Electron Inevitability Program: Main Theorem Paper and Proof-Bearing Companion on the Electron Sector in Gauge--Higgs--Yukawa Theories

# Electron Inevitability Program: Main Theorem Paper and Proof-Bearing Companion on the Electron Sector in Gauge--Higgs--Yukawa Theories ## Overview This Zenodo record contains the current two-paper theorem package of the Electron Inevitability Program: 1. the main theorem-facing paper **Nonperturbative Existence and Inclusive Asymptotic Closure of the Electron Sector in Gauge--Higgs--Yukawa Theories** (v4. 0), 2. the proof-bearing companion manuscript **Foundations and Proof Modules for the Electron Sector Theorem in Gauge--Higgs--Yukawa Theories** (companion note v2. 5). The two documents are intended to be read together as one integrated package. The main paper presents the front-facing theorem statements and exact theorem-level scope of the electron-sector result, while the companion carries the detailed proof-bearing discharge of the same package. ## What this record contains ### Main paperThe main paper reorganizes the Electron Inevitability Program into a theorem-facing paper on the electron sector in gauge--Higgs--Yukawa theories. Its core package consists of four theorem-level statements and one comparison theorem: - **Theorem A**: target-model instantiation of the class-uniform Osterwalder--Schrader window \ (U₁\), - **Theorem B**: nonperturbative existence of the realistic minimal-charge electron Buchholz--Fredenhagen sector, - **Theorem C**: inclusive, IR-safe asymptotic closure across all admissible hard BF channels/sectors, - **Theorem D**: universality and global completeness under admissible regulator/window/dressing changes, - **Comparison Theorem E**: Higgsed pole branch and pole-to-continuum bridge. The realistic final branch of the package is the BF-sector theorem: the electron is formulated nonperturbatively as a minimal-charge BF sector generated by a gauge-invariant composite \ (Oₑ\), with threshold at \ (mₑ\), threshold non-atomicity, pointwise infrared splitting near \ (mₑ²\), positive-energy projective Poincar\'e covariance, and inclusive asymptotic closure. ### Companion paperThe companion manuscript carries the proof-bearing burden behind the same theorem package. It is organized as one continuous proof-bearing chain covering: - the gauge-invariant Osterwalder--Schrader foundation, - the class-uniform OS window with strict interchange of limits, - the transfer package \ (TL1\) –\ (TL7+\), - the threshold structure of the realistic branch, - existence of the realistic Buchholz--Fredenhagen electron sector, - finite-family inclusive scattering, - the exhaustion upgrade to all-channel inclusive asymptotic closure, - regulator/window/dressing universality and the global-completeness seal. The role of the companion is not to state a separate physical claim, but to absorb the technical and proof-bearing burden of the main electron-sector theorem package into one integrated manuscript. ## Why the two papers are bundled together These two documents are intentionally archived in one record because the package is easiest to understand as a single theorem architecture with two reading layers: - the **main paper** gives the theorem-facing presentation and exact scope, - the **companion** gives the detailed proof-bearing discharge. Separating the two into unrelated records would obscure the dependency structure of the package. ## Exact scope of the present bundled record The exact core theorem package archived here is: 1. theorem-level target-model instantiation of the class-uniform OS window \ (U₁\), 2. theorem-level nonperturbative existence of the realistic minimal-charge electron BF sector, 3. theorem-level inclusive asymptotic closure across all admissible hard BF channels/sectors, 4. theorem-level universality under admissible regulator/window/dressing changes. The following are **not** claimed as part of the exact core theorem package of this record: - a full LSZ-wide exclusive completeness theorem across all channels, - a single fully consolidated Standard-Model-wide portability theorem. Such extensions remain supportive or future-upgrade layers beyond the exact theorem package archived here. ## Dependency map inside the bundle The proof-bearing dependency map 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 present Zenodo record should be read as one bundled theorem package rather than as two unrelated preprints. ## Files in this record - `ElectronInevitabilityProgramᵥ4. 0. pdf`- `EIPᵥ4companionᵥ2. 5. pdf` ## Author Lee Byoungwoo =================================== Author: Lee Byoungwoo (이병우) leeclinic@protonmail. com