Physicist here. I don’t buy some of these distinctions, like the chirality. Chirality is an observable, it’s like saying there are two photons because they can come in two polarizations, but polarization is not an inherent property: it depends on how we measure it. So I could describe any photon in the left/right chiral basis just as well as in the vertical/horizontal basis or any two antipodal points in the Poincaré sphere, so which is the “right one”? Neither. Spin on the other hand (which is where polarization comes from) is well-defined for any photon and it’s always 1 (the astute reader will wonder why the projection of spin 1 does not take 3 eigenvalues 1,0,-1 and it’s because photons are massless so the 0 projection never occurs because there is no rest frame for massless particles).

I'm not a physicist (so take this with a grain of salt) but I have spent a lot of time trying to find an answer to this question. If you interpret the physics before Spontaneous Symmetry Breaking as more fundamental, and you treat the antimatter fields as distinct, then I think you can reasonably claim that there are 30 fundamental fermion fields. Specifically, in each of the 3 generations, you have:

1. The left-handed lepton doublet field, and the antimatter equivalent. 2. The left-handed quark doublet field, and the antimatter equivalent. 3. The right-handed electron singlet field, and the antimatter equivalent. 4. The right-handed up-quark singlet field, and the antimatter equivalent. 5. The right-handed down-quark singlet field, and the antimatter equivalent.

The bosons are more confusing to me, but I think a reasonable person might say that there are 16 fundamental boson fields:

1. The four scalar boson fields. 2. The eight gluon fields. 3. The three W boson fields. 4. The B boson field.

The B boson couples to every fermion (via hypercharge), while gluons only couple to quarks (via color) and W bosons only couple to the doublets (via weak isospin).

I feel like you ought to be go lower than 17, down to 9, by not counting the 3 generations of fermions as distinct (so you've just got up-type quark, down-type quark, electron-type particle, and neutrino). After all, if they can mix with one another, should they really be considered entirely different particles?

There are also 17 wallpaper groups. That always seemed like a funny number. I know it's a long shot, but is there a relation?

Not being a Physicist, I have to wonder if all these particles are somehow manifestations of a simpler thing.

Might there have been a point in time (long ago) where the “wave photon” and the “particle photon” seemed like possibly different things?

1

As usual, the hard problem is how you define "Elementary" which is why the posters always show 17, and then you get numbers that go as high as 995.5 (and the .5 is an interesting result as well).

going in the opposite direction, as few as two

https://en.wikipedia.org/wiki/Preon

Some powerof two many actual states + a fractal deterministic random generator for particle Explorers?

D

The answer is 42.

There are no particles. Everything is a wave.

The Everything-Is-a-Quantum-Wave Interpretation of Quantum Physics

https://www.mdpi.com/2624-960X/5/2/31

Stopped reading after "Yet in the mathematical equations that define the Standard Model, the eight gluons are distinct from one another in the same way that the W and Z bosons differ."

W and Z bosons, photons, etc have fixed masses, charges, interaction strengths with other particles. These properties can exactly be listed and looked up in a table of elementary particles with discrete rows.

Gluon color is continuous property in a vector space. Gluons can have any color in that space, with any combination of the 8 basis vectors (and that choice of basis is also completely arbitrary). The color |g1> is no more valid than the color (|g1> + |g2> + |g8> / √3) or any other of infinite combinations.

Calling this "8 gluons" is like saying there's "3 photons" because they can have momentum in 3 dimensions. If you want to argue there's infinite kinds of gluons, go ahead, but there aren't 8.