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Abstract
Unified Number Theoretical Vision
Introduction
Number theoretic compactification and M^{8}H duality
Basic idea behind M^{8}M^{4}× CP_{2} duality
Hyperoctonionic Pauli "matrices"
Are Kähler and spinor structures necessary in M^{8}?
How could one solve associativity/coassociativity conditions?
Quaternionicity at the level of imbedding space quantum numbers
Questions
Summary
Quaternions and TGD
Are Euclidian Regions Of Preferred Extremals Quaternion Kähler Manifolds?
The Notion of Quaternion Analyticity
Are Preferred Extremals QuaternionAnalytic in Some Sense?
Octotwistors and twistor space
Two manners to twistorialize imbedding space
Octotwistorialization of M^{8}
Octonionicity, SO(1, 7), G_{2}, and nonassociative Malcev group
Octonionic spinors in M^{8} and real complexifiedquaternionic spinors in H?
What the replacement of SO(7, 1) sigma matrices with octonionic sigma matrices could mean?
About the twistorial description of lightlikeness in 8D sense using octonionic spinors
How preferred padic primes could be determined?
Earlier attempts
Could preferred primes characterize algebraic extensions of rationals?
A connection with Langlands program?
A connection with infinite primes?
More about physical interpretation of algebraic extensions of rationals
Some basic notions
How new degrees of freedom emerge for ramified primes?
About the physical interpretation of the parameters characterizing algebraic extension of rationals in TGD framework
pAdicization and adelic physics
Challenges
NTU and the correspondence between real and padic physics
NTU at spacetime level
NTU and WCW
Breaking of NTU at the level of scattering amplitudes
NTU and the spectrum of Kähler coupling strength
Generalization of Riemann zeta to Dedekind zeta and adelic physics
Other applications of NTU
Going to the roots of padicity
What could be the role of complexity theory in TGD?
Basic notions of chaos theory
How to assign chaos/complexity theory with TGD?
Why the nontrivial zeros of Riemann zeta should reside at critical line?
What is the origin of the troublesome 1/2 in nontrivial zeros of zeta?
Relation to number theoretical universality and existence of WCW
Why Mersenne primes are so special?
How to achieve stability against state function reductions?
How to realize M_{k}=2^{k}1dimensional Hilbert space physically?
Why Mersenne primes would be so special?
Number Theoretical Feats and TGD Inspired Theory of Consciousness
How Ramanujan did it?
Symplectic QFT, 3, 4, and 5 as Additive Primes, and Arithmetic Consciousness
pAdicizable discrete variants of classical Lie groups and coset spaces in TGD framework
pAdic variants of causal diamonds
Construction for SU(2), SU(3), and classical Lie groups
Abelian class field theory and TGD
Adeles and ideles
Questions about adeles, ideles and quantum TGD
