The Electron Inevitability Program: A Theorem-Facing Mathematical Package with Proof-Bearing Companion

## Overview This record contains a bundled two-manuscript release of the Electron Inevitability Program: 1. a theorem-facing main paper;2. a proof-bearing companion manuscript. The package studies the electron sector in gauge--Higgs--Yukawa theories from a mathematical-physics viewpoint. Its purpose is not primarily phenomenological model-building, but the nonperturbative theorem-level formulation and proof-bearing discharge of the electron-sector package itself. More precisely, the record treats the existence and structure of the realistic electron sector as a mathematical problem: target-model Osterwalder--Schrader instantiation, existence of the minimal-charge Buchholz--Fredenhagen electron sector, inclusive asymptotic closure across admissible hard BF channels/sectors, and universality/global completeness under admissible presentation changes. The two files are intended to be read together as one integrated package. The main paper presents the front-facing theorem package. The companion manuscript carries the detailed proof-bearing burden. ## Contents of this record - **Main paper (v4. 2): ** theorem-facing presentation of the electron-sector package. - **Companion manuscript (v3. 1r): ** foundations and proof modules carrying the proof-bearing burden of the main theorem package. The recommended reading order is: first the main paper, then the companion. ## Core theorem package The bundled package has four principal components. 1. **Target-model foundation. ** A class-uniform Osterwalder--Schrader window is instantiated on an admissible parameter box, with gauge-invariant reconstruction, fermionic reflection positivity, strict interchange of limits, and uniform control of the transfer package. 2. **Realistic electron sector. ** In the massless-photon branch, a gauge-invariant composite generates a nonperturbatively defined minimal-charge Buchholz--Fredenhagen sector with threshold at \ (mₑ\), no threshold atom, assumption-free pointwise infrared splitting on compact bands near \ (mₑ²\), and a positive-energy projective Poincaré representation. 3. **Inclusive asymptotic closure. ** The inclusive, IR-safe scattering theory closes across all admissible hard BF channels and sectors. The benchmark channel, the finite-family layer, and the exhaustion/consistency upgrade combine into an all-channel inclusive asymptotic-closure theorem. 4. **Universality and global completeness. ** The whole package is stable under admissible regulator, calibrated window, and dressing changes, and persists along admissible piecewise-\ (C¹\) window-connected paths. A Higgsed isolated-pole theorem is retained only as a comparison branch describing thepole-to-continuum transition as the abelian gap tends to zero. ## Scope and mathematical character Although the subject is an electron sector in quantum field theory, the present record is mathematically oriented in character. It should be read primarily as a theorem-facing mathematical-physics package, not as a phenomenological particle-physics model or a conventional physics paper centered on numerical prediction. The central question is whether the electron sector can be formulated and established nonperturbatively at theorem level inside the admissible gauge--Higgs--Yukawa framework. Accordingly, the core claims of the record are mathematical existence, structural, scattering, and universality statements: - theorem-level target-model instantiation of the class-uniform OS window;- theorem-level existence of the minimal-charge electron BF sector;- theorem-level all-channel inclusive asymptotic closure;- theorem-level universality/global completeness under admissible regulator, window, and dressing changes. In this sense, the record is closer in spirit to a mathematical existence-and-structure program in quantum field theory than to a standard phenomenological physics paper. ## What is included in the companion The companion manuscript carries the proof-bearing chain behind the main package: \[alignedgauge-invariant OS foundation- a single complete Standard Model closure theorem;- a phenomenological or numerical particle-physics model centered on experimental prediction. Those are natural downstream directions, but they are not part of the exact core theorem package of the present record. ## Reading guide This Zenodo record should be read as one integrated two-manuscript package rather than as two separate uploads. - Read the **main paper** first for the theorem-facing statements, scope, and mathematical position of the program. - Read the **companion manuscript** second for the detailed proof-bearing discharge of the foundational cluster, the realistic BF-sector theorem, the inclusive scattering closure, and the universality seal. =================================== Author: Lee Byoungwoo (이병우) leeclinic@protonmail. com