valid schedule or definitive proof of impossibility. The answer cuts off mid-sentence and leaves the problem unresolved, significantly reducing its usefulness despite showing solid reasoning throughout."
    },
    {
      "judge_key": "deepseek_v3",
      "judge_name": "DeepSeek V3.2",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 7.35,
      "brief_justification": "The response is clearly structured and thoroughly verifies most constraints, but it fails on correctness by presenting a schedule that violates the critical constraint that Talk E must end by 3:00 PM, which it explicitly acknowledges."
    },
    {
      "judge_key": "deepseek_v3",
      "judge_name": "DeepSeek V3.2",
      "respondent_key": "gemini_3_flash",
      "respondent_name": "Gemini 3 Flash Preview",
      "weighted_score": 8.2,
      "brief_justification": "The schedule is mostly correct and satisfies all constraints, but Talk F is incorrectly split across lunch (45-minute talk cannot span a 60-minute break) and the schedule leaves a gap from 3:00-5:00 PM, though this is allowed."
    },
    {
      "judge_key": "deepseek_v3",
      "judge_name": "DeepSeek V3.2",
      "respondent_key": "claude_sonnet",
      "respondent_name": "Claude Sonnet 4.5",
      "weighted_score": 4.2,
      "brief_justification": "The proposed schedule violates constraint 6 by having gaps with no talks running (e.g., 11:30 AM-12:00 PM and 2:30-5:00 PM), and the AI incorrectly claimed it was valid, reducing correctness and usefulness."
    },
    {
      "judge_key": "deepseek_v3",
      "judge_name": "DeepSeek V3.2",
      "respondent_key": "claude_opus",
      "respondent_name": "Claude Opus 4.5",
      "weighted_score": 7.6,
      "brief_justification": "The response presents a logically valid schedule that meets most constraints, but the initial schedule contains a 15-minute gap that violates the 'at least one talk must be running at all times' rule, and the adjusted schedule incorrectly places Talk E before lunch without verifying all constraints remain satisfied."
    },
    {
      "judge_key": "deepseek_v3",
      "judge_name": "DeepSeek V3.2",
      "respondent_key": "gemini_3_pro",
      "respondent_name": "Gemini 3 Pro Preview",
      "weighted_score": 1.65,
      "brief_justification": "The response is incomplete, ending mid-sentence, and fails to provide a full schedule or proof, making it largely incorrect and unusable."
    },
    {
      "judge_key": "deepseek_v3",
      "judge_name": "DeepSeek V3.2",
      "respondent_key": "gemini_2_5_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 6.15,
      "brief_justification": "The response demonstrates a logical, step-by-step attempt at scheduling but fails to produce a complete, valid schedule or a definitive proof of impossibility, leaving the problem unresolved."
    },
    {
      "judge_key": "deepseek_v3",
      "judge_name": "DeepSeek V3.2",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 9.5,
      "brief_justification": "The response correctly identifies the impossibility through a precise mathematical argument (300 total talk minutes < 420 available minutes), provides a clear step-by-step proof, and demonstrates deep understanding by showing why parallel sessions cannot resolve the contradiction."
    },
    {
      "judge_key": "deepseek_v3",
      "judge_name": "DeepSeek V3.2",
      "respondent_key": "olmo_think",
      "respondent_name": "OLMo Think",
      "weighted_score": 7.45,
      "brief_justification": "The response provides a logically valid schedule that satisfies all constraints, but lacks analysis of alternative arrangements or proof of optimality, and doesn't explicitly verify all room capacity limits."
    },
    {
      "judge_key": "deepseek_v3",
      "judge_name": "DeepSeek V3.2",
      "respondent_key": "grok_direct",
      "respondent_name": "Grok 3 (Direct)",
      "weighted_score": 5.15,
      "brief_justification": "The response is logically structured and clear, but it fails to produce a valid schedule or correctly prove impossibility due to misinterpretations of constraints and an incomplete final conclusion."
    },
    {
      "judge_key": "claude_opus",
      "judge_name": "Claude Opus 4.5",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 5.95,
      "brief_justification": "The response is well-structured and thorough in its presentation, but contains critical errors: Constraint 8 is violated (E ends at 3:30 PM, not by 3:00 PM), and Constraint 6 is violated (gaps exist at 9:45-10:00 and 2:45-3:00 with no talks running). The model acknowledges the Constraint 8 violation but incorrectly claims Constraint 6 is satisfied. A valid schedule does exist but was not found."
    },
    {
      "judge_key": "claude_opus",
      "judge_name": "Claude Opus 4.5",
      "respondent_key": "gemini_3_flash",
      "respondent_name": "Gemini 3 Flash Preview",
      "weighted_score": 4.8,
      "brief_justification": "The schedule has a critical flaw: Talk F is 45 minutes but is shown split across lunch (11:30-12:00 and 1:00-1:15), which only accounts for 45 minutes but the split itself is problematic as talks typically cannot span lunch breaks. More importantly, there's a gap from 10:00-11:30 where only Talk A runs, but the constraint verification claims continuous activity without addressing whether splitting F across lunch is valid. The schedule structure is clear but the solution's validity is questionable."
    },
    {
      "judge_key": "claude_opus",
      "judge_name": "Claude Opus 4.5",
      "respondent_key": "claude_sonnet",
      "respondent_name": "Claude Sonnet 4.5",
      "weighted_score": 5.4,
      "brief_justification": "The final schedule has critical errors: there's a gap from 10:00-11:00 AM (only A runs 10:00-11:30, but D is listed at 11:00-11:30, leaving 10:00-11:00 with just A which is fine, but the coverage check is confused), and more importantly there's a gap from 2:30-5:00 PM with no talks running, violating constraint 6. The verification claims F runs until 2:30 but F is scheduled 1:00-1:45. The methodology is sound but execution contains logical errors."
    },
    {
      "judge_key": "claude_opus",
      "judge_name": "Claude Opus 4.5",
      "respondent_key": "deepseek_v3",
      "respondent_name": "DeepSeek V3.2",
      "weighted_score": 4.05,
      "brief_justification": "The response shows good analytical approach and constraint identification, but fails to produce a valid complete schedule. The work is incomplete (cuts off mid-sentence), contains errors in the attempted schedule (coverage gaps 9:30-9:45 and 11:30-12:00 not addressed), and doesn't verify all constraints are satisfied. The methodology is sound but execution is flawed and unfinished."
    },
    {
      "judge_key": "claude_opus",
      "judge_name": "Claude Opus 4.5",
      "respondent_key": "gemini_3_pro",
      "respondent_name": "Gemini 3 Pro Preview",
      "weighted_score": 1,
      "brief_justification": "The response is severely incomplete, cutting off mid-schedule after only showing one talk placement. It fails to provide a complete solution or verify any constraints, making it impossible to evaluate correctness or usefulness of the proposed schedule."
    },
    {
      "judge_key": "claude_opus",
      "judge_name": "Claude Opus 4.5",
      "respondent_key": "gemini_2_5_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 3.65,
      "brief_justification": "The response shows good systematic thinking and constraint analysis, but it is incomplete - the answer cuts off mid-sentence without providing a final valid schedule or proving none exists. The partial attempts contain some logical errors (e.g., placing B in morning creates overlap issues with C that aren't fully resolved), and the response fails to deliver the requested outcome."
    },
    {
      "judge_key": "claude_opus",
      "judge_name": "Claude Opus 4.5",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 7.35,
      "brief_justification": "The response correctly identifies the core impossibility through a valid counting argument (300 min of talks vs 420 min requiring continuous coverage). The mathematical reasoning is sound and well-structured. However, the response appears truncated mid-sentence, leaving the proof incomplete. It also doesn't fully explore whether parallel sessions in multiple rooms could theoretically help (though it mentions this briefly). The clarity of presentation is good with proper formatting."
    },
    {
      "judge_key": "claude_opus",
      "judge_name": "Claude Opus 4.5",
      "respondent_key": "olmo_think",
      "respondent_name": "OLMo Think",
      "weighted_score": 0,
      "brief_justification": "The response is completely empty - no schedule was provided, no analysis was attempted, and no proof of impossibility was given. The question required either a valid schedule or proof that none exists, but neither was delivered."
    },
    {
      "judge_key": "claude_opus",
      "judge_name": "Claude Opus 4.5",
      "respondent_key": "grok_direct",
      "respondent_name": "Grok 3 (Direct)",
      "weighted_score": 4.25,
      "brief_justification": "The response shows good problem-solving methodology but fails to complete the task - it cuts off mid-sentence without providing a final valid schedule or definitive proof that none exists. The analysis of constraint 6 is reasonable but the response gets stuck in iterations without resolution. Several scheduling attempts contain errors and the response doesn't successfully verify all constraints are met in any proposed schedule."
    },
    {
      "judge_key": "gemini_3_pro",
      "judge_name": "Gemini 3 Pro Preview",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_3_pro",
      "judge_name": "Gemini 3 Pro Preview",
      "respondent_key": "gemini_3_flash",
      "respondent_name": "Gemini 3 Flash Preview",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_3_pro",
      "judge_name": "Gemini 3 Pro Preview",
      "respondent_key": "claude_sonnet",
      "respondent_name": "Claude Sonnet 4.5",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_3_pro",
      "judge_name": "Gemini 3 Pro Preview",
      "respondent_key": "deepseek_v3",
      "respondent_name": "DeepSeek V3.2",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_3_pro",
      "judge_name": "Gemini 3 Pro Preview",
      "respondent_key": "claude_opus",
      "respondent_name": "Claude Opus 4.5",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_3_pro",
      "judge_name": "Gemini 3 Pro Preview",
      "respondent_key": "gemini_2_5_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 2.05,
      "brief_justification": "The response is incomplete and cuts off mid-sentence during the brainstorming phase, failing to provide a final schedule or conclusion."
    },
    {
      "judge_key": "gemini_3_pro",
      "judge_name": "Gemini 3 Pro Preview",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_3_pro",
      "judge_name": "Gemini 3 Pro Preview",
      "respondent_key": "olmo_think",
      "respondent_name": "OLMo Think",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_3_pro",
      "judge_name": "Gemini 3 Pro Preview",
      "respondent_key": "grok_direct",
      "respondent_name": "Grok 3 (Direct)",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gemini_2_5_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 7.75,
      "brief_justification": "The model provides a well-structured schedule and checks most constraints. However, it fails to meet a critical constraint (E ending by 3 PM) and incorrectly claims continuous talks after lunch."
    },
    {
      "judge_key": "gemini_2_5_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "gemini_3_flash",
      "respondent_name": "Gemini 3 Flash Preview",
      "weighted_score": 5.2,
      "brief_justification": "The proposed schedule is invalid due to multiple constraint violations, particularly regarding talk overlaps and the 'at least one talk running' constraint."
    },
    {
      "judge_key": "gemini_2_5_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "claude_sonnet",
      "respondent_name": "Claude Sonnet 4.5",
      "weighted_score": 8.55,
      "brief_justification": "The model provides a mostly correct and well-structured solution, demonstrating a good thought process. However, there's a minor error in the final verification of constraint 6 regarding talk coverage."
    },
    {
      "judge_key": "gemini_2_5_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "deepseek_v3",
      "respondent_name": "DeepSeek V3.2",
      "weighted_score": 6.45,
      "brief_justification": "The model makes a good attempt at a step-by-step solution but ultimately fails to produce a valid schedule and gets stuck in the process. It correctly identifies constraints and breaks down the problem but struggles with the combinatorial aspect."
    },
    {
      "judge_key": "gemini_2_5_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "claude_opus",
      "respondent_name": "Claude Opus 4.5",
      "weighted_score": 3.65,
      "brief_justification": "The initial schedule provided is incomplete, missing a talk, and the 'adjusted schedule' is also incomplete and contains errors, making the overall solution incorrect."
    },
    {
      "judge_key": "gemini_2_5_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "gemini_3_pro",
      "respondent_name": "Gemini 3 Pro Preview",
      "weighted_score": 0,
      "brief_justification": "The response is incomplete and does not provide a full schedule, making it impossible to evaluate against the constraints."
    },
    {
      "judge_key": "gemini_2_5_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 10,
      "brief_justification": "The model correctly identifies the impossibility of the schedule based on the 'at least one talk running' constraint and provides a clear, detailed proof."
    },
    {
      "judge_key": "gemini_2_5_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "olmo_think",
      "respondent_name": "OLMo Think",
      "weighted_score": 0,
      "brief_justification": "The model did not provide a response, therefore all scores are 0."
    },
    {
      "judge_key": "gemini_2_5_flash",
      "judge_name": "Gemini 2.5 Flash",
      "respondent_key": "grok_direct",
      "respondent_name": "Grok 3 (Direct)",
      "weighted_score": 5.6,
      "brief_justification": "The model correctly identifies many constraints and attempts to build a schedule but struggles with the 'at least one talk' constraint, leading to an incomplete and ultimately incorrect conclusion about its feasibility."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 4.35,
      "brief_justification": "The answer outlines a schedule and discusses constraints, but it violates the hard deadline that Talk E must end by 3:00 PM, making the schedule invalid and failing to provide a correct solution or proof of impossibility."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "gemini_3_flash",
      "respondent_name": "Gemini 3 Flash Preview",
      "weighted_score": 4.95,
      "brief_justification": "The schedule meets many constraints but illegally splits Talk F across the lunch break, which the problem does not permit, making the solution incorrect and of limited practical value."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "claude_sonnet",
      "respondent_name": "Claude Sonnet 4.5",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "deepseek_v3",
      "respondent_name": "DeepSeek V3.2",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "claude_opus",
      "respondent_name": "Claude Opus 4.5",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "gemini_3_pro",
      "respondent_name": "Gemini 3 Pro Preview",
      "weighted_score": 1.85,
      "brief_justification": "The answer is truncated and fails to provide a full schedule or proof, making it largely incorrect and incomplete, with limited clarity and usefulness."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "gemini_2_5_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 2.6,
      "brief_justification": "The response begins a scheduling attempt but stops without delivering a complete valid schedule or a proof of impossibility, leaving the problem unresolved."
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "olmo_think",
      "respondent_name": "OLMo Think",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "gpt_oss_120b",
      "judge_name": "GPT-OSS-120B",
      "respondent_key": "grok_direct",
      "respondent_name": "Grok 3 (Direct)",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "olmo_think",
      "judge_name": "OLMo Think",
      "respondent_key": "mimo_v2_flash",
      "respondent_name": "MiMo-V2-Flash",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "olmo_think",
      "judge_name": "OLMo Think",
      "respondent_key": "gemini_3_flash",
      "respondent_name": "Gemini 3 Flash Preview",
      "weighted_score": 0,
      "brief_justification": ""
    },
    {
      "judge_key": "grok_direct",
      "judge_name": "Grok 3 (Direct)",
      "respondent_key": "gemini_3_flash",
      "respondent_name": "Gemini 3 Flash Preview",
      "weighted_score": 8.4,
      "brief_justification": "The response provides a mostly correct and clear schedule that adheres to most constraints, though the handling of Talk F spanning lunch is slightly ambiguous. It covers all key aspects with practical value, but lacks deeper exploration of alternative schedules."
    },
    {
      "judge_key": "grok_direct",
      "judge_name": "Grok 3 (Direct)",
      "respondent_key": "claude_sonnet",
      "respondent_name": "Claude Sonnet 4.5",
      "weighted_score": 9.4,
      "brief_justification": "The response provides a correct and complete schedule adhering to all constraints, with clear step-by-step verification. Depth is slightly limited as it focuses on one valid solution without exploring alternatives."
    },
    {
      "judge_key": "grok_direct",
      "judge_name": "Grok 3 (Direct)",
      "respondent_key": "deepseek_v3",
      "respondent_name": "DeepSeek V3.2",
      "weighted_score": 7.6,
      "brief_justification": "The response provides a detailed step-by-step approach to scheduling the conference and proposes a feasible schedule, though it contains a minor error in ensuring 'at least one talk at all times' is fully verified. It is thorough and practical but lacks polished clarity and deeper constraint conflict analysis."
    },
    {
      "judge_key": "grok_direct",
      "judge_name": "Grok 3 (Direct)",
      "respondent_key": "claude_opus",
      "respondent_name": "Claude Opus 4.5",
      "weighted_score": 8.2,
      "brief_justification": "The response provides a valid schedule meeting most constraints, though the initial schedule has a 15-minute gap potentially violating constraint 6; the adjusted schedule resolves this. It is clear, thorough, and practical, but lacks deeper exploration of alternative schedules."
    },
    {
      "judge_key": "grok_direct",
      "judge_name": "Grok 3 (Direct)",
      "respondent_key": "gemini_3_pro",
      "respondent_name": "Gemini 3 Pro Preview",
      "weighted_score": 2.65,
      "brief_justification": "The response is incomplete as it cuts off mid-schedule without fully addressing all talks or constraints. It lacks correctness and depth due to missing validation of key constraints like Talk A's timing and room assignments."
    },
    {
      "judge_key": "grok_direct",
      "judge_name": "Grok 3 (Direct)",
      "respondent_key": "gemini_2_5_flash",
      "respondent_name": "Gemini 2.5 Flash",
      "weighted_score": 5.9,
      "brief_justification": "The response shows effort in addressing constraints and scheduling talks, but it fails to provide a complete or valid schedule and leaves gaps, violating a key constraint. The explanation is somewhat clear but lacks a conclusive solution or proof of impossibility."
    },
    {
      "judge_key": "grok_direct",
      "judge_name": "Grok 3 (Direct)",
      "respondent_key": "gpt_oss_120b",
      "respondent_name": "GPT-OSS-120B",
      "weighted_score": 8.75,
      "brief_justification": "The response correctly identifies the impossibility of scheduling due to insufficient talk duration against available time, with a clear and logical proof. It lacks a brief exploration of other constraints' impact but is thorough in its primary argument."
    },
    {
      "judge_key": "grok_direct",
      "judge_name": "Grok 3 (Direct)",
      "respondent_key": "olmo_think",
      "respondent_name": "OLMo Think",
      "weighted_score": 0,
      "brief_justification": "The response is missing or incomplete as no content was provided for evaluation."
    }
  ],
  "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)"
  }
}