**Authors:** Frank Dodd Tony Smith Jr

This paper describes a research program based on the 240 E8 Root Vectors encoding the basic structure of a Unified Theory of Fundamental Physics by forming a local classical Lagrangian for the Standard Model plus Gravity and Dark Energy. The Root Vectors know where they belong in the Lagrangian because of their place in the geometric structure of E8 and its related symmetric spaces such as: E8 / D8 = 128-dim (OxO)P2; E8 / E7 x SU(2) = 112-dim set of (QxO)P2 in (OxO)P2; D8 / D4 x D4 = 64-dim Gr(8,16). Embedding E8 local classical Lagrangian into Cl(0,16) Clifford Algebra and taking the completion of the union of all tensor products of all the Cl(0,16)s produces a generalization of hyperfinite II1 von Neumann factor fermionic Fock space forming a global AQFT describing spacetime, the Standard Model, and Gravity with Dark Energy. The structure is related to unconventional 26D String Theory by Cl(0,16) -> Cl(0,16)xCl(0,8) = Cl(0,24) -> M(2,Cl(0,24)) = Cl(1,25). Completion of Union of All Tensor Products of Cl(1,25) = 2x2 matrices of Cl(0,24) is the String Theory formulation of the hyperfinite AQFT. The Cl(1,25) of 26D String Theory contains Cl(0,16) which contains E8 whose root vectors describe a Lagrangian for the Standard Model and Gravity + Dark Energy. The paper describes physical interpretations of the 240 Root Vectors and how they are used in calculating force strengths, particle masses, Kobayashi-Maskawa parameters, Dark Energy : Dark Matter : Ordinary Matter ratios, etc. that can be compared with Experimental Observations which are given up to and including the 2016 run of the LHC in the Higgs -> ZZ -> 4l channel which is relevant to the E8 Physics prediction of 3 Mass States of the Higgs and Truth Quark. Version 3 (v3) corrects particle identification of E8 Root Vectors in a diagram. Version 4 (v4) adds material about LHCP Bologna 2018.

**Comments:** 441 Pages.

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[v1] 2018-04-08 15:37:22

[v2] 2018-04-16 06:34:38

[v3] 2018-05-16 20:59:46

[v4] 2018-06-07 02:44:20

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