Electron Inevitability Program Manuscript Set: Finite-Window Chart Closure, OS-Positive Branch Activation, Minimal Charge Extraction, and Positive-Threshold/BF Interfaces

This upload contains the current manuscript set for the Electron Inevitability Program (EIP). The set should be read as a finite-window chart-closure and proof-architecture package, not as a numerical derivation of the electron mass or an unconditional derivation of the Standard-Model electron. The central question of the program is whether a stable minimal electric-charge sector can be organized as a theorem-level consequence of structural properties of a gauge--Higgs--Yukawa universe, rather than inserted as a primitive particle input. The present package develops this question through a layered chain of conditional and finite-window results. The proof-dependency chain is: regulator-level response implementation-parametrix gate-positive branch activation nonzero charge branch -generating source closure-threshold/BF-ready branch proof architecture. The package consists of the following files: 1. **EIP Seven-Paper Set Orientation Guide v0. 1** A short navigational guide explaining the reading order, dependency map, file-by-file role, and remaining burdens of the current EIP manuscript set. 2. **Paper I: A Proof Architecture for the Electron Inevitability Program, v5. 6** The downstream proof-architecture manuscript. It formulates the conditional theorem package for the realistic massless-photon branch as a gauge-invariant Buchholz--Fredenhagen sector with threshold, inclusive closure, and presentation-independence layers under visible standing burdens. 3. **Paper II: A Head-Theorem Reduction for the Electron Inevitability Program, v0. 7r1** A head-theorem reduction showing how charge-label discreteness, Gauss-law superselection, detected-set closedness, and OS-positive activation yield a minimal nonzero electric-charge branch. 4. **Paper III: OS-Positive Branch Activation in the Electron Inevitability Program, v1. 2r1** A finite-window activation note. It proves that a response identity, detector-overlap floor, response-defect control, and Paper IV response-parametrix gate yield an OS-norm floor for a dressed charged probe, hence branch activation. 5. **Paper IV: Dressing-Distortion Estimates in the Electron Inevitability Program, v2. 7r1** A response-parametrix and dressing-distortion note. It develops the finite-window response-kernel and scalar frozen-row implementation estimates needed by the activation-window closure theorem. 6. **Regulator-Level Closure of the Primitive Finite-Window Response Implementation, v1. 0r1** A regulator-level implementation note verifying the Wilson--Gaussian finite-window tail chart for the scalar response implementation used by Paper IV. 7. **Positive Threshold and BF Regularity for the Minimal Charged Branch, v1. 0r3** A threshold/BF interface note upgrading the minimal nonzero charge branch toward an EIP-ready positive-threshold and BF-regular branch, without identifying the lower edge with the physical electron mass. 8. **Mass-Generating Branch Source Estimates for the Minimal Charged Branch, v1. 9r1** A finite-window source-data closure note supplying the mass-generating source-floor input consumed by the threshold/BF interface. It unifies local positive mass-matrix reserve, componentwise local-remainder domination, packet-envelope active retention, branch-envelope Hessian lift, explicit off-packet lift estimates, and a lift-reserve smallness gate. The strongest current finite-window source statement in the package has the schematic form: Yₐ, ₓ=Y⁰ₐ, ₓ+EYₐ, ₓ \|Y⁰ₐ, ₓX₉, ₓ\| y₀\|X₉, ₓ\| \|EYₐ, ₓX₉, ₓ\| Y y₀\|X₉, ₓ\| which gives ₀= (1-Y) ²y₀²>0. Together with componentwise local-remainder domination, packet-envelope active retention, explicit branch-envelope lift estimates, and the reserve condition c ₏₊ₓ-^ Hcert, expT-^ bare, errT-^ mg, srcT_*²+^ mgT, the mass-generating source note obtains the finite-window branch-envelope source floor M^ mgₐ, ₓ (m_*²+^ mgT) ₐ, ₓ. The present manuscript set does **not** claim: - a numerical computation of the electron mass;- a proof that \ (Mₐ_=mₑ\) ;- spin, chirality, or leptonic-sector identification;- an isolated Wigner-particle pole in the massless-photon branch;- an unconditional derivation of the Standard-Model electron. Its current contribution is narrower but more precise: inside specified finite-window chart classes and visible compatibility burdens, it connects regulator-level response implementation, response-parametrix closure, OS-positive activation, minimal charge extraction, positive-threshold/BF regularity, and mass-generating source closure into one explicit theorem-facing package. The remaining external burdens are: 1. deriving the Wilson--Gaussian response chart and the finite-window source-data chart from a fully specified interacting gauge--Higgs--Yukawa/Osterwalder--Schrader construction; 2. proving the microscopic source-data estimates for \ (Y⁰ₐ, ₓ\), \ (EYₐ, ₓ\), and the component remainders \ (R^ dress\), \ (R^ ren\), \ (R^ cut\), \ (R^ os\), and \ (R^ br\) ; 3. calibrating or deriving the physical threshold value if a future electron-mass identification claim is attempted; 4. proving spin/chirality/leptonic-sector identification and full Standard-Model portability. Thus this upload should be cited as the current finite-window closure and proof-architecture package for the Electron Inevitability Program, not as a completed first-principles derivation of the electron. Author: Lee Byoungwoo (이병우) leeclinic@protonmail. com