{"schema_version":"ocme-site-results-v1","locale":"en","page_type":"practice","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"page":"13"},"kind":"batches","total":360,"pages":15,"page":13,"entries":[{"id":"batch-20261007-advance-20261009-r06-definite-integral-foundations","title":{"zh-Hant":"定積分密度：有向可加、奇偶與有限和誤差基礎 · 脈衝 R06","en":"Oriented Integral, Parity, and Finite-Sum Error Depth"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-definite-integral"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261009-r05-antiderivative-foundations","title":{"zh-Hant":"原函數密度：係數、常數差與錨點選擇基礎 · 脈衝 R05","en":"Primitive Coefficient, Constant, and Anchor Depth"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-antiderivative"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261009-r04-derivative-rules-foundations","title":{"zh-Hant":"微分規則密度：二階、乘積資格與合成次序基礎 · 脈衝 R04","en":"Polynomial Differentiation Order and Coefficient Depth"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-derivative-rules"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261009-r03-function-limit-foundations","title":{"zh-Hant":"去心極限密度：失敗δ的反例與點值邊界基礎 · 脈衝 R03","en":"Punctured Limit Witness and Point-Value Depth"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-function-limit"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261009-r02-tree-foundations","title":{"zh-Hant":"非空有限樹：連通、無環與唯一道路基礎 · 脈衝 R02","en":"Nonempty Finite Tree Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-tree"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261009-r01-fundamental-theorem-calculus-foundations","title":{"zh-Hant":"微積分基本定理：連續前提與有向端點基礎 · 脈衝 R01","en":"Continuous FTC and Oriented Endpoint Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-fundamental-theorem-calculus"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261008-r07-definite-integral-foundations","title":{"zh-Hant":"有限區間上的多項式定積分基礎 · 脈衝 R07","en":"Signed Polynomial Integral and Finite Left Sum Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-definite-integral"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261008-r06-antiderivative-foundations","title":{"zh-Hant":"多項式原函數與常數選擇基礎 · 脈衝 R06","en":"Polynomial Antiderivative and Constant Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-antiderivative"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261008-r05-derivative-rules-foundations","title":{"zh-Hant":"多項式的和、乘積與合成微分基礎 · 脈衝 R05","en":"Polynomial Differentiation Rule Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-derivative-rules"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261008-r04-derivative-foundations","title":{"zh-Hant":"實函數在一點的導數與差商基礎 · 脈衝 R04","en":"Real Derivative and Finite Quotient Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-derivative"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261008-r03-continuity-foundations","title":{"zh-Hant":"實函數的點值與連續基礎 · 脈衝 R03","en":"Real Point Value and Continuity Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-continuity"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261008-r02-function-limit-foundations","title":{"zh-Hant":"去心實數論域的函數極限基礎 · 脈衝 R02","en":"Punctured Real Function Limit Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-function-limit"],"state":"candidate_validated"},{"id":"batch-20261007-advance-20261008-r01-sequence-limit-foundations","title":{"zh-Hant":"數列極限與精確尾界基礎 · 脈衝 R01","en":"Sequence Limits and Exact Tail Cutoff Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-07","count":100,"mko_ids":["mko-sequence-limit"],"state":"candidate_validated"},{"id":"batch-20261006-advance-20261007-r07-geometric-transformations-foundations","title":{"zh-Hant":"平面座標的基本等距與均勻縮放基礎 · 脈衝 R07","en":"Plane Coordinate Isometry and Uniform Scaling Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-06","count":100,"mko_ids":["mko-geometric-transformations"],"state":"candidate_validated"},{"id":"batch-20261006-advance-20261007-r06-similarity-foundations","title":{"zh-Hant":"正倍率的標記三角形相似切片基礎 · 脈衝 R06","en":"Specified Positive-Scale Triangle Similarity Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-06","count":100,"mko_ids":["mko-similarity"],"state":"candidate_validated"},{"id":"batch-20261006-advance-20261007-r05-congruence-foundations","title":{"zh-Hant":"明示對應的非退化三角形全等基礎 · 脈衝 R05","en":"Labeled Nondegenerate Triangle Congruence Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-06","count":100,"mko_ids":["mko-congruence"],"state":"candidate_validated"},{"id":"batch-20261006-advance-20261007-r04-eigenvalue-foundations","title":{"zh-Hant":"實二階方陣的特徵值與非零特徵向量基礎 · 脈衝 R04","en":"Real 2×2 Eigenvalue and Nonzero Eigenvector Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-06","count":100,"mko_ids":["mko-eigenvalue"],"state":"candidate_validated"},{"id":"batch-20261006-advance-20261007-r03-determinant-foundations","title":{"zh-Hant":"實二階方陣的行列式基礎 · 脈衝 R03","en":"Real 2×2 Determinant Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-06","count":100,"mko_ids":["mko-determinant"],"state":"candidate_validated"},{"id":"batch-20261006-advance-20261007-r02-linear-transformation-foundations","title":{"zh-Hant":"矩陣表示的實平面線性映射基礎 · 脈衝 R02","en":"Real Plane Matrix Linear Map Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-06","count":100,"mko_ids":["mko-linear-transformation"],"state":"candidate_validated"},{"id":"batch-20261006-advance-20261007-r01-matrix-foundations","title":{"zh-Hant":"有限矩陣的尺寸、索引與轉置基礎 · 脈衝 R01","en":"Finite Real Matrix Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-06","count":100,"mko_ids":["mko-matrix"],"state":"candidate_validated"},{"id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","title":{"zh-Hant":"有限觀測列的描述統計基礎 · 脈衝 R07","en":"Nonempty Observation List Descriptive Statistics Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-05","count":100,"mko_ids":["mko-descriptive-statistics"],"state":"candidate_validated"},{"id":"batch-20261005-advance-20261006-r06-area-foundations","title":{"zh-Hant":"座標矩形與單位格的面積基礎 · 脈衝 R06","en":"Half-Open Rectangle and Unit-Cell Area Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-05","count":100,"mko_ids":["mko-area"],"state":"candidate_validated"},{"id":"batch-20261005-advance-20261006-r05-circle-foundations","title":{"zh-Hant":"圓的邊界與座標判定基礎 · 脈衝 R05","en":"Circle Boundaries and Zero-Radius Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-05","count":100,"mko_ids":["mko-circle"],"state":"candidate_validated"},{"id":"batch-20261005-advance-20261006-r04-distance-formula-foundations","title":{"zh-Hant":"等單位正交座標的歐氏距離基礎 · 脈衝 R04","en":"Equal-Unit Orthonormal Euclidean Distance Foundations"},"summary":{"zh-Hant":"","en":""},"date":"2026-10-05","count":100,"mko_ids":["mko-distance-formula"],"state":"candidate_validated"}],"title":"Question batches"}