## Overview This record contains a two-paper theorem package on the electron sector in gauge--Higgs--Yukawa theories. ### Paper I: Main theorem-facing paper**Nonperturbative Existence and Inclusive Asymptotic Closure of the Electron Sector in Gauge--Higgs--Yukawa Theories** This paper presents the front-facing theorem package. Its core statements are: 1. a target-model instantiation of a class-uniform gauge-invariant Osterwalder--Schrader window;2. a nonperturbative existence theorem for the realistic minimal-charge electron Buchholz--Fredenhagen sector;3. an inclusive asymptotic closure theorem for the admissible hard-channel scattering theory;4. a regulator/window/dressing universality theorem;5. together with a Higgsed isolated-pole comparison branch. The main paper is theorem-facing: it states the integrated package in a compact and readable form, fixes the exact scope of the claims, and records the referee-facing theorem ledger. ### Paper II: Proof-bearing companion**Foundations and Proof Modules for the Electron Sector Theorem in Gauge--Higgs--Yukawa Theories** This companion paper carries the proof-bearing burden of the main theorem package. Its structure mirrors the theorem architecture of the main paper: - Sections 3--5: target-model foundation cluster;- Sections 6--7: realistic Buchholz--Fredenhagen sector and threshold-structure cluster;- Sections 8--9: inclusive scattering and all-channel asymptotic-closure cluster;- Section 10: universality and global-completeness seal. The companion is intended to replace source-dependent references to earlier program papers by a single proof-bearing manuscript whose theorem chain is explicit and organized in direct correspondence with the main paper. ## Reading guide The two papers are intended to be read as a pair. - The **main paper** is theorem-facing. - The **companion paper** is proof-bearing. The correspondence is: - Main Theorem A <- Companion Sections 3--5- Main Theorem B <- Companion Sections 6--7- Main Theorem C <- Companion Sections 8--9- Main Theorem D <- Companion Section 10 Thus the main paper states the electron-sector theorem package in integrated form, while the companion discharges the detailed mathematical proof burden. ## Mathematical focus Although the subject belongs to mathematical physics, the emphasis of this record is on theorem structure, proof architecture, and mathematical completion rather than on phenomenology. The realistic branch is formulated through a minimal-charge Buchholz--Fredenhagen sector generated by a gauge-invariant electron composite. The proof package combines: - gauge-invariant Osterwalder--Schrader reconstruction, - fermionic reflection positivity, - class-uniform analytic control on an admissible parameter box, - threshold non-atomicity and pointwise infrared structure, - inclusive asymptotic closure of the hard-channel scattering theory, - and regulator/window/dressing universality with one common quantitative budget. ## Files in this record - `EletronMainᵥ4. 0. pdf`- `EIPCompanionᵥ2. 4. pdf` ## Scope note This upload should be read as a two-paper theorem package. The main paper is not intended to function as a standalone proof-complete manuscript without the companion; the companion supplies the explicit proof-bearing theorem chain corresponding to the front-facing statements of the main paper. =================================== Author: Lee Byoungwoo (이병우) leeclinic@protonmail. com
Byoungwoo Lee (Sat,) studied this question.