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 \(m_e\), no threshold atom, assumption-free pointwise infrared splitting on compact bands near \(m_e^2\), 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-\(C^1\) 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: \[{aligned}gauge-invariant OS foundation&-uniform OS window / strict IOA\& package package of the realistic branch\&-charge electron BF sector-family scattering\&-channel inclusive asymptotic closure / global completeness.{aligned}\] Its role is not to function as a separate historical continuation note,but to expose the mathematical burden of the main theorem package as one continuous proof-bearing chain. ## What is new in this bundled release - The program is presented as a bundled theorem package rather than as a dispersed architecture of earlier notes.- The main paper is fully theorem-facing.- The companion is organized as a proof-bearing manuscript rather than as a roadmap.- The realistic massless-photon electron sector is treated as the final branch, while the Higgsed isolated-pole statement is retained only as a comparison theorem.- The inclusive scattering layer is promoted to an all-channel theorem-level closure package.- The universality layer is stated as a class-level seal for regulator, window, and dressing changes.- The companion manuscript strengthens selected local proof blocks in the foundational, threshold, charged-sector, and all-channel closure layers while preserving the same global theorem architecture. ## What is not claimed This bundled record does **not** claim: - a fully exclusive LSZ-style all-channel theorem;- 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