Introduction

1. First series of questions

2. Second series of questions

3. The notion of elementary particle vacuum functional

Identification of elementary particles

1. Elementary fermions and bosons

2. Graviton and other stringy states

3. Spectrum of non-stringy states

Basic facts about Riemann surfaces

1. Mapping class group

2. Teichmueller parameters

3. Hyper-ellipticity

4. Theta functions

Elementary particle vacuum functionals

1. Extended Diff invariance and Lorentz invariance

2. Conformal invariance

3. Diff invariance

4. Cluster decomposition property

5. Finiteness requirement

6. Stability against the decay g --> g₁+g₂

7. Stability against the decay g --> g-1

8. Continuation of the vacuum functionals to higher genus topologies

Explanations for the absence of the g>2 elementary particles from spectrum

1. Hyper-ellipticity implies the separation of g≤ 2 and g>2 sectors to separate worlds

2. What about g> 2 vacuum functionals which do not vanish for hyper-elliptic surfaces?

3. Should higher elementary particle families be heavy?

4. Could higher genera have interpretation as many-particle states?

5. The newest piece to the TGD inspired model of family replication

Elementary particle vacuum functionals for dark matter

1. Hurwitz zetas cannot correspond to dark matter in TGD sense

2. ζ_H(s,1/2)$ inspires an explanation for why the number of fermion generations is three

3. About Hurwitz zetas