Math Islands Education 0.2 — Connected experiments

数学群岛教育 0.2 把数学对象之间的联系变成六组可操作实验。每组共享真实计算状态，同时展示两种结构或表示，并注明条件、反例和文献位置。

Math Islands education 0.2 adds six interactive connections whose paired views share actual computations, with assumptions, counterexamples and source passages.

• Fourier modes ↔ heat flow / 傅里叶模态与热流
• Graphs ↔ homology over F₂ / 图与 F₂ 同调
• Complex powers ↔ covering lifts / 复数幂与覆盖提升
• Probability distributions ↔ W₁ and CDFs / 概率分布、W₁ 与累积分布
• Polynomial ideals ↔ zero sets / 多项式理想与零点
• D₄ ↔ complex actions and real matrices / D₄、复数动作与实矩阵

保存实验的参数、计算结果和观察；导出 JSON / Markdown，导入 JSON。分享链接只包含实验入口和语言。记录保存在浏览器内。

Save parameters, computed observations and notes; export JSON / Markdown and import JSON. Share links include the entry and language only. Records remain in the browser.

The existing 24 bilingual object lessons and the 21,741-entry core atlas remain. These six teaching connections do not add or overwrite core relations. All 7,314 files in the recorded publication baseline are unchanged.

Validation and source-reading scope: independent review. Release execution: one-hour sprint.

Open the hosted site — currently owner-private. Download the public static site. GitHub Pages is not enabled; the static package can be served with a local HTTP server or another static host.

Automated checks cover the recorded finite models and browser states; they do not certify general theorems or full accessibility conformance. See the linked evidence for exact coverage and limitations.