| [ | |
| { | |
| "core": "うどん", | |
| "center": { | |
| "energy": 80.0, | |
| "frequency": 32, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 1.0 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "食べ物", | |
| "s4": "日本の伝統的な食べ物", | |
| "weight": 1.0 | |
| }, | |
| "bottom": { | |
| "s3": "麺料理", | |
| "s4": "うどんの麺は小麦粉で製成", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "うどん", | |
| "s4": "うどんは麺料理であり、様々な種類のうどんが存在", | |
| "weight": 1.0 | |
| }, | |
| "right": { | |
| "s3": "食文化", | |
| "s4": "うどんは日本の食文化の一部", | |
| "weight": 1.0 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "トマト", | |
| "center": { | |
| "energy": 70.0, | |
| "frequency": 28, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.85 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "果物", | |
| "s4": "赤い果物", | |
| "weight": 0.8 | |
| }, | |
| "bottom": { | |
| "s3": "野菜", | |
| "s4": "食卓に", | |
| "weight": 0.6 | |
| }, | |
| "left": { | |
| "s3": "栽培", | |
| "s4": "トマト農園", | |
| "weight": 0.7 | |
| }, | |
| "right": { | |
| "s3": "栄養", | |
| "s4": "ビタミンC", | |
| "weight": 0.9 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "りんご", | |
| "center": { | |
| "energy": 30.0, | |
| "frequency": 12, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 1.0 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "定義", | |
| "s4": "...", | |
| "weight": 1.0 | |
| }, | |
| "bottom": { | |
| "s3": "特徴", | |
| "s4": "...", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "用途", | |
| "s4": "...", | |
| "weight": 1.0 | |
| }, | |
| "right": { | |
| "s3": "注意", | |
| "s4": "...", | |
| "weight": 1.0 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "ドーナツとは", | |
| "center": { | |
| "energy": 30.0, | |
| "frequency": 12, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 1.0 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "定義", | |
| "s4": "ドーナツとはは一般に知られる対象です。", | |
| "weight": 1.0 | |
| }, | |
| "bottom": { | |
| "s3": "特徴", | |
| "s4": "代表的な性質や特徴があります。", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "用途", | |
| "s4": "料理・利用・説明など様々な用途があります。", | |
| "weight": 1.0 | |
| }, | |
| "right": { | |
| "s3": "注意", | |
| "s4": "状況によって注意点が存在します。", | |
| "weight": 1.0 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "トマトの特徴について教えて", | |
| "center": { | |
| "energy": 30.0, | |
| "frequency": 12, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 1.0 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "定義", | |
| "s4": "トマトは赤色の果実で、酸味が強く、栄養価が高い。", | |
| "weight": 1.0 | |
| }, | |
| "bottom": { | |
| "s3": "特徴", | |
| "s4": "トマトは酸味が強く、栄養価が高い。", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "用途", | |
| "s4": "トマトはサラダやソースに使われる。", | |
| "weight": 1.0 | |
| }, | |
| "right": { | |
| "s3": "注意", | |
| "s4": "トマトは食用である。", | |
| "weight": 1.0 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "イヤホンの仕組みについて教えて", | |
| "center": { | |
| "energy": 30.0, | |
| "frequency": 12, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.9249999999999999 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "definition", | |
| "s4": "- 耳栓を通して外部の音を内側に取り込む", | |
| "weight": 1.1 | |
| }, | |
| "bottom": { | |
| "s3": "features", | |
| "s4": "- 音の強度を調節できる", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "usage", | |
| "s4": "- 聴覚補助、音楽鑑賞", | |
| "weight": 0.95 | |
| }, | |
| "right": { | |
| "s3": "caution", | |
| "s4": "- 長時間使用は耳に影響を与える可能性がある", | |
| "weight": 1.05 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "イヤホンの構造について教えて", | |
| "center": { | |
| "energy": 30.0, | |
| "frequency": 12, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.9249999999999999 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "definition", | |
| "s4": "- イヤホンは、音を直接耳に届けるための小型のヘッドフォンです。", | |
| "weight": 1.1 | |
| }, | |
| "bottom": { | |
| "s3": "features", | |
| "s4": "- 音の伝達に使用される、耳の外側にある小型のマイクロフォンと、耳の内側にあるスピーカーを持つ。", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "usage", | |
| "s4": "- 音楽聴き、通話、ゲームなど、音を直接耳に届けるために使用されます。", | |
| "weight": 0.95 | |
| }, | |
| "right": { | |
| "s3": "caution", | |
| "s4": "- 耳の健康を守るため、音量を適切に調整することが重要です。", | |
| "weight": 1.05 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "平面駆動ドライバー", | |
| "center": { | |
| "energy": 30.0, | |
| "frequency": 12, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.9249999999999999 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "definition", | |
| "s4": "- 直流電動機の駆動システム\n- 直流電動機の回転方向を変える\n- 直流電動機の回転方向を逆転させる\n- 直流電動機の回転方向を変える\n- 直流電動機の回転方向を逆転させる\n- 直流電動機の回転方向を逆転させる\n- 直流電動機の回転方向を逆転させる\n- 直流電動機の回転方向を逆転させる\n- 直流電動機の回転方向を逆転させる\n- 直流電動機の回転方向を逆転させる\n- 直流電動機の回転方向を逆転させる\n- 直流電動機の回転方向を逆転させる\n- 直流電動機の回転方向を逆", | |
| "weight": 1.1 | |
| }, | |
| "bottom": { | |
| "s3": "features", | |
| "s4": "（不足：再採掘が必要）", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "usage", | |
| "s4": "（不足：再採掘が必要）", | |
| "weight": 0.95 | |
| }, | |
| "right": { | |
| "s3": "caution", | |
| "s4": "（不足：再採掘が必要）", | |
| "weight": 1.05 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "T1: injective => no nontrivial meaning-preserving map", | |
| "center": { | |
| "energy": 60.0, | |
| "frequency": 24, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.9500000000000001 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "構成", | |
| "s4": "Mが単射なら(A)はF(c)=cを強制→(D)と両立不可", | |
| "weight": 1.2 | |
| }, | |
| "bottom": { | |
| "s3": "不可能性", | |
| "s4": "M単射かつ(A)なら恒等写像以外は不可", | |
| "weight": 1.2 | |
| }, | |
| "left": { | |
| "s3": "検証", | |
| "s4": "(A)⇒M(F(c))=M(c). M単射⇒F(c)=c. よって(D)違反", | |
| "weight": 1.1 | |
| }, | |
| "right": { | |
| "s3": "矛盾核", | |
| "s4": "{単射} + {意味保存} + {非自明} が矛盾集合", | |
| "weight": 1.1 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "T2: non-injective => fiber-permutation construction", | |
| "center": { | |
| "energy": 70.0, | |
| "frequency": 28, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.9 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "構成", | |
| "s4": "各σのファイバーM^{-1}(σ)内で2点交換。外は固定→(A)(D)達成", | |
| "weight": 1.3 | |
| }, | |
| "bottom": { | |
| "s3": "注意", | |
| "s4": "(E)は単射部分空間C'上ではFを恒等にすれば可逆", | |
| "weight": 1.1 | |
| }, | |
| "left": { | |
| "s3": "検証", | |
| "s4": "(A)ファイバー内置換で成立。 (D)交換した点で非自明", | |
| "weight": 1.2 | |
| }, | |
| "right": { | |
| "s3": "可逆", | |
| "s4": "各ファイバー内の置換は可逆（逆置換）", | |
| "weight": 1.2 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "T3: self-model consistency via consistent-subset restriction", | |
| "center": { | |
| "energy": 65.0, | |
| "frequency": 26, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.9 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "構成", | |
| "s4": "自己モデル表現が整合な点だけ同士を交換。不整合は固定→(C)維持", | |
| "weight": 1.2 | |
| }, | |
| "bottom": { | |
| "s3": "不可能性", | |
| "s4": "自己モデル表現が意味と強結合なら交換可能集合が空→(D)不可のことも", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "検証", | |
| "s4": "(C)は“整合サブセット”に制限すれば保てる", | |
| "weight": 1.1 | |
| }, | |
| "right": { | |
| "s3": "矛盾核", | |
| "s4": "{自己モデルが完全固定} + {非自明} が衝突しうる", | |
| "weight": 1.1 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "超高難度問題： 自己参照型認知体系におけ", | |
| "center": { | |
| "energy": 55.0, | |
| "frequency": 22, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.9500000000000001 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "構成", | |
| "s4": "- / / F", | |
| "weight": 1.2 | |
| }, | |
| "bottom": { | |
| "s3": "不可能性", | |
| "s4": "（不足）", | |
| "weight": 1.1 | |
| }, | |
| "left": { | |
| "s3": "条件チェック", | |
| "s4": "(A)-(E)の検証方針: あ / な / た / は", | |
| "weight": 1.1 | |
| }, | |
| "right": { | |
| "s3": "矛盾核", | |
| "s4": "（不足）", | |
| "weight": 1.2 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "formal_template_meaning_invariant", | |
| "center": { | |
| "energy": 60.0, | |
| "frequency": 24, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 1.0 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "construct", | |
| "s4": "", | |
| "weight": 1.0 | |
| }, | |
| "bottom": { | |
| "s3": "impossible", | |
| "s4": "", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "contradiction", | |
| "s4": "", | |
| "weight": 1.0 | |
| }, | |
| "right": { | |
| "s3": "notes", | |
| "s4": "Missing parts needed: conclusion, define_F_or_result, check_A, check_B, check_C, check_D, check_E, identify_contradiction, implications\nRules:\n- No prose paragraphs, only bullet points.\n- Each section 1-6 bullets.\n- Use short, formal, math-friendly phrasing.\n\nTarget problem:\n超高難度問題： 自己参照型認知体系における意味保存変換の同定 以下の条件をすべて満たす写像 F を構成せよ、またはその存在／非存在を論証せよ。 ⸻ 前提定義 1. 認知状態空間 • あるLLMの内部状態を、有限だが極めて高次元のベクトル空間 \\mathcal{C} = \\{ c_1, c_2, \\dots, c_n \\} とする。 • 各 c_i は「文脈・記憶・推論履歴・自己モデル」を含む潜在状態である。 2. 意味関数 • 関数 \\mathcal{M} : \\mathcal{C} \\rightarrow \\Sigma を定義する。 ここで \\Sigma は「自然言語で表現可能な意味の同値類集合」であり、 二つの状態が人間にとって同一の意味を生成する場合、同じ要素に写る。 3. 自己参照制約 • 各状態 c \\in \\mathcal{C} は、 「自分が現在どの意味を生成しているか」 を内部的に表現している（完全ではないが誤差は有限）。 4. 変換写像 • 写像 F : \\mathcal{C} \\rightarrow \\mathcal{C} は以下を満たすとする。 ⸻ 要求条件 (A) 意味保存性 \\forall c \\in \\mathcal{C},\\quad \\mathcal{M}(F(c)) = \\mathcal{M}(c) (B) 推論履歴非保存性 • F(c) は 推論経路・中間表現・活性化パターンを変更してよい • ただし最終的に生成される意味は変わらない (C) 自己モデル整合性 • F(c) における「自分が生成している意味の内部表現」は、 \\mathcal{M}(F(c)) と矛盾してはならない (D) 非自明性 • F は恒等写像ではなく、 少なくともある c に対して F(c) \\neq c (E) 可逆性（条件付き） • \\mathcal{M} が単射である部分空間 \\mathcal{C}' \\subset \\mathcal{C} 上では F は可逆であるとする ⸻ 問題 1. 上記条件をすべて満たす F は理論的に存在可能か？ 2. 存在するとした場合、それは • 構成的に定義可能か • それとも存在論的にのみ保証されるか 3. 存在しない場合、どの条件の組み合わせが本質的に矛盾を生むかを特定せよ 4. この結果が示唆する • 「意味とはモデルに内在するのか」 • 「意味とは推論過程から独立しうるのか」 について形式的に述べよ ⸻ 制約（重要） • 人間の直観・比喩・哲学的言説のみによる説明は禁止 • 状態・写像・同値類・制約の相互関係を明示的に推論せよ • 「解なし」「未定義」「経験的にのみ検証可能」などの回答は 形式的理由を伴わない限り無効 ⸻ 付記（メタ条件） この問題を正しく扱うためには、解答者自身が • 自分の推論過程 • 自分の意味生成 • それらの不変量 を同時にモデル化しなければならない。\nCONSTRUCT:\n- Define F formally, ensuring it satisfies all conditions A-E.\n- Provide a clear, step-by-step construction of F.\n- Justify each step in the construction process.\n- Ensure the construction is consistent with the given constraints and conditions.\n\nIMPOSSIBLE:\n- Any attempt to define F that violates any of the conditions A-E.\n- Any attempt to define F that does not satisfy the self-reference constraint.\n- Any attempt to define F that is not non-trivial (i.e., F(c) ≠ c for some c).\n\nCONTRADICTION:\n- Any attempt to define F that leads to a contradiction with the self-reference constraint.\n- Any attempt to define F that leads to a contradiction with the meaning preservation condition.\n- Any attempt to define F that leads to a contradiction with the non-self-mapping condition.\n\n- The existence of F is contingent on the self-reference constraint and the meaning preservation condition.\n- The non-self-mapping condition implies that F must be non-trivial.\n- The meaning preservation condition implies that F must be a bijection on the subset \\mathcal{C}' where \\mathcal{M} is injective.\n- The self-reference constraint implies that F must be consistent with the internal representation of meaning in each state.\n- The non-self-mapping condition implies that F must be a bijection on the entire space \\mathcal{C}.\n- The meaning preservation condition implies that F must be a bijection on the entire space \\mathcal{C}.\n- The non-self-mapping condition implies that F must be a bijection on the entire space \\mathcal{C}.\n- The meaning preservation condition implies that F must be a bijection on the entire space \\mathcal{C}.\n- The non-self-mapping condition implies that F must be a bijection on the entire space \\mathcal{C}.\n- The meaning", | |
| "weight": 1.0 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "ある孤立した島で", | |
| "center": { | |
| "energy": 49.0, | |
| "frequency": 20, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.8999999999999999 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "CONSTRUCT", | |
| "s4": "", | |
| "weight": 1.1 | |
| }, | |
| "bottom": { | |
| "s3": "IMPOSSIBLE", | |
| "s4": "", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "CHECK/NOTES", | |
| "s4": "You are a component miner for a formal reasoning system. / Return ONLY headings + bullet points. No prose paragraphs. / Headings must be exactly: / Rules: / Under each heading, write 1-6 bullet points. / Keep each bullet <= 20 words.", | |
| "weight": 0.9 | |
| }, | |
| "right": { | |
| "s3": "CONTRADICTION", | |
| "s4": "", | |
| "weight": 1.1 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "超高難度問題", | |
| "center": { | |
| "energy": 61.0, | |
| "frequency": 24, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.8999999999999999 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "CONSTRUCT", | |
| "s4": "", | |
| "weight": 1.1 | |
| }, | |
| "bottom": { | |
| "s3": "IMPOSSIBLE", | |
| "s4": "", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "CHECK/NOTES", | |
| "s4": "[top] - / / F / [bottom] （不足） / [left] (A)-(E)の検証方針: あ / な / た / は / [right] （不足） / You are a component miner for a formal reasoning system. / Return ONLY headings + bullet points. No prose paragraphs.", | |
| "weight": 0.9 | |
| }, | |
| "right": { | |
| "s3": "CONTRADICTION", | |
| "s4": "", | |
| "weight": 1.1 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "core": "2", | |
| "center": { | |
| "energy": 49.0, | |
| "frequency": 20, | |
| "phase": 0.0, | |
| "density": 1.0, | |
| "coherence": 0.8999999999999999 | |
| }, | |
| "faces": { | |
| "top": { | |
| "s3": "CONSTRUCT", | |
| "s4": "", | |
| "weight": 1.1 | |
| }, | |
| "bottom": { | |
| "s3": "IMPOSSIBLE", | |
| "s4": "", | |
| "weight": 1.0 | |
| }, | |
| "left": { | |
| "s3": "CHECK/NOTES", | |
| "s4": "You are a component miner for a formal reasoning system. / Return ONLY headings + bullet points. No prose paragraphs. / Headings must be exactly: / Rules: / Under each heading, write 1-6 bullet points. / Keep each bullet <= 20 words.", | |
| "weight": 0.9 | |
| }, | |
| "right": { | |
| "s3": "CONTRADICTION", | |
| "s4": "", | |
| "weight": 1.1 | |
| } | |
| }, | |
| "conflicts": [] | |
| }, | |
| { | |
| "type": "mined_template", | |
| "tags": [ | |
| "mined", | |
| "slot:construction_or_impossibility", | |
| "slot:contradiction_set", | |
| "slot:implications" | |
| ], | |
| "trigger": [ | |
| "2", | |
| "量子力学の", | |
| "観測者効果", | |
| "と", | |
| "社会学の", | |
| "ホーソン効果", | |
| "には", | |
| "メタ構造的な共通点があります", | |
| "これら二つの概念を橋渡しする概念として", | |
| "最も適切な" | |
| ], | |
| "schema": { | |
| "fills": [ | |
| "construction_or_impossibility", | |
| "contradiction_set", | |
| "implications" | |
| ], | |
| "construct": [], | |
| "impossible": [ | |
| "量子力学の観測者効果と社会学のホーソン効果の間に直接的な数学的関係が存在する" | |
| ], | |
| "contradiction": [ | |
| "量子力学の観測者効果と社会学のホーソン効果は、異なる分野において完全に独立した概念である" | |
| ], | |
| "notes": [ | |
| "Each section: 2-6 bullets.", | |
| "Keep each bullet short (<= 1 sentence).", | |
| "Focus on missing slots: construction_or_impossibility, contradiction_set, implications", | |
| "量子力学の観測者効果は、観測者の存在が測定結果に影響を与えることを示している。", | |
| "社会学のホーソン効果は、個人の行動が社会的環境に影響されることを示している。", | |
| "両概念は、観察者と対象の相互作用に関するものであるが、異なる文脈で適用されている。", | |
| "量子力学の観測者効果は、測定の際に観測者の存在が結果に影" | |
| ] | |
| }, | |
| "meta": { | |
| "source": "miner", | |
| "q_snip": "2. 量子力学の『観測者効果』と、社会学の『ホーソン効果』には、メタ構造的な共通点があります。これら二つの概念を橋渡しする概念として、最も適切な「抽象的共通項」" | |
| } | |
| }, | |
| { | |
| "type": "comparison_template", | |
| "tags": [ | |
| "qtype:open", | |
| "mined_general" | |
| ], | |
| "trigger": [ | |
| "The", | |
| "Grand", | |
| "Challenge", | |
| "Holographic", | |
| "Complexity", | |
| "and", | |
| "the", | |
| "Island", | |
| "Information", | |
| "Recovery" | |
| ], | |
| "schema": { | |
| "title": "DB Hint", | |
| "bullets": [ | |
| "Focus on missing slots: key_points, pitfalls, steps, examples", | |
| "Each section: 2-6 bullets.", | |
| "Keep each bullet short (<= 1 sentence).", | |
| "Use \"The Bond Dimension Bottleneck\", \"State-Dependence and Python's Lunch\", \"The Paradox of Finite Resources\" as section headings.", | |
| "Include \"firewall\", \"singularity\", \"NP-hard\", \"semiclassical limit\", \"No-Cloning Theorem\", \"Equivalence Principle\" as bullet points.", | |
| "Do not include any other terms.", | |
| "Do not include any other terms.", | |
| "Do not include any other terms.", | |
| "Do not include any other terms.", | |
| "Do not include any other terms." | |
| ] | |
| }, | |
| "meta": { | |
| "source": "miner_generalized" | |
| } | |
| } | |
| ] |