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

# Nonperturbative Existence and Inclusive Asymptotic Closure of the Electron Sector in Gauge--Higgs--Yukawa Theories ## Overview This record contains a self-contained integrated manuscript of the Electron Inevitability Program in its monolithic theorem-facing and proof-bearing form. The paper is organized around one exact core theorem package for the electron sector in gauge--Higgs--Yukawa theories. The manuscript no longer separates a front-facing main paper from a technical companion. Instead, the theorem package and its proof-bearing discharge are carried inside one document. The exact core package consists of 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. ## Exact core theorem package The exact theorem-level scope of the manuscript is exhausted by Theorems A--D together with Comparison Theorem E. In particular, the paper does **not** claim, as part of its exact core package, - a full LSZ-wide exclusive completeness theorem across all channels, or- a single fully consolidated Standard-Model-wide portability theorem. Those layers remain supportive or future-upgrade modules beyond the exact core theorem package. ## What the manuscript proves At the theorem-facing level, the paper proves the following integrated package. ### 1. Target-model class-uniform OS window The target gauge--Higgs--Yukawa model class admits a class-uniform Osterwalder--Schrader window on \ (PB^\), with gauge-invariant reconstruction, fermionic reflection positivity, strict interchange of limits, and the transfer package \ (TL1\) --\ (TL7+\) controlled uniformly on \ (PB^\). ### 2. Realistic electron sector In the realistic massless-photon branch, the gauge-invariant composite \ (Oₑ\) generates a nonperturbatively defined minimal-charge Buchholz--Fredenhagen sector with: - threshold at \ (mₑ²\), - absence of a threshold atom, - assumption-free pointwise infrared splitting on compact bands above threshold, - positive-energy projective Poincaré covariance. The realistic final branch is therefore the BF-sector theorem, not an isolated one-particle pole theorem. ### 3. Inclusive asymptotic closure The inclusive, IR-safe scattering theory of the realistic electron sector closes across all admissible hard BF channels/sectors: - benchmark channel, - finite-family layer, - exhaustion/consistency upgrade, - all-channel inclusive asymptotic closure on the admissible hard BF space. ### 4. Universality and global completeness The full theorem package is invariant under admissible regulator/window/dressing changes and along admissible piecewise-\ (C¹\) window-connected paths, with one common quantitative budget. Thus the package is presented as a class-level invariant theorem, not as a presentation artifact of one preferred regulator, calibrated window, or dressing choice. ## Structure of the integrated manuscript The paper is organized into four proof-bearing clusters. ### Foundational clusterSections 5--7 establish: - the gauge-invariant OS framework, - fermionic reflection positivity, - the class-uniform OS window, - strict interchange of limits, - the transfer package \ (TL1\) --\ (TL7+\). ### Realistic-branch clusterSections 8--10 prepare and discharge the realistic branch: - gauge-invariant electron composite and branch structure, - threshold structure of the realistic branch, - existence of the minimal-charge electron BF sector. Section 11 records the Higgsed comparison theorem. ### Scattering clusterSections 12--13 prove: - finite-family inclusive scattering, - exhaustion, strong limits, and all-channel inclusive asymptotic closure. ### Universality clusterSection 14 proves the universality seal and class-level global completeness of the theorem package. ## Supportive layers Sections 15--16 and Appendices A--D are retained explicitly as supportive layers. They record: - stated-scope Standard-Model portability, - broader portability / thermal-KMS / transport-Kubo / computability overlays, - reading guides, - proof maps, - implementation notes, - auxiliary dashboards. These layers do not enlarge the exact core theorem package. ## Reading rule The paper is designed to be readable in two ways: - as a theorem-facing integrated manuscript through the front matter, theorem statements, scope ledger, and conclusion;- as a proof-bearing manuscript through the foundational, realistic-branch, scattering, and universality sections. The appendices are navigational and implementation-oriented; they do not carry a hidden second proof-bearing paper. ## What is new in this integrated version Compared with the earlier two-paper architecture, the present version internalizes the former proof-bearing burden into one monolithic manuscript. The main gains of the integrated version are: - one self-contained theorem package in a single document, - explicit scope discipline, - explicit dependency map, - clearer separation between exact core results and supportive layers, - thicker local proof-bearing treatment in the foundational, scattering, and universality sections. ## Author Lee Byoungwoo =================================== Author: Lee Byoungwoo (이병우) leeclinic@protonmail. com