Introduction
Basic notions of HFFs from TGD perspective
Bird's eye view of HFFs in TGD
M^{8}-H duality and HFFS
Infinite primes
Basic notions related to hyperfinite factors of type II_{1} from TGD point of view
Basic concepts related to von Neumann algebras
Standard construction for the hierarchy of HFFs
Classification of inclusions of HFFs using extended ADE diagrams
TGD and hyperfinite factors of type II_{1}: a bird's eye of view
Identification of HFFs in the TGD framework
Could the notion of free probability be relevant in TGD?
Some objections against HFFs
M^{8}-H duality and HFFs
Number theoretical level: M^{8} picture
Geometric level: H picture
Wild speculations about McKay correspondence
About the selection of the action defining the Kähler function of the "world of classical worlds" (WCW)
Could twistor lift fix the choice of the action uniquely?
Two paradoxes
About the TGD based notions of mass, of twistors and hyperbolic counterpart of Fermi torus
Conformal confinement
About the notion of twistor space
About the analogies of Fermi torus and Fermi surface in H^{3}
The notion of generalized integer
The first reactions to the abstract
Fundamental discretization as a cognitive representation?
Infinite primes as a basic mathematical building block
Construction of infinite primes
Questions about infinite primes
P=Q hypothesis
Summary of the proposed big picture
The relation between M^{8}-H and M-M' dualities
Basic mathematical building blocks
Basic algebraic structures at number theoretic side
Basic algebraic structures at the geometric side
Appendix: The reduction of quantum TGD to WCW geometry and spinor structure
The problems
3-D surfaces or 4-surfaces associated to them by holography replace point-like particles
WCW Kähler geometry as s geometrization of the entire quantum physics
Quantum physics as physics of free, classical spinor fields in WCW
Dirac equation for WCW spinor fields
M^{>8}-H duality at the level of WCW