miaolay research

Explain first; keep limits visible

Research

Research contains explanation-led work. The three newly supplied interactive pages are visible but marked beta / 未完成 while their wording, interaction, and numerical expressions are checked.

interactive explainers

Three public betas, not three finished claims.

The pages are preserved as working explainers. Their beta label is part of the content-honesty contract, not decoration.

  1. 珍珠球体与双圈发光纽带 01 quantum / 2026-07-14 · beta / 未完成spin ½ — two turns to closeThe authoritative replacement includes a Dirac belt that returns to a flat state at 720°.
  2. 半透明高维曲面与坐标网格 02 geometry / 2026-07-14 · beta / 未完成hypersurfaceA scroll-led explanation through constraint, slice, projection, and ambient dimension.
  3. 蓝红概率场与主动学习边界 03 reliability / 2026-07-14 · beta / 未完成AK–MCS — learning the boundaryKnown incomplete: interaction, wording, and numerical expressions are still under review.

research practice

Tools and systems around the work.

  1. 01 browser-localresearch toolsLanguage and figure checks with explicit limits.
  2. 02 workflowacademic language systemProtect technical logic before polishing sentences.
  3. 03 aboutfactual contextThe narrow human context supplied for this edition; no projects, institutions, or results are invented.