Published April 28, 2026 | Version v1
Technical note Open

Preliminary LHFT Research Program on Standard-Model Gaps, Candidate Normal Forms, and Open Closure Targets

Authors/Creators

Description

Status: closed normal forms ≠ candidate structures open ≠ microscopic proof targets

Koide, Alpha, and the Charged-Lepton Mass Sector in LHFT

Program for Closing Standard-Model Gaps Using LHFT Research Program 

Module 1: Charged-Lepton Flavor Closure

Module 2: Radius and Flavor Phase of the Charged-Lepton Sector

Module 3: Structural Origin of the Charged-Lepton Scale and Flavor Phase

Module 4: Numerical Scan for Structural Forms of Rℓ and φℓ

Module 5: Alpha-Coupled Mass-Scale Constraint and Tau-Readout Residual

Module 6: Structural Model for Δτ^(K−αm)

Module 7: Candidate Derivation of Ξτ

Module 8: Numerical Audit of the Ξτ Expansion

Module 9: Structural Origin of the Tau Residual Coefficients

Module 10: Reconstructing the Charged-Lepton Mass Vector from Koide, Alpha, and the Tau Residual

Module 11: From Charged-Lepton Masses to Yukawa Couplings

Module 12: Higgs Scale and Electroweak Vacuum Closure

Module 13: Electroweak Mixing Angle and U(1)diag Embedding

Module 14: Non-Abelian Gauge-Origin Program — SU(2)L and SU(3)c

Module 15: Hypercharge, Electric Charge, and Projection Consistency

Module 16: Gauge Anomaly Cancellation as Zero-Defect Projection Consistency

Module 17: Three Generations as Flavor-Branch Closure

Module 18: CKM and PMNS Mixing as Relative Projection Frames

Module 19: Neutrino Sector, PMNS Closure, and Mass Suppression

Module 20: QCD, Confinement Scale, and Proton Mass Anchor

Module 21: Higgs–QCD–Alpha Scale Triangle

Module 22: Strong CP Problem as Projection-Phase Defect

Module 23: Standard-Model Parameter Ledger in LHFT

Module 24: Publication-Level Closure Map

Module 25: Charged-Lepton Normal Form in Yukawa Space

Module 26: Alpha-Driven Ansatz for the Charged-Lepton Yukawa Radius Rᵧ

Module 27: Numerical Audit of the Alpha-Driven Charged-Lepton Yukawa Radius

Module 28: Structural Candidate for the Charged-Lepton Flavor Phase φℓ

Module 29: Numerical Audit of the Charged-Lepton Phase Candidate

Module 30: Charged-Lepton Yukawa Normal Form

Module 31: Proton-Anchor Reading of the Charged-Lepton Yukawa Radius

Module 32: Higgs Scale Candidate from Proton Anchor, Alpha, and ρ₅₀

Module 33: Numerical Audit of the Higgs Scale Candidate

Module 34: Charged-Lepton Radius Revisited After Higgs-Scale Closure

Module 35: Unified Charged-Lepton Closure Formula

Module 36: Numerical Full Audit of the Charged-Lepton Closure Formula

Module 37: Correcting the Charged-Lepton Phase Lock

Module 38: Exact Phase Readout from Charged-Lepton Data

Module 39: Corrected Structural Phase Ansatz

Module 40: Final Charged-Lepton Phase Candidate

Module 41: Final Numerical Audit of the Charged-Lepton Normal Form

Module 42: Publication Theorem — Charged-Lepton Normal-Form Reconstruction

Module 43: Standard-Model Closure Ledger After Charged-Lepton Normal Form

Module 44: Electroweak Scale and Weak-Boson Mass Recovery

Module 45: Weak Mixing Angle Candidate from Finite-Sector Recovery

Module 46: Numerical Audit of the Weak Mixing Angle Candidate

Module 47: Tree-Level Weak-Boson Mass Readout

Module 48: Electroweak Running and Pole-Mass Boundary

Module 49: Electroweak Closure Status and Next Targets

Module 50: Halfway Status — LHFT Standard-Model Closure Program

Module 51: Quark-Sector Entry — Why Quarks Are Harder Than Charged Leptons

Module 52: Quark Yukawa Geometry and Color-Flavor Separation

Module 53: Up-Type Quark Yukawa Normal-Form Search

Module 54: Down-Type Quark Yukawa Normal-Form Search

Module 55: CKM Matrix as Relative Projection Frame

Module 56: Wolfenstein Parameters as Finite-Sector Readouts

Module 57: Numerical Audit of the Wolfenstein Finite-Sector Ansatz

Module 58: Quark Sector Status After CKM Normal-Form Search

Module 59: Neutrino-Sector Entry — Why Neutrinos Require a Separate Closure

Module 60: Neutrino Mass Ordering and PMNS Geometry

Module 61: PMNS Matrix as Lepton-Sector Relative Projection Frame

Module 62: Neutrino Mass-Suppression Mechanisms in LHFT

Module 63: Dirac, Majorana, and Projective Seesaw Readings

Module 64: Neutrino Closure Ledger and Open Targets

Module 65: Higgs Potential Parameters and Vacuum Stability

Module 66: Higgs Self-Coupling and Structural Vacuum Curvature

Module 67: Higgs Mass Readout and Electroweak Curvature

Module 68: Higgs-Sector Status and Open Microscopic Closure

Module 69: QCD Entry — Confinement, Proton Mass, and Color Projection

Module 70: QCD Scale ΛQCD as Projection Anchor

Module 71: Proton Mass as Confinement Recovery Readout

Module 72: Strong CP as Projection-Phase Defect

Module 73: QCD Sector Status and Proton-Anchor Open Remainder

Module 74: Global Coupling Running and Scale Dependence

Module 75: Running Couplings as Scale-Dependent Projection Readouts

Module 76: Matching Low-Energy Alpha to Electroweak Alpha

Module 77: Renormalization Group Reading in LHFT

Module 78: Running-Coupling Status Ledger

Module 79: Standard-Model Defect Ledger — Full Version

Module 80: Publication Roadmap for the LHFT Standard-Model Program

Module 81: Charged-Lepton Sector Final Appendix Draft

Module 82: Alpha Sector Final Appendix Draft

Module 83: Electroweak Sector Appendix Draft

Module 84: Quark and CKM Sector Appendix Draft

Module 85: Neutrino and PMNS Sector Appendix Draft

Module 86: Higgs and QCD Sector Appendix Draft

Module 87: Master Conclusion for the Standard-Model Closure Program

Module 88: Final Status — What Is Closed, What Is Candidate, What Is Open

Module 89: From Program to Formal Paper Architecture

Module 90: Formal Paper Outline — LHFT and the Standard-Model Parameter Problem

Module 91: Alpha as Projection Impedance — Paper Core

Module 92: Charged Leptons as Flavor-Projection Closure — Paper Core

Module 93: Electroweak Recovery and Higgs Scale — Paper Core

Module 94: Quark and CKM Candidate Normal Forms — Paper Core

Module 95: Neutrino, Higgs, and QCD Open Remainders — Paper Core

Module 96: Flavor-Sector Status — Charged Leptons, Quark Eigenvalues, and CKM Frame

Module 97: Coupling Flavor Normal Forms to Electroweak Mass Recovery

Module 98: Master Standard-Model Closure Ledger in LHFT

Module 99: Normal-Form Achievements, Empirical Audit Targets, and Microscopic Proof Obligations

Module 100: Program Status at the Hundred-Module Boundary

Module 101: Proof Program for the 1+7 Schur Alpha Block

Module 102: Derivation Target for the 8 = 1+7 Finite Recovery Sector

Module 103: Hidden Complement Metric C₇ and Canonical Whitening

Module 104: Distinguished Hidden Directions h, s, p and the Three-Term Coupling Vector

Module 105: Observer Compression Term ΔKobs = ¾ρ³

Module 106: Conditional Alpha Theorem After Schur and Observer Compression

Module 107: Derivation Target for F = 1 ⇒ c_F = 5 ⇒ N* = 50

Module 108: Why the Minimal Projectively Accessible Bright Sector Is F = 1

Module 109: Derivation Target for the Selector Rule c_F = 2F + 3

Module 110: Conditional Selector Theorem for N* = 50

Module 111: Moment-Ratio Mixing Degree ρ₅₀ and the 23/110 Prefactor

Module 112: Final Alpha-Proof Status and End of the Current Continuation Block

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