---
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---
## 已经得到的结果
正二阶梯度能、正四阶梯度能与非负体势的尺度竞争已经给出唯一正驻点 R_*，其径向二阶导数为正。四阶项抵抗整体收缩的机制已有解析表达；第四章与第五章的缩放参数互为倒数，幂次须按各自定义比较。
## 仍需完成的研究
保持同一目标空间、真空和边界，构造完整三维有限能量解，求 Hessian 或周期背景 Floquet 谱；检查分裂、辐射、零模及幅度过零路径，再将拓扑量映射到粒子属性。
## 下一份可复核成果
先复算解析半径及 A_0→0 极限，再交付带方程残差、边界与网格收敛的场解和非径向谱；明确正径向曲率之外还检查了哪些扰动。
## 适用范围与研究入口
一参数尺度模型已解决其径向极值问题；这既不应被说成“没有解析稳定尺度”，也不能被放大为完整电子或质子稳定性证明。
[stability](/theory/matter/stability) · [master equation](/theory/space-dynamics/master-equation) · [electron solution](/open-problems/matter/electron-solution) · [space dynamics](/theory/space-dynamics)