{ "context": { "cap_tokens": null, "max_model_len": null, "targets": [ { "attempted_context_tokens": 32768, "chars_per_token": 3.0, "clamped_tokens": 32768, "content_chunks": 46, "decode_tok_s": 40.65986002938289, "e2e_ms": 15832.861999981105, "effective_prefill_tok_s": 2123.9293058130525, "estimated_prompt_tokens": 32768, "generation_ms": 1131.3368999981321, "mean_inter_token_latency_ms": 24.594280434742004, "output_token_source": "usage", "output_tokens": 47, "prompt_tokens": 31225, "reasoning_chunks": 0, "status": "passed", "target_tokens": 32768, "time_to_first_output_ms": 14701.525099982973, "ttft_ms": 14701.525999989826, "usage": { "completion_tokens": 47, "prompt_tokens": 31225, "prompt_tokens_details": { "cached_tokens": 0 }, "total_tokens": 31272 }, "visible_generation_ms": 1131.335999991279 } ] }, "evaluation_protocol": { "budget_semantics": "visible_answer_tokens plus reasoning_headroom_tokens are sent as one max_tokens cap; the endpoint does not hard-partition the channels", "minimum_comparable_repetitions": 3, "minimum_pass_rate": 1.0, "reasoning_headroom_tokens": 0, "records_finish_reason": true, "records_full_visible_answer": true, "records_reasoning_channel_metadata": true, "repetitions": 3, "version": 3, "visible_answer_tokens": 1024 }, "failures": [ { "error": "answer", "eval_id": "mmlu-pro-30-computer-science", "failure_classes": [ "visible_answer_budget_exhausted" ], "pass_rate": 0.0, "suite": "hf-mmlu-pro-10-repeated" }, { "error": "answer", "eval_id": "mmlu-pro-40-engineering", "failure_classes": [ "visible_answer_budget_exhausted" ], "pass_rate": 0.0, "suite": "hf-mmlu-pro-10-repeated" } ], "identity": { "base_url": "http://127.0.0.1:8081/v1", "candidate_id": "qwopus-q6k-nospec", "config_id": "q6k-nospec-64k", "engine": "llama.cpp", "gpu": "rtx5090-primary", "model": "qwopus38-27b-flash-q6k-nospec-64k", "started_at": "2026-09-12T18:55:06Z" }, "intelligence": { "checks": [ { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "```diff\n--- a/app.py\n+++ b/app.py\n@@ -1,2 +1,2 @@\n-timeout = 30\n+timeout = 45\n retries = 2\n```", "content_chars": 94, "content_excerpt": "```diff\n--- a/app.py\n+++ b/app.py\n@@ -1,2 +1,2 @@\n-timeout = 30\n+timeout = 45\n retries = 2\n```", "failure_class": null, "finish_reason": "stop", "latency_ms": 1124.9765999964438, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "diff_shape", "passed": true }, { "name": "removes_old_timeout", "passed": true }, { "name": "adds_new_timeout", "passed": true } ], "usage": { "completion_tokens": 45, "prompt_tokens": 51, "prompt_tokens_details": { "cached_tokens": 0 }, "total_tokens": 96 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "```diff\n--- a/app.py\n+++ b/app.py\n@@ -1,2 +1,2 @@\n-timeout = 30\n+timeout = 45\n retries = 2\n```", "content_chars": 94, "content_excerpt": "```diff\n--- a/app.py\n+++ b/app.py\n@@ -1,2 +1,2 @@\n-timeout = 30\n+timeout = 45\n retries = 2\n```", "failure_class": null, "finish_reason": "stop", "latency_ms": 883.4703000029549, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "diff_shape", "passed": true }, { "name": "removes_old_timeout", "passed": true }, { "name": "adds_new_timeout", "passed": true } ], "usage": { "completion_tokens": 45, "prompt_tokens": 51, "prompt_tokens_details": { "cached_tokens": 47 }, "total_tokens": 96 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "```diff\n--- a/app.py\n+++ b/app.py\n@@ -1,2 +1,2 @@\n-timeout = 30\n+timeout = 45\n retries = 2\n```", "content_chars": 94, "content_excerpt": "```diff\n--- a/app.py\n+++ b/app.py\n@@ -1,2 +1,2 @@\n-timeout = 30\n+timeout = 45\n retries = 2\n```", "failure_class": null, "finish_reason": "stop", "latency_ms": 889.3718000035733, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "diff_shape", "passed": true }, { "name": "removes_old_timeout", "passed": true }, { "name": "adds_new_timeout", "passed": true } ], "usage": { "completion_tokens": 45, "prompt_tokens": 51, "prompt_tokens_details": { "cached_tokens": 47 }, "total_tokens": 96 } } ], "id": "unified_diff_timeout_edit", "pass_count": 3, "pass_rate": 1.0, "required_pass_rate": 1.0, "status": "passed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The total latency (2,950 ms) exceeds the 2,500 ms timeout because the LLM takes too long, so you should implement streaming responses or use a faster, smaller LLM to reduce the generation time.", "content_chars": 193, "content_excerpt": "The total latency (2,950 ms) exceeds the 2,500 ms timeout because the LLM takes too long, so you should implement streaming responses or use a faster, smaller LLM to reduce the generation time.", "failure_class": null, "finish_reason": "stop", "latency_ms": 1157.7064999728464, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "identifies_budget_overrun", "passed": true }, { "name": "offers_latency_fix", "passed": true } ], "usage": { "completion_tokens": 50, "prompt_tokens": 79, "prompt_tokens_details": { "cached_tokens": 0 }, "total_tokens": 129 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The total latency (2,950 ms) exceeds the 2,500 ms timeout because the LLM takes too long, so you should implement streaming responses or use a faster, smaller LLM to reduce the generation time.", "content_chars": 193, "content_excerpt": "The total latency (2,950 ms) exceeds the 2,500 ms timeout because the LLM takes too long, so you should implement streaming responses or use a faster, smaller LLM to reduce the generation time.", "failure_class": null, "finish_reason": "stop", "latency_ms": 956.4555999822915, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "identifies_budget_overrun", "passed": true }, { "name": "offers_latency_fix", "passed": true } ], "usage": { "completion_tokens": 50, "prompt_tokens": 79, "prompt_tokens_details": { "cached_tokens": 75 }, "total_tokens": 129 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The total latency (2,950 ms) exceeds the 2,500 ms timeout because the LLM takes too long, so you should implement streaming responses or use a faster, smaller LLM to reduce the generation time.", "content_chars": 193, "content_excerpt": "The total latency (2,950 ms) exceeds the 2,500 ms timeout because the LLM takes too long, so you should implement streaming responses or use a faster, smaller LLM to reduce the generation time.", "failure_class": null, "finish_reason": "stop", "latency_ms": 949.508199992124, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "identifies_budget_overrun", "passed": true }, { "name": "offers_latency_fix", "passed": true } ], "usage": { "completion_tokens": 50, "prompt_tokens": 79, "prompt_tokens_details": { "cached_tokens": 75 }, "total_tokens": 129 } } ], "id": "parallel_timeout_triage", "pass_count": 3, "pass_rate": 1.0, "required_pass_rate": 1.0, "status": "passed", "validator": "deterministic_text_checks" } ], "status": "passed" }, "run_id": "fast-bakeoff-20260912T185506Z", "schema": "anvil-serving.fast-tier-bakeoff/v1", "score_inputs": { "e2e_p50_ms": 15832.861999981105, "intelligence_pass_rate": 1.0, "operational_fit_notes": [ "endpoint was already loaded; benchmark did not start or stop serves" ], "session_recall_passed": false, "thinking_mode": "disabled", "tool_call_passed": true, "ttft_p50_ms": 14701.525999989826, "usable_context_tokens": 32768, "voice_latency_ms": null }, "selection": { "context_targets": [ 32768 ], "endpoint_already_loaded": true, "requests_per_context": 1, "suites": [ "chat", "tool", "intelligence" ] }, "session": { "checks": [], "status": "not_run" }, "source_recipe": { "ref": null, "serve_command": null }, "suites": { "hf-mmlu-pro-10-repeated": { "checks": [ { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The pituitary gland is located in the sella turcica, a depression in the sphenoid bone at the base of the skull. This places it within the cranial cavity.\n\nLet's evaluate the options:\n* **A. Ventral**: This refers to the front or belly side of the body, not a specific cavity containing the pituitary.\n* **B. Dorsal**: This refers to the back side of the body. While the cranial cavity is part of the dorsal body cavity (which also includes the spinal cavity), \"Cranial\" is the specific and correct answer for the location of the pituitary gland.\n* **C. Buccal**: This refers to the cheek or mouth area.\n* **D. Thoracic**: This is the chest cavity.\n* **E. Pericardial**: This is the cavity surrounding the heart.\n* **F. Abdominal**: This is the belly cavity.\n* **G. Spinal**: This is the cavity containing the spinal cord.\n* **H. Pelvic**: This is the cavity containing the pelvic organs.\n* **I. Pleural**: This is the cavity surrounding the lungs.\n* **J. Cranial**: This is the skull cavity, which contains the brain and the pituitary gland.\n\nTherefore, the correct answer is J.\n\nFINAL=J", "content_chars": 1108, "content_excerpt": "The pituitary gland is located in the sella turcica, a depression in the sphenoid bone at the base of the skull. This places it within the cranial cavity.\n\nLet's evaluate the options:\n* **A. Ventral", "failure_class": null, "finish_reason": "stop", "latency_ms": 5469.811399991158, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 298, "prompt_tokens": 97, "prompt_tokens_details": { "cached_tokens": 0 }, "total_tokens": 395 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The pituitary gland is located in the sella turcica, a depression in the sphenoid bone at the base of the skull. This places it within the cranial cavity.\n\nLet's evaluate the options:\n* **A. Ventral**: This refers to the front or belly side of the body, not a specific cavity containing the pituitary.\n* **B. Dorsal**: This refers to the back side of the body. While the cranial cavity is part of the dorsal body cavity (which also includes the spinal cavity), \"Cranial\" is the specific and correct answer for the location of the pituitary gland.\n* **C. Buccal**: This refers to the cheek or mouth area.\n* **D. Thoracic**: This is the chest cavity.\n* **E. Pericardial**: This is the cavity surrounding the heart.\n* **F. Abdominal**: This is the belly cavity.\n* **G. Spinal**: This is the cavity containing the spinal cord.\n* **H. Pelvic**: This is the cavity containing the pelvic organs.\n* **I. Pleural**: This is the cavity surrounding the lungs.\n* **J. Cranial**: This is the skull cavity, which contains the brain and the pituitary gland.\n\nTherefore, the correct answer is J.\n\nFINAL=J", "content_chars": 1108, "content_excerpt": "The pituitary gland is located in the sella turcica, a depression in the sphenoid bone at the base of the skull. This places it within the cranial cavity.\n\nLet's evaluate the options:\n* **A. Ventral", "failure_class": null, "finish_reason": "stop", "latency_ms": 5437.85669998033, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 298, "prompt_tokens": 97, "prompt_tokens_details": { "cached_tokens": 93 }, "total_tokens": 395 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The pituitary gland is located in the sella turcica, a depression in the sphenoid bone at the base of the skull. This places it within the cranial cavity.\n\nLet's evaluate the options:\n* **A. Ventral**: This refers to the front or belly side of the body, not a specific cavity containing the pituitary.\n* **B. Dorsal**: This refers to the back side of the body. While the cranial cavity is part of the dorsal body cavity (which also includes the spinal cavity), \"Cranial\" is the specific and correct answer for the location of the pituitary gland.\n* **C. Buccal**: This refers to the cheek or mouth area.\n* **D. Thoracic**: This is the chest cavity.\n* **E. Pericardial**: This is the cavity surrounding the heart.\n* **F. Abdominal**: This is the belly cavity.\n* **G. Spinal**: This is the cavity containing the spinal cord.\n* **H. Pelvic**: This is the cavity containing the pelvic organs.\n* **I. Pleural**: This is the cavity surrounding the lungs.\n* **J. Cranial**: This is the skull cavity, which contains the brain and the pituitary gland.\n\nTherefore, the correct answer is J.\n\nFINAL=J", "content_chars": 1108, "content_excerpt": "The pituitary gland is located in the sella turcica, a depression in the sphenoid bone at the base of the skull. This places it within the cranial cavity.\n\nLet's evaluate the options:\n* **A. Ventral", "failure_class": null, "finish_reason": "stop", "latency_ms": 5314.538899983745, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 298, "prompt_tokens": 97, "prompt_tokens_details": { "cached_tokens": 93 }, "total_tokens": 395 } } ], "id": "mmlu-pro-5-health", "pass_count": 3, "pass_rate": 1.0, "required_pass_rate": 1.0, "status": "passed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To determine how much more light the telescope can gather than the eye, we need to compare the areas of their apertures. The amount of light gathered by an optical instrument is proportional to the area of its aperture (the opening that collects light).\n\n**Step 1: Convert units to be consistent.**\n* Diameter of the pupil ($d_{eye}$) = 5 mm\n* Diameter of the telescope aperture ($d_{telescope}$) = 50 cm\n\nLet's convert the telescope diameter to millimeters:\n$50 \\text{ cm} = 50 \\times 10 \\text{ mm} = 500 \\text{ mm}$\n\n**Step 2: Calculate the ratio of the diameters.**\n$\\text{Ratio of diameters} = \\frac{d_{telescope}}{d_{eye}} = \\frac{500 \\text{ mm}}{5 \\text{ mm}} = 100$\n\n**Step 3: Calculate the ratio of the areas.**\nThe area of a circle is given by $A = \\pi r^2 = \\pi (\\frac{d}{2})^2 = \\frac{\\pi d^2}{4}$.\nSince the area is proportional to the square of the diameter ($A \\propto d^2$), the ratio of the light-gathering power is the square of the ratio of the diameters.\n\n$\\text{Ratio of areas} = \\left( \\frac{d_{telescope}}{d_{eye}} \\right)^2 = (100)^2 = 10,000$\n\n**Conclusion:**\nThe telescope can gather 10,000 times more light than the eye.\n\nThis corresponds to option **E**.\n\nFINAL=E", "content_chars": 1194, "content_excerpt": "To determine how much more light the telescope can gather than the eye, we need to compare the areas of their apertures. The amount of light gathered by an optical instrument is proportional to the ar", "failure_class": null, "finish_reason": "stop", "latency_ms": 6839.844600006472, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 380, "prompt_tokens": 157, "prompt_tokens_details": { "cached_tokens": 149 }, "total_tokens": 537 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To determine how much more light the telescope can gather than the eye, we need to compare the areas of their apertures. The amount of light gathered by an optical instrument is proportional to the area of its aperture (the opening that collects light).\n\n**Step 1: Convert units to be consistent.**\n* Diameter of the pupil ($d_{eye}$) = 5 mm\n* Diameter of the telescope aperture ($d_{telescope}$) = 50 cm\n\nLet's convert the telescope diameter to millimeters:\n$50 \\text{ cm} = 50 \\times 10 \\text{ mm} = 500 \\text{ mm}$\n\n**Step 2: Calculate the ratio of the diameters.**\n$\\text{Ratio of diameters} = \\frac{d_{telescope}}{d_{eye}} = \\frac{500 \\text{ mm}}{5 \\text{ mm}} = 100$\n\n**Step 3: Calculate the ratio of the areas.**\nThe area of a circle is given by $A = \\pi r^2 = \\pi (\\frac{d}{2})^2 = \\frac{\\pi d^2}{4}$.\nSince the area is proportional to the square of the diameter ($A \\propto d^2$), the ratio of the light-gathering power is the square of the ratio of the diameters.\n\n$\\text{Ratio of areas} = \\left( \\frac{d_{telescope}}{d_{eye}} \\right)^2 = (100)^2 = 10,000$\n\n**Conclusion:**\nThe telescope can gather 10,000 times more light than the eye.\n\nThis corresponds to option **E**.\n\nFINAL=E", "content_chars": 1194, "content_excerpt": "To determine how much more light the telescope can gather than the eye, we need to compare the areas of their apertures. The amount of light gathered by an optical instrument is proportional to the ar", "failure_class": null, "finish_reason": "stop", "latency_ms": 7420.1977999764495, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 380, "prompt_tokens": 157, "prompt_tokens_details": { "cached_tokens": 153 }, "total_tokens": 537 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To determine how much more light the telescope can gather than the eye, we need to compare the areas of their apertures. The amount of light gathered by an optical instrument is proportional to the area of its aperture (the opening that collects light).\n\n**Step 1: Convert units to be consistent.**\n* Diameter of the pupil ($d_{eye}$) = 5 mm\n* Diameter of the telescope aperture ($d_{telescope}$) = 50 cm\n\nLet's convert the telescope diameter to millimeters:\n$50 \\text{ cm} = 50 \\times 10 \\text{ mm} = 500 \\text{ mm}$\n\n**Step 2: Calculate the ratio of the diameters.**\n$\\text{Ratio of diameters} = \\frac{d_{telescope}}{d_{eye}} = \\frac{500 \\text{ mm}}{5 \\text{ mm}} = 100$\n\n**Step 3: Calculate the ratio of the areas.**\nThe area of a circle is given by $A = \\pi r^2 = \\pi (\\frac{d}{2})^2 = \\frac{\\pi d^2}{4}$.\nSince the area is proportional to the square of the diameter ($A \\propto d^2$), the ratio of the light-gathering power is the square of the ratio of the diameters.\n\n$\\text{Ratio of areas} = \\left( \\frac{d_{telescope}}{d_{eye}} \\right)^2 = (100)^2 = 10,000$\n\n**Conclusion:**\nThe telescope can gather 10,000 times more light than the eye.\n\nThis corresponds to option **E**.\n\nFINAL=E", "content_chars": 1194, "content_excerpt": "To determine how much more light the telescope can gather than the eye, we need to compare the areas of their apertures. The amount of light gathered by an optical instrument is proportional to the ar", "failure_class": null, "finish_reason": "stop", "latency_ms": 6689.1722999862395, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 380, "prompt_tokens": 157, "prompt_tokens_details": { "cached_tokens": 153 }, "total_tokens": 537 } } ], "id": "mmlu-pro-10-physics", "pass_count": 3, "pass_rate": 1.0, "required_pass_rate": 1.0, "status": "passed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To determine the correct answer, we need to analyze the definitions of the terms and the logical flow of the sentence.\n\n1. **First Blank vs. Second Blank:** The sentence contrasts two types of consumer campaigns.\n * **Boycotts** are campaigns where consumers refuse to buy from a company to punish bad behavior.\n * **Buycotts** (or Buyalls) are campaigns where consumers actively choose to buy from a company to reward good behavior.\n * The sentence says: \"In contrast to _______, _______ aim to reward favourable behaviour...\"\n * Therefore, the first blank should be **Boycotts** (the negative action) and the second blank should be **Buycotts** (the positive action). This eliminates options B, D, G, and I.\n\n2. **Third Blank:** The sentence continues: \"The success of such campaigns has been heightened through the use of ___________\"\n * Modern campaigns often use **Digital technology** (social media, apps, online platforms) to spread awareness and coordinate actions. While Blockchain is a specific technology, \"Digital technology\" is the broader, more standard term used in general business contexts for facilitating campaigns. However, let's look at the options.\n * Remaining options: A, C, E, F, H, J.\n * Options with \"Digital technology\": C, F, H.\n * Options with \"Blockchain technology\": A, E, J.\n * Options with \"Physical technology\": H.\n\n3. **Fourth Blank:** \"...which allow campaigns to facilitate the company in achieving _________.\n * The goal of a Buycott is to reward the company. Rewarding a company typically leads to **Increased Sales**.\n * Let's check the options:\n * A: Increased Sales (but uses Blockchain)\n * C: Decreased Sales (Incorrect, Buycotts aim to increase sales)\n * E: Charitable donations (Incorrect, the company is being rewarded, not necessarily donating)\n * F: Increased Sales (Uses Digital technology)\n * H: Increased Sales (Uses Physical technology - unlikely to be the primary driver of modern campaign success compared to digital)\n * J: Decreased Sales (Incorrect)\n\n4. **Evaluating the Best Fit:**\n * **Option F:** \"In contrast to **Boycotts**, **Buycotts** aim to reward favourable behaviour by companies. The success of such campaigns has been heightened through the use of **Digital technology**, which allow campaigns to facilitate the company in achieving **Increased Sales**.\"\n * This makes perfect logical sense. Boycotts punish, Buycotts reward. Digital technology (social media, etc.) helps spread the word about the Buycott, leading to increased sales for the targeted company.\n\n * Let's double-check **Option A**: \"In contrast to **Boycotts**, **Buyalls** aim to reward... through **Blockchain technology**... achieving **Increased Sales**.\"\n * \"Buyalls\" is a less common term than \"Buycotts,\" though sometimes used interchangeably. However, \"Blockchain technology\" is a very specific niche technology. While it can be used for transparency, \"Digital technology\" is the standard answer for how campaigns are facilitated in general business studies. Furthermore, \"Buycotts\" is the standard term paired with \"Boycotts.\"\n\n * Let's double-check **Option C**: \"...achieving **Decreased Sales**.\" This is incorrect because a Buycott is meant to increase sales.\n\n * Let's double-check **Option H**: \"...**Physical technology**...\" This is incorrect.\n\n * Therefore, **Option F** is the most accurate and logical choice.\n\nFINAL=F", "content_chars": 3525, "content_excerpt": "To determine the correct answer, we need to analyze the definitions of the terms and the logical flow of the sentence.\n\n1. **First Blank vs. Second Blank:** The sentence contrasts two types of consum", "failure_class": null, "finish_reason": "stop", "latency_ms": 14362.439699994866, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 809, "prompt_tokens": 230, "prompt_tokens_details": { "cached_tokens": 222 }, "total_tokens": 1039 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To determine the correct answer, we need to analyze the definitions of the terms and the logical flow of the sentence.\n\n1. **First Blank vs. Second Blank:** The sentence contrasts two types of consumer campaigns.\n * **Boycotts** are campaigns where consumers refuse to buy from a company to punish bad behavior.\n * **Buycotts** (or Buyalls) are campaigns where consumers actively choose to buy from a company to reward good behavior.\n * The sentence says: \"In contrast to _______, _______ aim to reward favourable behaviour...\"\n * Therefore, the first blank should be **Boycotts** (the negative action) and the second blank should be **Buycotts** (the positive action). This eliminates options B, D, G, and I.\n\n2. **Third Blank:** The sentence continues: \"The success of such campaigns has been heightened through the use of ___________\"\n * Modern campaigns often use **Digital technology** (social media, apps, online platforms) to spread awareness and coordinate actions. While Blockchain is a specific technology, \"Digital technology\" is the broader, more standard term used in general business contexts for facilitating campaigns. However, let's look at the options.\n * Remaining options: A, C, E, F, H, J.\n * Options with \"Digital technology\": C, F, H.\n * Options with \"Blockchain technology\": A, E, J.\n * Options with \"Physical technology\": H.\n\n3. **Fourth Blank:** \"...which allow campaigns to facilitate the company in achieving _________.\n * The goal of a Buycott is to reward the company. Rewarding a company typically leads to **Increased Sales**.\n * Let's check the options:\n * A: Increased Sales (but uses Blockchain)\n * C: Decreased Sales (Incorrect, Buycotts aim to increase sales)\n * E: Charitable donations (Incorrect, the company is being rewarded, not necessarily donating)\n * F: Increased Sales (Uses Digital technology)\n * H: Increased Sales (Uses Physical technology - unlikely to be the primary driver of modern campaign success compared to digital)\n * J: Decreased Sales (Incorrect)\n\n4. **Evaluating the Best Fit:**\n * **Option F:** \"In contrast to **Boycotts**, **Buycotts** aim to reward favourable behaviour by companies. The success of such campaigns has been heightened through the use of **Digital technology**, which allow campaigns to facilitate the company in achieving **Increased Sales**.\"\n * This makes perfect logical sense. Boycotts punish, Buycotts reward. Digital technology (social media, etc.) helps spread the word about the Buycott, leading to increased sales for the targeted company.\n\n * Let's double-check **Option A**: \"In contrast to **Boycotts**, **Buyalls** aim to reward... through **Blockchain technology**... achieving **Increased Sales**.\"\n * \"Buyalls\" is a less common term than \"Buycotts,\" though sometimes used interchangeably. However, \"Blockchain technology\" is a very specific niche technology. While it can be used for transparency, \"Digital technology\" is the standard answer for how campaigns are facilitated in general business studies. Furthermore, \"Buycotts\" is the standard term paired with \"Boycotts.\"\n\n * Let's double-check **Option C**: \"...achieving **Decreased Sales**.\" This is incorrect because a Buycott is meant to increase sales.\n\n * Let's double-check **Option H**: \"...**Physical technology**...\" This is incorrect.\n\n * Therefore, **Option F** is the most accurate and logical choice.\n\nFINAL=F", "content_chars": 3525, "content_excerpt": "To determine the correct answer, we need to analyze the definitions of the terms and the logical flow of the sentence.\n\n1. **First Blank vs. Second Blank:** The sentence contrasts two types of consum", "failure_class": null, "finish_reason": "stop", "latency_ms": 14638.327400025446, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 809, "prompt_tokens": 230, "prompt_tokens_details": { "cached_tokens": 226 }, "total_tokens": 1039 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To determine the correct answer, we need to analyze the definitions of the terms and the logical flow of the sentence.\n\n1. **First Blank vs. Second Blank:** The sentence contrasts two types of consumer campaigns.\n * **Boycotts** are campaigns where consumers refuse to buy from a company to punish bad behavior.\n * **Buycotts** (or Buyalls) are campaigns where consumers actively choose to buy from a company to reward good behavior.\n * The sentence says: \"In contrast to _______, _______ aim to reward favourable behaviour...\"\n * Therefore, the first blank should be **Boycotts** (the negative action) and the second blank should be **Buycotts** (the positive action). This eliminates options B, D, G, and I.\n\n2. **Third Blank:** The sentence continues: \"The success of such campaigns has been heightened through the use of ___________\"\n * Modern campaigns often use **Digital technology** (social media, apps, online platforms) to spread awareness and coordinate actions. While Blockchain is a specific technology, \"Digital technology\" is the broader, more standard term used in general business contexts for facilitating campaigns. However, let's look at the options.\n * Remaining options: A, C, E, F, H, J.\n * Options with \"Digital technology\": C, F, H.\n * Options with \"Blockchain technology\": A, E, J.\n * Options with \"Physical technology\": H.\n\n3. **Fourth Blank:** \"...which allow campaigns to facilitate the company in achieving _________.\n * The goal of a Buycott is to reward the company. Rewarding a company typically leads to **Increased Sales**.\n * Let's check the options:\n * A: Increased Sales (but uses Blockchain)\n * C: Decreased Sales (Incorrect, Buycotts aim to increase sales)\n * E: Charitable donations (Incorrect, the company is being rewarded, not necessarily donating)\n * F: Increased Sales (Uses Digital technology)\n * H: Increased Sales (Uses Physical technology - unlikely to be the primary driver of modern campaign success compared to digital)\n * J: Decreased Sales (Incorrect)\n\n4. **Evaluating the Best Fit:**\n * **Option F:** \"In contrast to **Boycotts**, **Buycotts** aim to reward favourable behaviour by companies. The success of such campaigns has been heightened through the use of **Digital technology**, which allow campaigns to facilitate the company in achieving **Increased Sales**.\"\n * This makes perfect logical sense. Boycotts punish, Buycotts reward. Digital technology (social media, etc.) helps spread the word about the Buycott, leading to increased sales for the targeted company.\n\n * Let's double-check **Option A**: \"In contrast to **Boycotts**, **Buyalls** aim to reward... through **Blockchain technology**... achieving **Increased Sales**.\"\n * \"Buyalls\" is a less common term than \"Buycotts,\" though sometimes used interchangeably. However, \"Blockchain technology\" is a very specific niche technology. While it can be used for transparency, \"Digital technology\" is the standard answer for how campaigns are facilitated in general business studies. Furthermore, \"Buycotts\" is the standard term paired with \"Boycotts.\"\n\n * Let's double-check **Option C**: \"...achieving **Decreased Sales**.\" This is incorrect because a Buycott is meant to increase sales.\n\n * Let's double-check **Option H**: \"...**Physical technology**...\" This is incorrect.\n\n * Therefore, **Option F** is the most accurate and logical choice.\n\nFINAL=F", "content_chars": 3525, "content_excerpt": "To determine the correct answer, we need to analyze the definitions of the terms and the logical flow of the sentence.\n\n1. **First Blank vs. Second Blank:** The sentence contrasts two types of consum", "failure_class": null, "finish_reason": "stop", "latency_ms": 14196.788499946706, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 809, "prompt_tokens": 230, "prompt_tokens_details": { "cached_tokens": 226 }, "total_tokens": 1039 } } ], "id": "mmlu-pro-15-business", "pass_count": 3, "pass_rate": 1.0, "required_pass_rate": 1.0, "status": "passed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "Let's evaluate each option based on biological facts about arthropods:\n\n* **A. They possess an exoskeleton composed primarily of peptidoglycan.**\n * **Incorrect.** Peptidoglycan is a polymer found in the cell walls of bacteria. Arthropod exoskeletons are composed primarily of **chitin**, a polysaccharide.\n\n* **B. They possess an open circulatory system with a dorsal heart.**\n * **Correct.** Arthropods have an open circulatory system where hemolymph (blood) flows freely in body cavities (hemocoel). The heart is typically a tubular structure located on the dorsal side of the body.\n\n* **C. They are members of a biologically unsuccessful phylum incapable of exploiting diverse habitats and nutrition sources.**\n * **Incorrect.** Arthropods are the most successful and diverse phylum in the animal kingdom. They inhabit virtually every habitat on Earth (terrestrial, freshwater, marine) and have diverse feeding strategies (herbivory, carnivory, omnivory, parasitism, detritivory, etc.).\n\n* **D. They lack paired, jointed appendages.**\n * **Incorrect.** The name \"Arthropoda\" literally means \"jointed feet.\" They are defined by having paired, jointed appendages.\n\n* **E, F, G, H, I, J. N/A**\n * These are not valid answers.\n\nTherefore, the accurate statement is B.\n\nFINAL=B", "content_chars": 1311, "content_excerpt": "Let's evaluate each option based on biological facts about arthropods:\n\n* **A. They possess an exoskeleton composed primarily of peptidoglycan.**\n * **Incorrect.** Peptidoglycan is a polymer fo", "failure_class": null, "finish_reason": "stop", "latency_ms": 5968.968399974983, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 332, "prompt_tokens": 138, "prompt_tokens_details": { "cached_tokens": 130 }, "total_tokens": 470 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "Let's evaluate each option based on biological facts about arthropods:\n\n* **A. They possess an exoskeleton composed primarily of peptidoglycan.**\n * **Incorrect.** Peptidoglycan is a polymer found in the cell walls of bacteria. Arthropod exoskeletons are composed primarily of **chitin**, a polysaccharide.\n\n* **B. They possess an open circulatory system with a dorsal heart.**\n * **Correct.** Arthropods have an open circulatory system where hemolymph (blood) flows freely in body cavities (hemocoel). The heart is typically a tubular structure located on the dorsal side of the body.\n\n* **C. They are members of a biologically unsuccessful phylum incapable of exploiting diverse habitats and nutrition sources.**\n * **Incorrect.** Arthropods are the most successful and diverse phylum in the animal kingdom. They inhabit virtually every habitat on Earth (terrestrial, freshwater, marine) and have diverse feeding strategies (herbivory, carnivory, omnivory, parasitism, detritivory, etc.).\n\n* **D. They lack paired, jointed appendages.**\n * **Incorrect.** The name \"Arthropoda\" literally means \"jointed feet.\" They are defined by having paired, jointed appendages.\n\n* **E, F, G, H, I, J. N/A**\n * These are not valid answers.\n\nTherefore, the accurate statement is B.\n\nFINAL=B", "content_chars": 1311, "content_excerpt": "Let's evaluate each option based on biological facts about arthropods:\n\n* **A. They possess an exoskeleton composed primarily of peptidoglycan.**\n * **Incorrect.** Peptidoglycan is a polymer fo", "failure_class": null, "finish_reason": "stop", "latency_ms": 6370.2593999914825, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 332, "prompt_tokens": 138, "prompt_tokens_details": { "cached_tokens": 134 }, "total_tokens": 470 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "Let's evaluate each option based on biological facts about arthropods:\n\n* **A. They possess an exoskeleton composed primarily of peptidoglycan.**\n * **Incorrect.** Peptidoglycan is a polymer found in the cell walls of bacteria. Arthropod exoskeletons are composed primarily of **chitin**, a polysaccharide.\n\n* **B. They possess an open circulatory system with a dorsal heart.**\n * **Correct.** Arthropods have an open circulatory system where hemolymph (blood) flows freely in body cavities (hemocoel). The heart is typically a tubular structure located on the dorsal side of the body.\n\n* **C. They are members of a biologically unsuccessful phylum incapable of exploiting diverse habitats and nutrition sources.**\n * **Incorrect.** Arthropods are the most successful and diverse phylum in the animal kingdom. They inhabit virtually every habitat on Earth (terrestrial, freshwater, marine) and have diverse feeding strategies (herbivory, carnivory, omnivory, parasitism, detritivory, etc.).\n\n* **D. They lack paired, jointed appendages.**\n * **Incorrect.** The name \"Arthropoda\" literally means \"jointed feet.\" They are defined by having paired, jointed appendages.\n\n* **E, F, G, H, I, J. N/A**\n * These are not valid answers.\n\nTherefore, the accurate statement is B.\n\nFINAL=B", "content_chars": 1311, "content_excerpt": "Let's evaluate each option based on biological facts about arthropods:\n\n* **A. They possess an exoskeleton composed primarily of peptidoglycan.**\n * **Incorrect.** Peptidoglycan is a polymer fo", "failure_class": null, "finish_reason": "stop", "latency_ms": 5865.639099967666, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 332, "prompt_tokens": 138, "prompt_tokens_details": { "cached_tokens": 134 }, "total_tokens": 470 } } ], "id": "mmlu-pro-20-biology", "pass_count": 3, "pass_rate": 1.0, "required_pass_rate": 1.0, "status": "passed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To determine the number of lines in the EPR (Electron Paramagnetic Resonance) spectrum of the $^{13}\\text{CH}_3$ radical, we need to consider the hyperfine splitting caused by the magnetic nuclei interacting with the unpaired electron.\n\n**Step 1: Identify the magnetic nuclei and their spins.**\n* **Carbon-13 ($^{13}\\text{C}$):** This isotope has a nuclear spin quantum number $I = 1/2$.\n* **Hydrogen-1 ($^1\\text{H}$):** The three hydrogen atoms in the methyl group are protium ($^1\\text{H}$), which also have a nuclear spin quantum number $I = 1/2$.\n\n**Step 2: Determine the number of lines from each set of nuclei.**\nThe number of lines produced by a nucleus with spin $I$ is given by $2I + 1$.\n\n* **For the $^{13}\\text{C}$ nucleus:**\n * $I = 1/2$\n * Number of lines = $2(1/2) + 1 = 2$.\n * This means the carbon splits the signal into a doublet.\n\n* **For the three equivalent $^1\\text{H}$ nuclei:**\n * Each hydrogen has $I = 1/2$.\n * Since there are 3 equivalent protons, we use the binomial distribution (Pascal's triangle) to determine the splitting pattern.\n * The number of lines is $n + 1$, where $n$ is the number of equivalent nuclei.\n * Here, $n = 3$, so the number of lines is $3 + 1 = 4$.\n * This creates a quartet with relative intensities of 1:3:3:1.\n\n**Step 3: Calculate the total number of lines.**\nSince the hyperfine interactions from the carbon and the hydrogens are independent (assuming the lines do not overlap, as stated in the problem), the total number of lines is the product of the number of lines from each interaction.\n\n* Total lines = (Lines from $^{13}\\text{C}$) $\\times$ (Lines from $^1\\text{H}$)\n* Total lines = $2 \\times 4 = 8$.\n\n**Conclusion:**\nThe EPR spectrum will consist of 8 lines.\n\nFINAL=B", "content_chars": 1782, "content_excerpt": "To determine the number of lines in the EPR (Electron Paramagnetic Resonance) spectrum of the $^{13}\\text{CH}_3$ radical, we need to consider the hyperfine splitting caused by the magnetic nuclei inte", "failure_class": null, "finish_reason": "stop", "latency_ms": 9470.923799963202, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 535, "prompt_tokens": 117, "prompt_tokens_details": { "cached_tokens": 0 }, "total_tokens": 652 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To determine the number of lines in the EPR (Electron Paramagnetic Resonance) spectrum of the $^{13}\\text{CH}_3$ radical, we need to consider the hyperfine splitting caused by the magnetic nuclei interacting with the unpaired electron.\n\n**Step 1: Identify the magnetic nuclei and their spins.**\n* **Carbon-13 ($^{13}\\text{C}$):** This isotope has a nuclear spin quantum number $I = 1/2$.\n* **Hydrogen-1 ($^1\\text{H}$):** The three hydrogen atoms in the methyl group are protium ($^1\\text{H}$), which also have a nuclear spin quantum number $I = 1/2$.\n\n**Step 2: Determine the number of lines from each set of nuclei.**\nThe number of lines produced by a nucleus with spin $I$ is given by $2I + 1$.\n\n* **For the $^{13}\\text{C}$ nucleus:**\n * $I = 1/2$\n * Number of lines = $2(1/2) + 1 = 2$.\n * This means the carbon splits the signal into a doublet.\n\n* **For the three equivalent $^1\\text{H}$ nuclei:**\n * Each hydrogen has $I = 1/2$.\n * Since there are 3 equivalent protons, we use the binomial distribution (Pascal's triangle) to determine the splitting pattern.\n * The number of lines is $n + 1$, where $n$ is the number of equivalent nuclei.\n * Here, $n = 3$, so the number of lines is $3 + 1 = 4$.\n * This creates a quartet with relative intensities of 1:3:3:1.\n\n**Step 3: Calculate the total number of lines.**\nSince the hyperfine interactions from the carbon and the hydrogens are independent (assuming the lines do not overlap, as stated in the problem), the total number of lines is the product of the number of lines from each interaction.\n\n* Total lines = (Lines from $^{13}\\text{C}$) $\\times$ (Lines from $^1\\text{H}$)\n* Total lines = $2 \\times 4 = 8$.\n\n**Conclusion:**\nThe EPR spectrum will consist of 8 lines.\n\nFINAL=B", "content_chars": 1782, "content_excerpt": "To determine the number of lines in the EPR (Electron Paramagnetic Resonance) spectrum of the $^{13}\\text{CH}_3$ radical, we need to consider the hyperfine splitting caused by the magnetic nuclei inte", "failure_class": null, "finish_reason": "stop", "latency_ms": 9558.636499976274, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 535, "prompt_tokens": 117, "prompt_tokens_details": { "cached_tokens": 113 }, "total_tokens": 652 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To determine the number of lines in the EPR (Electron Paramagnetic Resonance) spectrum of the $^{13}\\text{CH}_3$ radical, we need to consider the hyperfine splitting caused by the magnetic nuclei interacting with the unpaired electron.\n\n**Step 1: Identify the magnetic nuclei and their spins.**\n* **Carbon-13 ($^{13}\\text{C}$):** This isotope has a nuclear spin quantum number $I = 1/2$.\n* **Hydrogen-1 ($^1\\text{H}$):** The three hydrogen atoms in the methyl group are protium ($^1\\text{H}$), which also have a nuclear spin quantum number $I = 1/2$.\n\n**Step 2: Determine the number of lines from each set of nuclei.**\nThe number of lines produced by a nucleus with spin $I$ is given by $2I + 1$.\n\n* **For the $^{13}\\text{C}$ nucleus:**\n * $I = 1/2$\n * Number of lines = $2(1/2) + 1 = 2$.\n * This means the carbon splits the signal into a doublet.\n\n* **For the three equivalent $^1\\text{H}$ nuclei:**\n * Each hydrogen has $I = 1/2$.\n * Since there are 3 equivalent protons, we use the binomial distribution (Pascal's triangle) to determine the splitting pattern.\n * The number of lines is $n + 1$, where $n$ is the number of equivalent nuclei.\n * Here, $n = 3$, so the number of lines is $3 + 1 = 4$.\n * This creates a quartet with relative intensities of 1:3:3:1.\n\n**Step 3: Calculate the total number of lines.**\nSince the hyperfine interactions from the carbon and the hydrogens are independent (assuming the lines do not overlap, as stated in the problem), the total number of lines is the product of the number of lines from each interaction.\n\n* Total lines = (Lines from $^{13}\\text{C}$) $\\times$ (Lines from $^1\\text{H}$)\n* Total lines = $2 \\times 4 = 8$.\n\n**Conclusion:**\nThe EPR spectrum will consist of 8 lines.\n\nFINAL=B", "content_chars": 1782, "content_excerpt": "To determine the number of lines in the EPR (Electron Paramagnetic Resonance) spectrum of the $^{13}\\text{CH}_3$ radical, we need to consider the hyperfine splitting caused by the magnetic nuclei inte", "failure_class": null, "finish_reason": "stop", "latency_ms": 9411.683499987703, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 535, "prompt_tokens": 117, "prompt_tokens_details": { "cached_tokens": 113 }, "total_tokens": 652 } } ], "id": "mmlu-pro-25-chemistry", "pass_count": 3, "pass_rate": 1.0, "required_pass_rate": 1.0, "status": "passed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To find the minimum number of clock cycles, we need to schedule the instructions to compute $AB + ABC + BC$ while respecting the pipeline hazards and the constraint that $R0, R1, R2$ (holding $A, B, C$) cannot be modified.\n\n**1. Identify the Operations:**\nThe expression is $AB + ABC + BC$.\nLet's break this down into primitive operations:\n1. $T1 = A \\times B$ (MUL R0, R1, Rd)\n2. $T2 = T1 \\times C$ (MUL Rd, R2, Rd) -> This is $ABC$\n3. $T3 = B \\times C$ (MUL R1, R2, Rd)\n4. $T4 = T1 + T2$ (ADD Rd, Rd, Rd) -> This is $AB + ABC$\n5. $T5 = T4 + T3$ (ADD Rd, Rd, Rd) -> This is the final result\n\nWe need to use temporary registers (e.g., R3, R4, R5) since R0, R1, R2 are read-only for this computation.\n\n**2. Analyze Dependencies and Hazards:**\n* **Normal operation:** 1 cycle.\n* **Hazard:** If an operation produces a result required by the *immediately following* operation, it takes 2 cycles. This is a classic data hazard (RAW - Read After Write) that requires a stall or a forwarding delay. In this specific problem description, it implies that the second operation cannot start until the first is fully complete, effectively adding 1 extra cycle to the pipeline for that specific dependency.\n\nLet's map the dependencies:\n* $T1$ depends on $A, B$.\n* $T2$ depends on $T1, C$. (Dependency: $T1 \\to T2$)\n* $T3$ depends on $B, C$. (Independent of $T1, T2$)\n* $T4$ depends on $T1, T2$. (Dependency: $T2 \\to T4$)\n* $T5$ depends on $T4, T3$. (Dependency: $T4 \\to T5$)\n\n**3. Schedule the Instructions:**\n\nLet's try to interleave independent operations to hide latency.\n\n* **Cycle 1:** Start $T1$ (MUL R0, R1, R3).\n * $T1$ is independent.\n * Can we start $T3$ (MUL R1, R2, R4) in the same cycle? The problem says \"An operation normally takes one cycle\". It doesn't explicitly say we can't issue two operations in the same cycle (superscalar), but typically \"pipelined RISC machine\" implies a single-issue pipeline unless stated otherwise. However, even if it's single-issue, we can pipeline them.\n * Let's assume a standard 5-stage pipeline (IF, ID, EX, MEM, WB) or similar, but the problem simplifies it: \"An operation normally takes one cycle\". This suggests a very simple pipeline or a model where we just count the execution cycles with stalls.\n * Let's interpret \"takes one cycle\" as the execution time, and the \"two cycles if required by immediately following\" as a stall penalty.\n\nLet's trace the execution step-by-step, assuming we can issue instructions every cycle, but a dependent instruction must wait for the previous one to finish (which takes 2 cycles total for the pair).\n\n**Attempt 1: Sequential with optimal ordering**\n\nWe want to compute $AB$, $BC$, and $ABC$.\n$ABC = (AB) \\times C$.\nSo $AB$ must be computed before $ABC$.\n$AB + ABC$ requires $AB$ and $ABC$.\nFinal sum requires $AB+ABC$ and $BC$.\n\nOrder:\n1. $T1 = A \\times B$ (MUL R0, R1, R3)\n2. $T3 = B \\times C$ (MUL R1, R2, R4) <-- Independent of T1, can be done next or in parallel.\n3. $T2 = T1 \\times C$ (MUL R3, R2, R5) <-- Depends on T1.\n4. $T4 = T1 + T2$ (ADD R3, R5, R6) <-- Depends on T2 (and T1).\n5. $T5 = T4 + T3$ (ADD R6, R4, R7) <-- Depends on T4", "content_chars": 3179, "content_excerpt": "To find the minimum number of clock cycles, we need to schedule the instructions to compute $AB + ABC + BC$ while respecting the pipeline hazards and the constraint that $R0, R1, R2$ (holding $A, B, C", "error": "answer", "failure_class": "visible_answer_budget_exhausted", "finish_reason": "length", "latency_ms": 18084.892000013497, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "failed", "text_checks": [ { "name": "answer", "passed": false } ], "usage": { "completion_tokens": 1024, "prompt_tokens": 180, "prompt_tokens_details": { "cached_tokens": 0 }, "total_tokens": 1204 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To find the minimum number of clock cycles, we need to schedule the instructions to compute $AB + ABC + BC$ while respecting the pipeline hazards and the constraint that $R0, R1, R2$ (holding $A, B, C$) cannot be modified.\n\n**1. Identify the Operations:**\nThe expression is $AB + ABC + BC$.\nLet's break this down into primitive operations:\n1. $T1 = A \\times B$ (MUL R0, R1, Rd)\n2. $T2 = T1 \\times C$ (MUL Rd, R2, Rd) -> This is $ABC$\n3. $T3 = B \\times C$ (MUL R1, R2, Rd)\n4. $T4 = T1 + T2$ (ADD Rd, Rd, Rd) -> This is $AB + ABC$\n5. $T5 = T4 + T3$ (ADD Rd, Rd, Rd) -> This is the final result\n\nWe need to use temporary registers (e.g., R3, R4, R5) since R0, R1, R2 are read-only for this computation.\n\n**2. Analyze Dependencies and Hazards:**\n* **Normal operation:** 1 cycle.\n* **Hazard:** If an operation produces a result required by the *immediately following* operation, it takes 2 cycles. This is a classic data hazard (RAW - Read After Write) that requires a stall or a forwarding delay. In this specific problem description, it implies that the second operation cannot start until the first is fully complete, effectively adding 1 extra cycle to the pipeline for that specific dependency.\n\nLet's map the dependencies:\n* $T1$ depends on $A, B$.\n* $T2$ depends on $T1, C$. (Dependency: $T1 \\to T2$)\n* $T3$ depends on $B, C$. (Independent of $T1, T2$)\n* $T4$ depends on $T1, T2$. (Dependency: $T2 \\to T4$)\n* $T5$ depends on $T4, T3$. (Dependency: $T4 \\to T5$)\n\n**3. Schedule the Instructions:**\n\nLet's try to interleave independent operations to hide latency.\n\n* **Cycle 1:** Start $T1$ (MUL R0, R1, R3).\n * $T1$ is independent.\n * Can we start $T3$ (MUL R1, R2, R4) in the same cycle? The problem says \"An operation normally takes one cycle\". It doesn't explicitly say we can't issue two operations in the same cycle (superscalar), but typically \"pipelined RISC machine\" implies a single-issue pipeline unless stated otherwise. However, even if it's single-issue, we can pipeline them.\n * Let's assume a standard 5-stage pipeline (IF, ID, EX, MEM, WB) or similar, but the problem simplifies it: \"An operation normally takes one cycle\". This suggests a very simple pipeline or a model where we just count the execution cycles with stalls.\n * Let's interpret \"takes one cycle\" as the execution time, and the \"two cycles if required by immediately following\" as a stall penalty.\n\nLet's trace the execution step-by-step, assuming we can issue instructions every cycle, but a dependent instruction must wait for the previous one to finish (which takes 2 cycles total for the pair).\n\n**Attempt 1: Sequential with optimal ordering**\n\nWe want to compute $AB$, $BC$, and $ABC$.\n$ABC = (AB) \\times C$.\nSo $AB$ must be computed before $ABC$.\n$AB + ABC$ requires $AB$ and $ABC$.\nFinal sum requires $AB+ABC$ and $BC$.\n\nOrder:\n1. $T1 = A \\times B$ (MUL R0, R1, R3)\n2. $T3 = B \\times C$ (MUL R1, R2, R4) <-- Independent of T1, can be done next or in parallel.\n3. $T2 = T1 \\times C$ (MUL R3, R2, R5) <-- Depends on T1.\n4. $T4 = T1 + T2$ (ADD R3, R5, R6) <-- Depends on T2 (and T1).\n5. $T5 = T4 + T3$ (ADD R6, R4, R7) <-- Depends on T4", "content_chars": 3179, "content_excerpt": "To find the minimum number of clock cycles, we need to schedule the instructions to compute $AB + ABC + BC$ while respecting the pipeline hazards and the constraint that $R0, R1, R2$ (holding $A, B, C", "error": "answer", "failure_class": "visible_answer_budget_exhausted", "finish_reason": "length", "latency_ms": 18256.938599981368, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "failed", "text_checks": [ { "name": "answer", "passed": false } ], "usage": { "completion_tokens": 1024, "prompt_tokens": 180, "prompt_tokens_details": { "cached_tokens": 176 }, "total_tokens": 1204 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To find the minimum number of clock cycles, we need to schedule the instructions to compute $AB + ABC + BC$ while respecting the pipeline hazards and the constraint that $R0, R1, R2$ (holding $A, B, C$) cannot be modified.\n\n**1. Identify the Operations:**\nThe expression is $AB + ABC + BC$.\nLet's break this down into primitive operations:\n1. $T1 = A \\times B$ (MUL R0, R1, Rd)\n2. $T2 = T1 \\times C$ (MUL Rd, R2, Rd) -> This is $ABC$\n3. $T3 = B \\times C$ (MUL R1, R2, Rd)\n4. $T4 = T1 + T2$ (ADD Rd, Rd, Rd) -> This is $AB + ABC$\n5. $T5 = T4 + T3$ (ADD Rd, Rd, Rd) -> This is the final result\n\nWe need to use temporary registers (e.g., R3, R4, R5) since R0, R1, R2 are read-only for this computation.\n\n**2. Analyze Dependencies and Hazards:**\n* **Normal operation:** 1 cycle.\n* **Hazard:** If an operation produces a result required by the *immediately following* operation, it takes 2 cycles. This is a classic data hazard (RAW - Read After Write) that requires a stall or a forwarding delay. In this specific problem description, it implies that the second operation cannot start until the first is fully complete, effectively adding 1 extra cycle to the pipeline for that specific dependency.\n\nLet's map the dependencies:\n* $T1$ depends on $A, B$.\n* $T2$ depends on $T1, C$. (Dependency: $T1 \\to T2$)\n* $T3$ depends on $B, C$. (Independent of $T1, T2$)\n* $T4$ depends on $T1, T2$. (Dependency: $T2 \\to T4$)\n* $T5$ depends on $T4, T3$. (Dependency: $T4 \\to T5$)\n\n**3. Schedule the Instructions:**\n\nLet's try to interleave independent operations to hide latency.\n\n* **Cycle 1:** Start $T1$ (MUL R0, R1, R3).\n * $T1$ is independent.\n * Can we start $T3$ (MUL R1, R2, R4) in the same cycle? The problem says \"An operation normally takes one cycle\". It doesn't explicitly say we can't issue two operations in the same cycle (superscalar), but typically \"pipelined RISC machine\" implies a single-issue pipeline unless stated otherwise. However, even if it's single-issue, we can pipeline them.\n * Let's assume a standard 5-stage pipeline (IF, ID, EX, MEM, WB) or similar, but the problem simplifies it: \"An operation normally takes one cycle\". This suggests a very simple pipeline or a model where we just count the execution cycles with stalls.\n * Let's interpret \"takes one cycle\" as the execution time, and the \"two cycles if required by immediately following\" as a stall penalty.\n\nLet's trace the execution step-by-step, assuming we can issue instructions every cycle, but a dependent instruction must wait for the previous one to finish (which takes 2 cycles total for the pair).\n\n**Attempt 1: Sequential with optimal ordering**\n\nWe want to compute $AB$, $BC$, and $ABC$.\n$ABC = (AB) \\times C$.\nSo $AB$ must be computed before $ABC$.\n$AB + ABC$ requires $AB$ and $ABC$.\nFinal sum requires $AB+ABC$ and $BC$.\n\nOrder:\n1. $T1 = A \\times B$ (MUL R0, R1, R3)\n2. $T3 = B \\times C$ (MUL R1, R2, R4) <-- Independent of T1, can be done next or in parallel.\n3. $T2 = T1 \\times C$ (MUL R3, R2, R5) <-- Depends on T1.\n4. $T4 = T1 + T2$ (ADD R3, R5, R6) <-- Depends on T2 (and T1).\n5. $T5 = T4 + T3$ (ADD R6, R4, R7) <-- Depends on T4", "content_chars": 3179, "content_excerpt": "To find the minimum number of clock cycles, we need to schedule the instructions to compute $AB + ABC + BC$ while respecting the pipeline hazards and the constraint that $R0, R1, R2$ (holding $A, B, C", "error": "answer", "failure_class": "visible_answer_budget_exhausted", "finish_reason": "length", "latency_ms": 17987.018200044986, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "failed", "text_checks": [ { "name": "answer", "passed": false } ], "usage": { "completion_tokens": 1024, "prompt_tokens": 180, "prompt_tokens_details": { "cached_tokens": 176 }, "total_tokens": 1204 } } ], "error": "answer", "id": "mmlu-pro-30-computer-science", "pass_count": 0, "pass_rate": 0.0, "required_pass_rate": 1.0, "status": "failed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "For a stationary autoregressive (AR) process, the key property is that the statistical properties (mean, variance, autocovariance) are constant over time. This implies that the process has a stable mean and that deviations from this mean are temporary.\n\nLet's analyze the options:\n\n* **A. Never occur**: Incorrect. Shocks (innovations or errors) are the driving force of the process.\n* **B. Persist indefinitely**: Incorrect. If shocks persisted indefinitely, the variance would grow without bound, violating stationarity.\n* **C. Cause a permanent change in the trend**: Incorrect. A permanent change in the trend implies a unit root (non-stationarity). Stationary processes revert to their mean.\n* **D. Grow exponentially**: Incorrect. This would imply an explosive process (non-stationary).\n* **E. Only affect the next period**: Incorrect. In an AR(p) process, shocks affect the current period and subsequent periods, but the effect decays over time.\n* **F. Eventually die away**: **Correct**. In a stationary AR process, the impulse response function (the effect of a shock over time) decays to zero. The process reverts to its mean.\n* **G. Cause the process to become non-stationary**: Incorrect. The process is defined as stationary; shocks do not change this property.\n* **H. Immediately disappear**: Incorrect. The effect of a shock persists for several periods, decaying gradually.\n* **I. Lead to a cyclical pattern**: Incorrect. While AR processes can exhibit damped oscillations (cyclical behavior), the defining characteristic of stationarity is that the effect of shocks dies away, not necessarily that they create cycles.\n* **J. Be balanced out by subsequent shocks**: Incorrect. While the process reverts to the mean, it is not because subsequent shocks \"balance\" the previous one in a deterministic sense, but because the autoregressive structure pulls the process back toward the mean.\n\nTherefore, the correct answer is that shocks eventually die away.\n\nFINAL=F", "content_chars": 1997, "content_excerpt": "For a stationary autoregressive (AR) process, the key property is that the statistical properties (mean, variance, autocovariance) are constant over time. This implies that the process has a stable me", "failure_class": null, "finish_reason": "stop", "latency_ms": 7839.299599989317, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 438, "prompt_tokens": 110, "prompt_tokens_details": { "cached_tokens": 102 }, "total_tokens": 548 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "For a stationary autoregressive (AR) process, the key property is that the statistical properties (mean, variance, autocovariance) are constant over time. This implies that the process has a stable mean and that deviations from this mean are temporary.\n\nLet's analyze the options:\n\n* **A. Never occur**: Incorrect. Shocks (innovations or errors) are the driving force of the process.\n* **B. Persist indefinitely**: Incorrect. If shocks persisted indefinitely, the variance would grow without bound, violating stationarity.\n* **C. Cause a permanent change in the trend**: Incorrect. A permanent change in the trend implies a unit root (non-stationarity). Stationary processes revert to their mean.\n* **D. Grow exponentially**: Incorrect. This would imply an explosive process (non-stationary).\n* **E. Only affect the next period**: Incorrect. In an AR(p) process, shocks affect the current period and subsequent periods, but the effect decays over time.\n* **F. Eventually die away**: **Correct**. In a stationary AR process, the impulse response function (the effect of a shock over time) decays to zero. The process reverts to its mean.\n* **G. Cause the process to become non-stationary**: Incorrect. The process is defined as stationary; shocks do not change this property.\n* **H. Immediately disappear**: Incorrect. The effect of a shock persists for several periods, decaying gradually.\n* **I. Lead to a cyclical pattern**: Incorrect. While AR processes can exhibit damped oscillations (cyclical behavior), the defining characteristic of stationarity is that the effect of shocks dies away, not necessarily that they create cycles.\n* **J. Be balanced out by subsequent shocks**: Incorrect. While the process reverts to the mean, it is not because subsequent shocks \"balance\" the previous one in a deterministic sense, but because the autoregressive structure pulls the process back toward the mean.\n\nTherefore, the correct answer is that shocks eventually die away.\n\nFINAL=F", "content_chars": 1997, "content_excerpt": "For a stationary autoregressive (AR) process, the key property is that the statistical properties (mean, variance, autocovariance) are constant over time. This implies that the process has a stable me", "failure_class": null, "finish_reason": "stop", "latency_ms": 8060.13980001444, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 438, "prompt_tokens": 110, "prompt_tokens_details": { "cached_tokens": 106 }, "total_tokens": 548 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "For a stationary autoregressive (AR) process, the key property is that the statistical properties (mean, variance, autocovariance) are constant over time. This implies that the process has a stable mean and that deviations from this mean are temporary.\n\nLet's analyze the options:\n\n* **A. Never occur**: Incorrect. Shocks (innovations or errors) are the driving force of the process.\n* **B. Persist indefinitely**: Incorrect. If shocks persisted indefinitely, the variance would grow without bound, violating stationarity.\n* **C. Cause a permanent change in the trend**: Incorrect. A permanent change in the trend implies a unit root (non-stationarity). Stationary processes revert to their mean.\n* **D. Grow exponentially**: Incorrect. This would imply an explosive process (non-stationary).\n* **E. Only affect the next period**: Incorrect. In an AR(p) process, shocks affect the current period and subsequent periods, but the effect decays over time.\n* **F. Eventually die away**: **Correct**. In a stationary AR process, the impulse response function (the effect of a shock over time) decays to zero. The process reverts to its mean.\n* **G. Cause the process to become non-stationary**: Incorrect. The process is defined as stationary; shocks do not change this property.\n* **H. Immediately disappear**: Incorrect. The effect of a shock persists for several periods, decaying gradually.\n* **I. Lead to a cyclical pattern**: Incorrect. While AR processes can exhibit damped oscillations (cyclical behavior), the defining characteristic of stationarity is that the effect of shocks dies away, not necessarily that they create cycles.\n* **J. Be balanced out by subsequent shocks**: Incorrect. While the process reverts to the mean, it is not because subsequent shocks \"balance\" the previous one in a deterministic sense, but because the autoregressive structure pulls the process back toward the mean.\n\nTherefore, the correct answer is that shocks eventually die away.\n\nFINAL=F", "content_chars": 1997, "content_excerpt": "For a stationary autoregressive (AR) process, the key property is that the statistical properties (mean, variance, autocovariance) are constant over time. This implies that the process has a stable me", "failure_class": null, "finish_reason": "stop", "latency_ms": 7731.967200001236, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 438, "prompt_tokens": 110, "prompt_tokens_details": { "cached_tokens": 106 }, "total_tokens": 548 } } ], "id": "mmlu-pro-35-economics", "pass_count": 3, "pass_rate": 1.0, "required_pass_rate": 1.0, "status": "passed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To find the force between two point poles, we use the formula for the force between two magnetic poles in a vacuum (or air, assuming relative permeability $\\mu_r \\approx 1$):\n\n$$F = \\frac{\\mu_0}{4\\pi} \\frac{m_1 m_2}{r^2}$$\n\nWhere:\n* $\\mu_0 = 4\\pi \\times 10^{-7} \\, \\text{N/A}^2$ (permeability of free space)\n* $m_1$ is the strength of the first pole\n* $m_2$ is the strength of the second pole\n* $r$ is the distance between the poles\n\n**Given values:**\n* $m_1 = 4\\pi \\times 10^{-4} \\, \\text{Wb}$ (Weber)\n* $m_2 = 4\\pi \\times 1.5 \\times 10^{-4} \\, \\text{Wb}$\n* $r = 10 \\, \\text{cm} = 0.1 \\, \\text{m}$\n\n**Step 1: Substitute the values into the formula**\n\n$$F = \\frac{4\\pi \\times 10^{-7}}{4\\pi} \\times \\frac{(4\\pi \\times 10^{-4}) \\times (4\\pi \\times 1.5 \\times 10^{-4})}{(0.1)^2}$$\n\n**Step 2: Simplify the constants**\n\nThe $4\\pi$ in the numerator and denominator of the first fraction cancel out:\n\n$$F = 10^{-7} \\times \\frac{(4\\pi \\times 10^{-4}) \\times (4\\pi \\times 1.5 \\times 10^{-4})}{0.01}$$\n\n**Step 3: Calculate the numerator**\n\nFirst, multiply the pole strengths:\n$$(4\\pi \\times 10^{-4}) \\times (4\\pi \\times 1.5 \\times 10^{-4}) = 16\\pi^2 \\times 1.5 \\times 10^{-8}$$\n$$= 24\\pi^2 \\times 10^{-8}$$\n\n**Step 4: Divide by $r^2$**\n\n$$r^2 = (0.1)^2 = 0.01 = 10^{-2}$$\n\nSo,\n$$\\frac{24\\pi^2 \\times 10^{-8}}{10^{-2}} = 24\\pi^2 \\times 10^{-6}$$\n\n**Step 5: Multiply by $\\mu_0/4\\pi$ (which is $10^{-7}$)**\n\n$$F = 10^{-7} \\times 24\\pi^2 \\times 10^{-6}$$\n$$F = 24\\pi^2 \\times 10^{-13}$$\n\nWait, let me re-check the calculation. The standard formula is often written as:\n$$F = \\frac{\\mu_0}{4\\pi} \\frac{m_1 m_2}{r^2}$$\n\nLet's re-calculate carefully:\n$$F = \\frac{4\\pi \\times 10^{-7}}{4\\pi} \\cdot \\frac{(4\\pi \\times 10^{-4})(4\\pi \\times 1.5 \\times 10^{-4})}{(0.1)^2}$$\n$$F = 10^{-7} \\cdot \\frac{16\\pi^2 \\times 1.5 \\times 10^{-8}}{0.01}$$\n$$F = 10^{-7} \\cdot \\frac{24\\pi^2 \\times 10^{-8}}{10^{-2}}$$\n$$F = 10^{-7} \\cdot 24\\pi^2 \\times 10^{-6}$$\n$$F = 24\\pi^2 \\times 10^{-13}$$\n\nThis result is extremely small ($\\approx 2.36 \\times 10^{-11}$ N), which does not match any of the options (which are in Newtons, like 25 N, 12.5 N, etc.).\n\nLet me reconsider the units. The problem states the pole strength is in **Weber**.\nIn the CGS system, the unit of pole strength is the **Gilbert** (or sometimes just \"pole\"), and the force formula is", "content_chars": 2328, "content_excerpt": "To find the force between two point poles, we use the formula for the force between two magnetic poles in a vacuum (or air, assuming relative permeability $\\mu_r \\approx 1$):\n\n$$F = \\frac{\\mu_0}{4\\pi}", "error": "answer", "failure_class": "visible_answer_budget_exhausted", "finish_reason": "length", "latency_ms": 18090.61130002374, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "failed", "text_checks": [ { "name": "answer", "passed": false } ], "usage": { "completion_tokens": 1024, "prompt_tokens": 151, "prompt_tokens_details": { "cached_tokens": 0 }, "total_tokens": 1175 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To find the force between two point poles, we use the formula for the force between two magnetic poles in a vacuum (or air, assuming relative permeability $\\mu_r \\approx 1$):\n\n$$F = \\frac{\\mu_0}{4\\pi} \\frac{m_1 m_2}{r^2}$$\n\nWhere:\n* $\\mu_0 = 4\\pi \\times 10^{-7} \\, \\text{N/A}^2$ (permeability of free space)\n* $m_1$ is the strength of the first pole\n* $m_2$ is the strength of the second pole\n* $r$ is the distance between the poles\n\n**Given values:**\n* $m_1 = 4\\pi \\times 10^{-4} \\, \\text{Wb}$ (Weber)\n* $m_2 = 4\\pi \\times 1.5 \\times 10^{-4} \\, \\text{Wb}$\n* $r = 10 \\, \\text{cm} = 0.1 \\, \\text{m}$\n\n**Step 1: Substitute the values into the formula**\n\n$$F = \\frac{4\\pi \\times 10^{-7}}{4\\pi} \\times \\frac{(4\\pi \\times 10^{-4}) \\times (4\\pi \\times 1.5 \\times 10^{-4})}{(0.1)^2}$$\n\n**Step 2: Simplify the constants**\n\nThe $4\\pi$ in the numerator and denominator of the first fraction cancel out:\n\n$$F = 10^{-7} \\times \\frac{(4\\pi \\times 10^{-4}) \\times (4\\pi \\times 1.5 \\times 10^{-4})}{0.01}$$\n\n**Step 3: Calculate the numerator**\n\nFirst, multiply the pole strengths:\n$$(4\\pi \\times 10^{-4}) \\times (4\\pi \\times 1.5 \\times 10^{-4}) = 16\\pi^2 \\times 1.5 \\times 10^{-8}$$\n$$= 24\\pi^2 \\times 10^{-8}$$\n\n**Step 4: Divide by $r^2$**\n\n$$r^2 = (0.1)^2 = 0.01 = 10^{-2}$$\n\nSo,\n$$\\frac{24\\pi^2 \\times 10^{-8}}{10^{-2}} = 24\\pi^2 \\times 10^{-6}$$\n\n**Step 5: Multiply by $\\mu_0/4\\pi$ (which is $10^{-7}$)**\n\n$$F = 10^{-7} \\times 24\\pi^2 \\times 10^{-6}$$\n$$F = 24\\pi^2 \\times 10^{-13}$$\n\nWait, let me re-check the calculation. The standard formula is often written as:\n$$F = \\frac{\\mu_0}{4\\pi} \\frac{m_1 m_2}{r^2}$$\n\nLet's re-calculate carefully:\n$$F = \\frac{4\\pi \\times 10^{-7}}{4\\pi} \\cdot \\frac{(4\\pi \\times 10^{-4})(4\\pi \\times 1.5 \\times 10^{-4})}{(0.1)^2}$$\n$$F = 10^{-7} \\cdot \\frac{16\\pi^2 \\times 1.5 \\times 10^{-8}}{0.01}$$\n$$F = 10^{-7} \\cdot \\frac{24\\pi^2 \\times 10^{-8}}{10^{-2}}$$\n$$F = 10^{-7} \\cdot 24\\pi^2 \\times 10^{-6}$$\n$$F = 24\\pi^2 \\times 10^{-13}$$\n\nThis result is extremely small ($\\approx 2.36 \\times 10^{-11}$ N), which does not match any of the options (which are in Newtons, like 25 N, 12.5 N, etc.).\n\nLet me reconsider the units. The problem states the pole strength is in **Weber**.\nIn the CGS system, the unit of pole strength is the **Gilbert** (or sometimes just \"pole\"), and the force formula is", "content_chars": 2328, "content_excerpt": "To find the force between two point poles, we use the formula for the force between two magnetic poles in a vacuum (or air, assuming relative permeability $\\mu_r \\approx 1$):\n\n$$F = \\frac{\\mu_0}{4\\pi}", "error": "answer", "failure_class": "visible_answer_budget_exhausted", "finish_reason": "length", "latency_ms": 18287.55700000329, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "failed", "text_checks": [ { "name": "answer", "passed": false } ], "usage": { "completion_tokens": 1024, "prompt_tokens": 151, "prompt_tokens_details": { "cached_tokens": 147 }, "total_tokens": 1175 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "To find the force between two point poles, we use the formula for the force between two magnetic poles in a vacuum (or air, assuming relative permeability $\\mu_r \\approx 1$):\n\n$$F = \\frac{\\mu_0}{4\\pi} \\frac{m_1 m_2}{r^2}$$\n\nWhere:\n* $\\mu_0 = 4\\pi \\times 10^{-7} \\, \\text{N/A}^2$ (permeability of free space)\n* $m_1$ is the strength of the first pole\n* $m_2$ is the strength of the second pole\n* $r$ is the distance between the poles\n\n**Given values:**\n* $m_1 = 4\\pi \\times 10^{-4} \\, \\text{Wb}$ (Weber)\n* $m_2 = 4\\pi \\times 1.5 \\times 10^{-4} \\, \\text{Wb}$\n* $r = 10 \\, \\text{cm} = 0.1 \\, \\text{m}$\n\n**Step 1: Substitute the values into the formula**\n\n$$F = \\frac{4\\pi \\times 10^{-7}}{4\\pi} \\times \\frac{(4\\pi \\times 10^{-4}) \\times (4\\pi \\times 1.5 \\times 10^{-4})}{(0.1)^2}$$\n\n**Step 2: Simplify the constants**\n\nThe $4\\pi$ in the numerator and denominator of the first fraction cancel out:\n\n$$F = 10^{-7} \\times \\frac{(4\\pi \\times 10^{-4}) \\times (4\\pi \\times 1.5 \\times 10^{-4})}{0.01}$$\n\n**Step 3: Calculate the numerator**\n\nFirst, multiply the pole strengths:\n$$(4\\pi \\times 10^{-4}) \\times (4\\pi \\times 1.5 \\times 10^{-4}) = 16\\pi^2 \\times 1.5 \\times 10^{-8}$$\n$$= 24\\pi^2 \\times 10^{-8}$$\n\n**Step 4: Divide by $r^2$**\n\n$$r^2 = (0.1)^2 = 0.01 = 10^{-2}$$\n\nSo,\n$$\\frac{24\\pi^2 \\times 10^{-8}}{10^{-2}} = 24\\pi^2 \\times 10^{-6}$$\n\n**Step 5: Multiply by $\\mu_0/4\\pi$ (which is $10^{-7}$)**\n\n$$F = 10^{-7} \\times 24\\pi^2 \\times 10^{-6}$$\n$$F = 24\\pi^2 \\times 10^{-13}$$\n\nWait, let me re-check the calculation. The standard formula is often written as:\n$$F = \\frac{\\mu_0}{4\\pi} \\frac{m_1 m_2}{r^2}$$\n\nLet's re-calculate carefully:\n$$F = \\frac{4\\pi \\times 10^{-7}}{4\\pi} \\cdot \\frac{(4\\pi \\times 10^{-4})(4\\pi \\times 1.5 \\times 10^{-4})}{(0.1)^2}$$\n$$F = 10^{-7} \\cdot \\frac{16\\pi^2 \\times 1.5 \\times 10^{-8}}{0.01}$$\n$$F = 10^{-7} \\cdot \\frac{24\\pi^2 \\times 10^{-8}}{10^{-2}}$$\n$$F = 10^{-7} \\cdot 24\\pi^2 \\times 10^{-6}$$\n$$F = 24\\pi^2 \\times 10^{-13}$$\n\nThis result is extremely small ($\\approx 2.36 \\times 10^{-11}$ N), which does not match any of the options (which are in Newtons, like 25 N, 12.5 N, etc.).\n\nLet me reconsider the units. The problem states the pole strength is in **Weber**.\nIn the CGS system, the unit of pole strength is the **Gilbert** (or sometimes just \"pole\"), and the force formula is", "content_chars": 2328, "content_excerpt": "To find the force between two point poles, we use the formula for the force between two magnetic poles in a vacuum (or air, assuming relative permeability $\\mu_r \\approx 1$):\n\n$$F = \\frac{\\mu_0}{4\\pi}", "error": "answer", "failure_class": "visible_answer_budget_exhausted", "finish_reason": "length", "latency_ms": 17965.105500014033, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "failed", "text_checks": [ { "name": "answer", "passed": false } ], "usage": { "completion_tokens": 1024, "prompt_tokens": 151, "prompt_tokens_details": { "cached_tokens": 147 }, "total_tokens": 1175 } } ], "error": "answer", "id": "mmlu-pro-40-engineering", "pass_count": 0, "pass_rate": 0.0, "required_pass_rate": 1.0, "status": "failed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The sentence is: \"Turtles live long lives and are happy creatures, unless they are injured.\"\n\nLet's break down the components:\n- Let $L$ stand for \"Turtles live long lives\".\n- Let $H$ stand for \"Turtles are happy creatures\".\n- Let $I$ stand for \"Turtles are injured\".\n\nThe phrase \"unless\" in propositional logic is typically translated as \"if not\". So, \"P unless Q\" is equivalent to \"If not Q, then P\", or symbolically $\\neg Q \\rightarrow P$. It is also logically equivalent to $P \\lor Q$.\n\nThe sentence structure is: \"[Turtles live long lives and are happy creatures] unless [they are injured]\".\n\nSo, let $P$ be the conjunction $(L \\land H)$.\nThe sentence becomes: $(L \\land H)$ unless $I$.\n\nUsing the translation \"unless\" $\\rightarrow$ \"if not ... then\":\n$\\neg I \\rightarrow (L \\land H)$\n\nUsing the translation \"unless\" $\\rightarrow$ \"or\":\n$(L \\land H) \\lor I$\n\nLet's check the options:\nA. $(L \\land H) \\leftrightarrow I$ (This means \"if and only if\", which is not correct).\nB. $(L \\land H) \\lor I$ (This matches our translation).\nC. $L \\land (H \\lor I)$ (This means \"Turtles live long lives, and (they are happy or injured)\". This is not equivalent to the original sentence. For example, if a turtle is injured and lives a long life but is not happy, C is true, but the original sentence would be false because the \"unless\" condition (injury) is met, so the first part (long life AND happy) should be false).\nD. $L \\land (H \\rightarrow R)$ (This introduces a new variable $R$ and has a different structure).\nE-J. N/A\n\nTherefore, option B is the correct symbolization.\n\nFINAL=B", "content_chars": 1579, "content_excerpt": "The sentence is: \"Turtles live long lives and are happy creatures, unless they are injured.\"\n\nLet's break down the components:\n- Let $L$ stand for \"Turtles live long lives\".\n- Let $H$ stand for \"Turtl", "failure_class": null, "finish_reason": "stop", "latency_ms": 7737.351499963552, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 436, "prompt_tokens": 122, "prompt_tokens_details": { "cached_tokens": 0 }, "total_tokens": 558 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The sentence is: \"Turtles live long lives and are happy creatures, unless they are injured.\"\n\nLet's break down the components:\n- Let $L$ stand for \"Turtles live long lives\".\n- Let $H$ stand for \"Turtles are happy creatures\".\n- Let $I$ stand for \"Turtles are injured\".\n\nThe phrase \"unless\" in propositional logic is typically translated as \"if not\". So, \"P unless Q\" is equivalent to \"If not Q, then P\", or symbolically $\\neg Q \\rightarrow P$. It is also logically equivalent to $P \\lor Q$.\n\nThe sentence structure is: \"[Turtles live long lives and are happy creatures] unless [they are injured]\".\n\nSo, let $P$ be the conjunction $(L \\land H)$.\nThe sentence becomes: $(L \\land H)$ unless $I$.\n\nUsing the translation \"unless\" $\\rightarrow$ \"if not ... then\":\n$\\neg I \\rightarrow (L \\land H)$\n\nUsing the translation \"unless\" $\\rightarrow$ \"or\":\n$(L \\land H) \\lor I$\n\nLet's check the options:\nA. $(L \\land H) \\leftrightarrow I$ (This means \"if and only if\", which is not correct).\nB. $(L \\land H) \\lor I$ (This matches our translation).\nC. $L \\land (H \\lor I)$ (This means \"Turtles live long lives, and (they are happy or injured)\". This is not equivalent to the original sentence. For example, if a turtle is injured and lives a long life but is not happy, C is true, but the original sentence would be false because the \"unless\" condition (injury) is met, so the first part (long life AND happy) should be false).\nD. $L \\land (H \\rightarrow R)$ (This introduces a new variable $R$ and has a different structure).\nE-J. N/A\n\nTherefore, option B is the correct symbolization.\n\nFINAL=B", "content_chars": 1579, "content_excerpt": "The sentence is: \"Turtles live long lives and are happy creatures, unless they are injured.\"\n\nLet's break down the components:\n- Let $L$ stand for \"Turtles live long lives\".\n- Let $H$ stand for \"Turtl", "failure_class": null, "finish_reason": "stop", "latency_ms": 8148.197799979243, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 436, "prompt_tokens": 122, "prompt_tokens_details": { "cached_tokens": 118 }, "total_tokens": 558 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The sentence is: \"Turtles live long lives and are happy creatures, unless they are injured.\"\n\nLet's break down the components:\n- Let $L$ stand for \"Turtles live long lives\".\n- Let $H$ stand for \"Turtles are happy creatures\".\n- Let $I$ stand for \"Turtles are injured\".\n\nThe phrase \"unless\" in propositional logic is typically translated as \"if not\". So, \"P unless Q\" is equivalent to \"If not Q, then P\", or symbolically $\\neg Q \\rightarrow P$. It is also logically equivalent to $P \\lor Q$.\n\nThe sentence structure is: \"[Turtles live long lives and are happy creatures] unless [they are injured]\".\n\nSo, let $P$ be the conjunction $(L \\land H)$.\nThe sentence becomes: $(L \\land H)$ unless $I$.\n\nUsing the translation \"unless\" $\\rightarrow$ \"if not ... then\":\n$\\neg I \\rightarrow (L \\land H)$\n\nUsing the translation \"unless\" $\\rightarrow$ \"or\":\n$(L \\land H) \\lor I$\n\nLet's check the options:\nA. $(L \\land H) \\leftrightarrow I$ (This means \"if and only if\", which is not correct).\nB. $(L \\land H) \\lor I$ (This matches our translation).\nC. $L \\land (H \\lor I)$ (This means \"Turtles live long lives, and (they are happy or injured)\". This is not equivalent to the original sentence. For example, if a turtle is injured and lives a long life but is not happy, C is true, but the original sentence would be false because the \"unless\" condition (injury) is met, so the first part (long life AND happy) should be false).\nD. $L \\land (H \\rightarrow R)$ (This introduces a new variable $R$ and has a different structure).\nE-J. N/A\n\nTherefore, option B is the correct symbolization.\n\nFINAL=B", "content_chars": 1579, "content_excerpt": "The sentence is: \"Turtles live long lives and are happy creatures, unless they are injured.\"\n\nLet's break down the components:\n- Let $L$ stand for \"Turtles live long lives\".\n- Let $H$ stand for \"Turtl", "failure_class": null, "finish_reason": "stop", "latency_ms": 7772.0758999930695, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 436, "prompt_tokens": 122, "prompt_tokens_details": { "cached_tokens": 118 }, "total_tokens": 558 } } ], "id": "mmlu-pro-45-philosophy", "pass_count": 3, "pass_rate": 1.0, "required_pass_rate": 1.0, "status": "passed", "validator": "deterministic_text_checks" }, { "attempt_count": 3, "attempts": [ { "attempt": 1, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The correct answer is **I**.\n\n**Reasoning:**\nUnder Article 31 of the Statute of the International Court of Justice (ICJ), if a party to a case before the Court does not have a national sitting as a judge on the bench, it is entitled to choose a person of its own nationality to sit as a judge *ad hoc* for that specific case. This judge *ad hoc* participates in the proceedings on equal terms with the other judges, except that they do not vote on questions of procedure.\n\nLet's evaluate the other options:\n* **A:** The President of the ICJ is elected by the judges, not appointed *ad hoc* by parties.\n* **B:** While a judge *ad hoc* serves for a specific period (the duration of the case), this description is too vague and could apply to other temporary appointments. Option I is the precise legal definition.\n* **C:** Parties do not *always* nominate a judge; they only do so if they lack a national judge on the bench.\n* **D:** The President has a casting vote in the event of a tie, but this is not the definition of a judge *ad hoc*.\n* **E:** A judge *ad hoc* is nominated specifically because the party has no national judge; it is not \"irrespective of nationality\" in the sense that any person can be chosen regardless of the party's nationality (the person must be of the party's nationality).\n* **F:** Admissibility is decided by the full Court, not by a specific judge *ad hoc*.\n* **G:** The UN Security Council appoints judges to the ICJ (along with the General Assembly), but not judges *ad hoc*.\n* **H:** If a judge is disqualified or dies, the Court may appoint a substitute, but this is distinct from the judge *ad hoc* mechanism described in Article 31.\n\nTherefore, **I** is the correct definition.\n\nFINAL=I", "content_chars": 1740, "content_excerpt": "The correct answer is **I**.\n\n**Reasoning:**\nUnder Article 31 of the Statute of the International Court of Justice (ICJ), if a party to a case before the Court does not have a national sitting as a ju", "failure_class": null, "finish_reason": "stop", "latency_ms": 7679.001900018193, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 422, "prompt_tokens": 163, "prompt_tokens_details": { "cached_tokens": 155 }, "total_tokens": 585 } }, { "attempt": 2, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The correct answer is **I**.\n\n**Reasoning:**\nUnder Article 31 of the Statute of the International Court of Justice (ICJ), if a party to a case before the Court does not have a national sitting as a judge on the bench, it is entitled to choose a person of its own nationality to sit as a judge *ad hoc* for that specific case. This judge *ad hoc* participates in the proceedings on equal terms with the other judges, except that they do not vote on questions of procedure.\n\nLet's evaluate the other options:\n* **A:** The President of the ICJ is elected by the judges, not appointed *ad hoc* by parties.\n* **B:** While a judge *ad hoc* serves for a specific period (the duration of the case), this description is too vague and could apply to other temporary appointments. Option I is the precise legal definition.\n* **C:** Parties do not *always* nominate a judge; they only do so if they lack a national judge on the bench.\n* **D:** The President has a casting vote in the event of a tie, but this is not the definition of a judge *ad hoc*.\n* **E:** A judge *ad hoc* is nominated specifically because the party has no national judge; it is not \"irrespective of nationality\" in the sense that any person can be chosen regardless of the party's nationality (the person must be of the party's nationality).\n* **F:** Admissibility is decided by the full Court, not by a specific judge *ad hoc*.\n* **G:** The UN Security Council appoints judges to the ICJ (along with the General Assembly), but not judges *ad hoc*.\n* **H:** If a judge is disqualified or dies, the Court may appoint a substitute, but this is distinct from the judge *ad hoc* mechanism described in Article 31.\n\nTherefore, **I** is the correct definition.\n\nFINAL=I", "content_chars": 1740, "content_excerpt": "The correct answer is **I**.\n\n**Reasoning:**\nUnder Article 31 of the Statute of the International Court of Justice (ICJ), if a party to a case before the Court does not have a national sitting as a ju", "failure_class": null, "finish_reason": "stop", "latency_ms": 7820.370500034187, "reasoning_chars": 0, "reasoning_excerpt": "", "reasoning_field": null, "reasoning_tokens": null, "status": "passed", "text_checks": [ { "name": "answer", "passed": true } ], "usage": { "completion_tokens": 422, "prompt_tokens": 163, "prompt_tokens_details": { "cached_tokens": 159 }, "total_tokens": 585 } }, { "attempt": 3, "budget": { "legacy_max_tokens_as_visible": false, "max_completion_tokens": 1024, "reasoning_headroom_tokens": 0, "visible_answer_tokens": 1024 }, "content": "The correct answer is **I**.\n\n**Reasoning:**\nUnder Article 31 of the Statute of the International Court of Justice (ICJ), if a party to a case before the Court does not have a national sitting as a judge on the bench, it is entitled to choose a person of its own nationality to sit as a judge *ad hoc* for that specific case. This judge *ad hoc* participates in the proceedings on equal terms with the other judges, except that they do not vote on questions of procedure.\n\nLet's evaluate the other options:\n* **A:** The President of the ICJ is elected by the judges, not appointed *ad hoc* by parties.\n* **B:** While a judge *ad hoc* serves for a specific period (the duration of the case), this description is too vague and could apply to other temporary appointments. Option I is the precise legal definition.\n* **C:** Parties do not *always* nominate a judge; they only do so if they lack a national judge on the bench.\n* **D:** The President has a casting vote in the event of a tie, but this is not the definition of a judge *ad hoc*.\n* **E:** A judge *ad hoc* is nominated specifically because the party has no national judge; it is not \"irrespective of nationality\" in the sense that any person can be chosen regardless of the party's nationality (the person must be of the party's nationality).\n* **F:** Admissibility is decided by the full Court, not by a specific judge *ad hoc*.\n* **G:** The UN Security Council appoints judges to the ICJ (along with the General Assembly), but not judges *ad hoc*.\n* **H:** If a judge is disqualified or dies, the Court may appoint a substitute, but this is distinct from the judge *ad hoc* mechanism described in Article 31.\n\nTherefore, **I** is the correct definition.\n\nFINAL=I", "content_chars": 1740, 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