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668825f80a642802bdfeadfa | qwen/qwen3-235b-a22b:free | Explanation: Arrhenius's Sixth Impossibility Theorem identifies a set of conditions that cannot coexist in a population ethical theory. Critical-level views evaluate welfare by subtracting a critical threshold, meaning only lives above this level contribute positively. **Egalitarian Dominance** requires that if two pop... | {"completion_tokens": 5236, "prompt_tokens": 118, "total_tokens": 5354, "completion_tokens_details": null, "prompt_tokens_details": null} |
668828540a642802bdfeadfc | qwen/qwen3-235b-a22b:free | <think>We are given a multi-part problem to solve. Let's break it down step by step.
Step 1: The concept of logical "depth" mentioned in _The Quark and the Jaguar_ has a reciprocal/inverse concept (associated with Charles Bennett); take the third letter of that reciprocal concept word and call it c1.
In the book "T... | {"completion_tokens": 9321, "prompt_tokens": 583, "total_tokens": 9904, "completion_tokens_details": null, "prompt_tokens_details": null} |
6696c3734c196f1af6a16fcb | qwen/qwen3-235b-a22b:free | Explanation: The classification of torsion subgroups for elliptic curves over quadratic fields like $\mathbb{Q}(\sqrt{-3})$ is based on results from Kamienny and Najman. For a non-cyclic torsion subgroup, the structure must be a product of two cyclic groups $Z/mZ \times Z/nZ$ with $m \mid n$. Over $\mathbb{Q}(\sqrt{-3}... | {"completion_tokens": 9838, "prompt_tokens": 93, "total_tokens": 9931, "completion_tokens_details": null, "prompt_tokens_details": null} |
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