Electron Inevitability Program Manuscript Set: Finite-Window Chart Closure, Source-Data Realization, and Positive-Threshold/BF Interfaces, Version v5.7

This record contains Version v5.7 of the Electron Inevitability Program (EIP) manuscript set. The EIP asks whether the appearance of a stable minimal electric-charge sector can be organized as a mathematical consequence of gauge-invariant structural, Osterwalder-Schrader, Gauss-law, Buchholz-Fredenhagen, threshold, and finite-window source conditions, rather than inserted only as a primitive particle input. Version v5.7 is a synchronization and source-chart refinement release. It updates the previous v5.6 finite-window closure package by incorporating the post-v5.6 companion note *A Canonical Finite-Window Source-Data Chart for the Minimal Charged Branch*, Version v1.2r1, and by synchronizing Paper I, Paper II, and the orientation guide with that new source-data interface. The proof-dependency spine of the package is: $$\text{regulator response chart}\Rightarrow\text{response-parametrix gate}\Rightarrow\text{OS-positive activation}\Rightarrow\text{minimal nonzero charge branch}$$ followed by $$\text{canonical source-data chart}\Rightarrow\text{mass-generating source floor}\Rightarrow\text{positive-threshold/BF-ready branch}\Rightarrow\text{downstream proof architecture}.$$ The new source-data chart note moves one layer lower than the mass-generating source closure theorem. It fixes a chosen finite-window GHY/OS source model with exact packet-generated branch envelope $$\Pi_{q,T}:=\Pi^{\rm pkt}_{q,T},\qquad\alpha_T=0,\qquad\varepsilon_T^{\rm act}=0,$$ and gives theorem-level sufficient conditions under which that finite-window source model realizes the canonical source-data chart consumed by the mass-generating source closure theorem. The source-data burden is reduced to explicit finite-window source-block and scale estimates. In particular, the effective coefficient layer is treated as a normalized finite-window source-strength assignment: $$C^{\rm eff}_{j,T}=Y^{\rm eff}_{j,T}\Phi^{\rm eff}_{j,T},\qquad\sigma_{\min}(Y^{\rm eff}_{j,T})\ge y^{\rm eff}_T,\qquad\sigma_{\min}(\Phi^{\rm eff}_{j,T})\ge v^{\rm eff}_T,$$ so that $$m^{\rm src}_T:=y^{\rm eff}_T v^{\rm eff}_T.$$ This is not an electron-mass formula, not a Standard-Model Yukawa/Higgs identification, and not a calibrated physical threshold. It is a finite-window source-strength scale inside the normalized chart. The v5.7 release also synchronizes Paper I and Paper II with the new interface. Paper I is updated as a downstream proof-architecture manuscript whose theorem package is not enlarged, but whose dependency map now records the source-data chart, mass-generating source floor, and threshold/BF interface in the correct order. Paper II is updated only as an upstream minimal-branch extraction note: its output remains a minimal nonzero electric-charge branch, while the source-data and threshold/BF notes are recorded as post-extraction interfaces. The strongest current claim of this manuscript set is finite-window chart closure under specified response, activation, source, threshold/BF, and compatibility hypotheses. The set does not claim a numerical derivation of the electron mass, the equality \(M_{q_{\min}}=m_e\), spin/chirality/leptonic identification, an unconditional construction of every interacting gauge-Higgs-Yukawa/Osterwalder-Schrader model, or a full derivation of the Standard-Model electron. The main remaining mathematical burdens after v5.7 are: 1. to verify the microscopic source-coefficient floors \(y^{\rm eff}_T\) and \(v^{\rm eff}_T\) in a chosen finite-window realization;2. to prove the local source-block margin and block-defect estimates;3. to verify the five source-defect channels: cutoff, OS-domain, renormalization, dressing-transfer, and branch-comparison;4. to verify the corresponding five quadratic local-remainder channels;5. to compare the packet-generated source branch with a larger interacting charged branch;6. to formulate any later physical threshold calibration only after a mathematically stable positive lower edge has first been obtained. This v5.7 release should therefore be read as a source-data chart synchronization and finite-window theorem-architecture package, not as a final physical electron-identification theorem. Author: Lee Byoungwoo(이병우) [email protected]