一个长期存在的研究背景A long-lived research context
研究Research
研究指向长期存在的学术与技术领域。交互解释、工具与系统仍归入项目，并通过共享元数据在此引用。Research names the long-lived academic and technical domain. Interactive explanations, tools, and systems remain Projects and are referenced here from shared metadata.
相关作品与笔记Connected works & notes
-
AK–MCS——学习边界AK–MCS — Learning the Boundary测试版beta
以可运行 beta 的形式呈现蒙特卡洛可能性、Kriging 推断、主动学习与学习得到的极限状态边界，而非经过验证的科学结果。Monte Carlo possibilities, Kriging inference, active learning, and a learned limit-state boundary are visualized as a working beta rather than a validated scientific result.
-
超曲面Hypersurface测试版beta
通过约束、内在自由度、切片、投影与环境维度建立超曲面的直觉，同时不把可视化当作证明。Constraint, intrinsic freedom, slicing, projection, and ambient dimension build an intuition for a hypersurface without presenting the visualization as proof.
-
自旋 ½——两圈闭合Spin ½ — two turns to close测试版beta
以交互方式呈现 Bloch 球方向、旋量相位、干涉与带子同伦；措辞和科学表达仍在审校。Bloch-sphere direction, spinor phase, interference, and a belt homotopy are presented interactively; wording and scientific communication remain under review.
-
学术表达清理器Academic Phrase Cleaner
本地检测器报告空泛强调、通用抽象与论断强度风险，不声称能够让文字变得更像人写。A local detector reports empty emphasis, generic abstraction, and claim-strength risks without claiming to humanize prose.
-
提示词系统Prompt Systems
面向科研图、学术语言与视觉工作的提示结构，呈现决策过程而非神奇措辞。Prompt structures for scientific figures, academic language, and visual work expose decisions rather than magic wording.
-
科研图像检查器Scientific Figure Checker
本地像素检查覆盖尺寸、透明度、边缘、对比度与导出基础，但不能验证科学真实性。Local pixel checks cover dimensions, transparency, edges, contrast, and export basics but cannot verify scientific truth.