Introduction
Hyper-octonions and hyper-quaternions
Number theoretical compactification and M8-H duality
Romantic stuff
Notations
Quaternion and octonion structures and their hyper counterparts
Octonions and quaternions
Hyper-octonions and hyper-quaternions
Basic constraints
How to define hyper-quaternionic and hyper-octonionic structures?
How to end up to quantum TGD from number theory?
p-Adic length scale hypothesis and quaternionic and hyper-quaternionic primes
Quantum TGD in nutshell
Geometric ideas
The notions of imbedding space, 3-surface, and configuration space
The construction of M-matrix
Number theoretic compactification and M8-H duality
Basic idea behind M8-M4× CP2 duality
Hyper-octonionic Pauli "matrices" and the definition of associativity
Are Kähler and spinor structures necessary in M8?
How could one solve associativity/co-associativity conditions?
Quaternionicity at the level of imbedding space quantum numbers
Questions
Summary
Octo-twistors and twistor space
Two manners to twistorialize imbedding space
Octotwistorialization of M8
Octonionicity, SO(1,7), G2, and non-associative Malcev group
Octonionic spinors in M8 and real complexified-quaternionic spinors in H?
What the replacement of SO(7,1) sigma matrices with octonionic sigma matrices could mean?
About the twistorial description of light-likeness in 8-D sense using octonionic spinors
An attempt to understand preferred extremals of Kähler action
What "preferred" could mean?
Basic ideas about preferred extremals
What could be the construction recipe for the preferred extremals assuming CP2= CP2mod?
In what sense TGD could be an integrable theory?
What integrable theories are?
Why TGD could be integrable theory in some sense?
Questions
Could TGD be an integrable theory?
Could quaternion analyticity make sense for the preferred extremals?
Are Euclidian regions of preferred extremals quaternion-Kähler manifolds?
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