1. Introduction

    1. Basic notions of HFFs from TGD perspective

    2. Bird's eye view of HFFs in TGD

    3. M8-H duality and HFFS

    4. Infinite primes

  2. Basic notions related to hyperfinite factors of type II1 from TGD point of view

    1. Basic concepts related to von Neumann algebras

    2. Standard construction for the hierarchy of HFFs

    3. Classification of inclusions of HFFs using extended ADE diagrams

  3. TGD and hyperfinite factors of type II1: a bird's eye of view

    1. Identification of HFFs in the TGD framework

    2. Could the notion of free probability be relevant in TGD?

    3. Some objections against HFFs

  4. M8-H duality and HFFs

    1. Number theoretical level: M8 picture

    2. Geometric level: H picture

    3. Wild speculations about McKay correspondence

  5. About the selection of the action defining the Kähler function of the "world of classical worlds" (WCW)

    1. Could twistor lift fix the choice of the action uniquely?

    2. Two paradoxes

  6. About the TGD based notions of mass, of twistors and hyperbolic counterpart of Fermi torus

    1. Conformal confinement

    2. About the notion of twistor space

    3. About the analogies of Fermi torus and Fermi surface in H3

  7. The notion of generalized integer

    1. The first reactions to the abstract

    2. Fundamental discretization as a cognitive representation?

  8. Infinite primes as a basic mathematical building block

    1. Construction of infinite primes

    2. Questions about infinite primes

    3. P=Q hypothesis

  9. Summary of the proposed big picture

    1. The relation between M8-H and M-M' dualities

    2. Basic mathematical building blocks

    3. Basic algebraic structures at number theoretic side

    4. Basic algebraic structures at the geometric side

  10. Appendix: The reduction of quantum TGD to WCW geometry and spinor structure

    1. The problems

    2. 3-D surfaces or 4-surfaces associated to them by holography replace point-like particles

    3. WCW Kähler geometry as s geometrization of the entire quantum physics

    4. Quantum physics as physics of free, classical spinor fields in WCW

    5. Dirac equation for WCW spinor fields

    6. M>8-H duality at the level of WCW