Arc Topological Homeomorphisms and Underlying Group Structure / 弧拓扑同胚与群底构

Arcman

Arc Topological Homeomorphisms and Underlying Group Structure

弧拓扑同胚与群底构

弧拓扑同胚与群底构

This fifteen-chapter preprint studies group and groupoid realizations, homeomorphic descent, readout kernels, and recovery from source-permitted objects, operations, and composition laws. The supplied fixed-scale marked action yields O(2) × C2 and its topological torsor; base marks, equivariant homeomorphisms, normalizers, and finite-readout conjugacies identify the retained structure. Oriented histories, tensor qualification, finite responses, error propagation, and the distinct D/W/G recovery routes are retained. The all-scale theorem keeps its full GENERAL premises and positive-growth threshold m < M/2. Full-source faithfulness, an independent actual flow, full-field identification of a specified step, and complete generative return remain conditional on their respective evidence. The edition contains 173 original results and 19 central additions: 192 numbered results and 844 numbered equations. The frozen NWL45 v0.62 baseline supplies full-result certificates for 87 of them; 105 lack complete formalization. This preparation reuses integrity-checked historical evidence without rerunning Lean and does not claim an independent reproof of all 192 results. Chinese and English PDFs are language versions of the same research output.

本十五章预印本从弧源许可的对象、操作及合成关系出发,研究群或群胚实现、同胚下降、读出核和恢复。固定尺度原标记作用给出 O(2)×C2 及其拓扑挠子;基标记、等变同胚、正规化子和有限读出共轭明确所保留的结构。全文保留有向历史、张量资格、有限响应、误差传播及 D/W/G 三条恢复路线。一般全尺度定理保留完整 GENERAL 前件和原正增长阈值 m<M/2;全源忠实性、独立实际流、指定一步全字段识别和完整发生回返仍按各自证据作条件陈述。本版含原173项及19项主线增补,共192项编号结果、844条编号公式。冻结的NWL45 v0.62基线为其中87项提供完整结果证书,105项尚未完整形式化;本次发布准备复用经校验的既有证据,未重新运行Lean,也不声称192项已经独立全部复证。中英文PDF为同一研究成果的两个语言文本。

Keywords:

Arc theory; arc topology; groupoids; homeomorphic descent; readout kernels; topological torsors; equivariant reconstruction; finite responses; conditional source realization; Lean formalization; mean dimension; shift embeddings