AI 中文总结
本文针对莫泽蠕虫问题，研究特定等腰三角形的贝尔曼森林迷路逃生路径，通过多类精确分析与穷举分支推导，得到该三角形对应通用覆盖的下界及面积比值。
AI 中文摘要
莫泽蠕虫问题是寻找一个最小面积的平面区域，使其能包含每一条长度为1的可求长平面弧的全等副本。本文研究等腰三角形 \\( T = \text{conv}\{(-c,0),(c,0),(0,s)\} \\) 的贝尔曼森林迷路问题逃生路径，其中 \\( s = \frac{766}{\sqrt{625565}} \\)，\\( c = \frac{197}{\sqrt{625565}} \\)。论文给出了精确的四源正支撑校准、连续体到标准多边形的归约、选定的\\( \Lambda \\)-间隙估计、修正的高角边会合论证以及精确的有限台账。原始内锚台账涵盖25个时间顺序：其275个非零后缀状态归约为13个精确平方范数，且满足\\( \\|R\\| < 27131/25000 \\)。若任一近锚失效，新的分隔符间隙引理会产生1或2条遗漏的包络边，其法向量在精确紧致扇形区间内取值。无依赖的有理重放检查了512个单分隔符顺序（涉及1540个带符号半角区间）和4096个双分隔符顺序（涉及有限带符号矩形覆盖）。这三个穷举分支无条件给出\\( E(T) \ge D := \frac{82074390584}{84861020075} = 0.9671624323094728\ldots \\)。因此，莫泽蠕虫的凸通用覆盖面积为\\( \frac{\text{area}(T)}{D^2} = \frac{11511821678274125}{44639604443512928} = 0.257883595112076188\ldots \\)。
英文摘要
Moser's worm problem asks for a planar region of minimum area containing a congruent copy of every rectifiable planar arc of length one. We study the Bellman's lost-in-a-forest problem escape path for the isosceles triangle \[ T=\text{conv}\{(-c,0),(c,0),(0,s)\},\qquad s=\frac{766}{\sqrt{625565}},\qquad c=\frac{197}{\sqrt{625565}}. \] The paper gives an exact positive four-source support calibration, a continuum to standard-polygonal reduction, a selected $Λ$-gap estimate, a corrected high-angle side-meeting argument, and exact finite ledgers. The original inner-anchor ledger covers 25 temporal orders: its 275 nonzero suffix states reduce to 13 exact squared norms and satisfy $\|R\|<27131/25000$. If either near anchor fails, a new delimiter-gap lemma produces one or two omitted hull edges whose normals range over an exact compact fan interval. A dependency-free rational replay checks 512 one-delimiter orders over 1540 signed half-angle intervals and 4096 two-delimiter orders over a finite signed rectangle cover. These three exhaustive branches give unconditionally \[ E(T)\ge D:=\frac{82074390584}{84861020075} =0.9671624323094728\ldots \] Hence, the convex universal cover of Moser's worm \[ \frac{\text{area}(T)}{D^2} =\frac{11511821678274125}{44639604443512928} =0.257883595112076188\ldots. \]
Comments49 pages, 1 figure, Lean 4 code for formal proofs, and Python code for exact symbolic replay verifier
