Nonperturbative Existence and Inclusive Asymptotic Closure of the Electron Sector in Gauge–Higgs–Yukawa Theories

## Overview This record contains the integrated theorem-facing and proof-bearing manuscript **“Nonperturbative Existence and Inclusive Asymptotic Closure of the Electron Sector in Gauge–Higgs–Yukawa Theories”** by **Lee Byoungwoo** (version **v5. 2**, March 2026). The paper reorganizes the Electron Inevitability Program into one front-facing theorem package for the electron sector in gauge–Higgs–Yukawa theories. The exact core package is formulated as four theorem-level statements together with one comparison theorem: - **Theorem A**: target-model instantiation of a class-uniform Osterwalder–Schrader window on an admissible parameter box \ (PB^ \) - **Theorem B**: nonperturbative existence of the realistic minimal-charge electron Buchholz–Fredenhagen sector generated by a gauge-invariant composite \ (Oₑ \) - **Theorem C**: inclusive asymptotic closure across all admissible hard BF channels/sectors- **Theorem D**: universality and global completeness under admissible regulator/window/dressing changes and admissible window-connected paths- **Comparison Theorem E**: Higgsed pole branch and pole-to-continuum bridge The realistic final branch of the manuscript is the **BF-sector theorem** rather than an isolated-pole statement. The Higgsed pole theorem is retained only as a comparison branch describing the pole-to-continuum transition as the abelian gap tends to zero. ## What is proved in the exact core package Within the standing burden fixed in Section 2, the paper proves: 1. A gauge-invariant and class-uniform Osterwalder–Schrader foundation on \ (PB^ \), including fermionic reflection positivity, strict interchange of limits, and the transfer package \ (TL1\) –\ (TL7^+ \). 2. In the realistic massless-photon branch, a nonperturbatively defined minimal-charge electron BF sector generated by \ (Oₑ \), with: - threshold at \ (mₑ² \), - absence of a threshold atom, - assumption-free pointwise infrared splitting on compact bands above threshold, - positive-energy projective Poincaré covariance. 3. An inclusive, IR-safe scattering theory that closes across all admissible hard BF channels/sectors, from benchmark and finite-family layers to an all-channel exhaustion upgrade with limiting inclusive wave operators and a unitary limiting inclusive scattering operator. 4. Universality of the full theorem package under admissible regulator/window/dressing changes and along admissible piecewise-\ (C¹ \) window-connected paths, with one common quantitative budget. ## Structure of the integrated manuscript The proof-bearing burden is carried in the main body and discharged through four clusters: - Sections 5–7: foundational OS / strict-IOA / transfer layer- Sections 8–10: realistic electron-sector construction- Sections 12–13: inclusive scattering closure- Section 14: universality seal Section 11 records the Higgsed comparison branch. Appendix A is purely navigational: it provides the reading guide, dependency map, navigation table, and compact proof maps for Theorems A–D and Comparison Theorem E. It does **not** enlarge the exact core theorem package or introduce an independent hidden burden. ## Exact scope and non-claims The exact theorem-level scope of the manuscript is exhausted by **Theorems A–D** together with **Comparison Theorem E**. The paper does **not** claim, as part of its exact core package: - a full LSZ-wide exclusive completeness theorem across all channels, - a single fully consolidated Standard-Model-wide portability theorem. Those layers remain explicitly supportive or future-upgrade modules. ## Supportive layers retained in the manuscript The integrated version keeps several supportive body-level layers visible without enlarging the exact core theorem package: - stated-scope Standard-Model portability, - broader portability / thermal-KMS / transport-Kubo / computability overlays, - outlook and upgrade paths beyond the present exact closure. These modules are preserved to document external reach and future extensibility, but the exact theorem-facing claim remains sharply delimited. ## Keywords Gauge–Higgs–Yukawa theory; Osterwalder–Schrader reconstruction; reflection positivity; Buchholz–Fredenhagen sector; electron sector; inclusive scattering; asymptotic completeness; universality; infrared structure; gauge-invariant composite operators ## Version note This Zenodo record corresponds to the integrated monolithic version **v5. 2**. It is intended to be read as a self-contained theorem-facing and proof-bearing electron-sector paper, rather than as a continuation note for the earlier split architecture. =================================== Author: Lee Byoungwoo (이병우) leeclinic@protonmail. com