Introduction

1. Polynomials defining elliptic surfaces in finite fields and modular forms in hyperbolic plane

2. Galois group, dual group and number theoretic LC

3. LC and TGD

Number theoretic LC and TGD

1. How could the number theoretic LC relate to TGD?

2. How to identify the Galois group in the number theoretic picture?

3. Objections

Geometric LC and TGD

1. Space-time surfaces as numbers

2. About various passive symmetries

3. How to define the geometric analogs for rationals and their extensions?

4. How could various effective Planck constants emerge?

5. The counterpart of the Galois group in the geometric LC

6. The identification of the geometric Langlands group

7. Master formula for the construction of quantum states using the interpretation of space-time surfaces as numbers

About the relationship between geometric and number theoretic counterparts of WCW

1. Does number theoretic discretization mapping real WCW to its real counterpart involve canonical identification?

2. The relationship between K\"ahler function and discriminant

3. The notion of spin glass energy landscape

4. How do the coupling parameters  emerge in the transition from the number theoretical discretization  to the  QFT limit?

Space-time surfaces as numbers viz. Turing and Gödel

1. The replacement of the static universe with a Universe continuously recreating itself

2. A generalization of the number concept

3. Could space-time surfaces replaced as integers replace ordinary integers in computationalism?

4. Adeles and Gödel numbering

5. Numbering of theorems by space-time surfaces?

6. The physical interpretation for the arithmetics of space-time surfaces