While I am willing to entertain arguments and evidence to the contrary, I very strongly doubt that any of the following (which are common components of beyond the Standard Model theories except the last which is part of "core theory") are true (some of which are redundant):
1. The PMNS matrix has more than four parameters or does not imply percentages that add to 100%.
2. Sterile neutrinos that oscillate with active neutrinos exist.
3. There are right handed neutrinos and left handed anti-neutrinos.*
4. Neutrinos have Majorana mass.*
5. A seesaw mechanism gives rise to neutrino mass.*
6. Neutrinoless double beta decay is possible in a manner that does not conserve lepton number.
7. Proton decay occurs.
8. There are tree level flavor changing neutral currents.
9. Lepton number is not conserved or baryon number is not conserved outside sphaleron interactions.
10. The baryon number of the universe at t=0 plus an infinitesimal amount was 0.
11. The lepton number of the universe at t=0 plus an infinitesimal amount was 0.
12. The baryon number of the universe minus the lepton number of the universe at t=0 plus an infinitesimal amount was 0.
13. Dark matter particles (other than gravitons) exist.
14. Axions exist.
15. Supersymmetric particles exist.
16. There is a fourth generation of Standard Model fermions.
17. There are pseudo-scalar, charged or different mass scalar Higgs bosons.**
18. There are fundamental fermions other than those identified in the Standard Model below the GUT scale.**
19. There are fundamental bosons not identified in the Standard Model below the GUT scale, other than gravitons and possibly one or two bosons related to neutrino mass and/or neutrino oscillation.**
20. CPT symmetry is violated under any circumstances.
21. There are any interactions involving massless carrier bosons that show CP violation.
22. There are any massless particles that interact via the weak force.
23. There are any massive particles that do not interact via the weak force.
24. There are any neutrinos with zero mass.
25. There are massless fundamental fermions.
26. Thera are leptoquarks.
27. There are tachyons.
28. Negative mass exists.
29. There are more than four dimensions of space-time, either large or tiny.***
30. Mass-energy conversation is violated locally at t=0 plus an infinitesimal amount.
31. The topology of space-time is sufficiently warped or non-local to give rise to traversable worm-holes.****
31. Fundamental physical constants vary in space-time for any reason other than energy-scale.
32. Gravitons that have non-zero rest mass exist.
33. The actual physical value of muon g-2 differs from the correctly calculated value under the Standard Model.
34. The neutron lifetime discrepancy is anything other than measurement error or a theoretical error.
35. The muonic hydrogen radius discrepancy is anything other than measurement error or a theoretical error.
37. The CKM matrix has more than four parameters or does not imply percentages that add to 100%.
38. It is possible for anything resembling life as we know it to enter a black hole without dying.
39. The observed Higgs boson has properties different from those that the Standard Model Higgs boson is predicted to have at its experimentally observed mass.**
40. Gravity behaves exactly as predicted in classical General Relativity (as applied today) in all circumstances without modification even in the extremely weak field limit.
I doubt that any of the following (which are common components of beyond the Standard Model theories) are true (some of which are redundant), but far less intensely:
1. It is impossible to derive any of the experimentally determined physical constants of the Standard Model from a deeper theory.
2. The sum of the square of the fundamental particle masses does not when evaluated at some proper energy scale such as pole masses or the Higgs vev, equal the square of the Higgs vev.
3. The probability of a transition from a first generation fermion to a third generation fermion in the CKM matrix is ever not equal to product of the probability of a transition from a first generation fermion to a possible second generation fermion and to the probability of a transition from that possible second generation fermion to a third generation fermion.
4. There are violations of lepton universality significantly greater than the square root of the ratio of the neutrino masses to the charged lepton masses.
5. Koide's rule for charged leptons is inaccurate by significantly greater than the square root of the ratio of the neutrino masses to the charged lepton masses.
6. The reason that Koide's rule works for charged leptons cannot be generalized in some manner to explain the quark and neutrino masses.
7. The differences in mass between the charged leptons and the neutrinos is unrelated to the relative strengths of the electromagnetic coupling constant and the weak force coupling constant.
8. The neutrinos have an inverse mass hierarchy.
9. The lightest neutrino mass is as large as the difference between the lightest and second lightest neutrino mass.
10. The net electric charge of the universe is non-zero.
11. Sphaleron interactions actually occur physically.
12. There is a multiverse other than an anti-universe at times before the Big Bang.
13. Cosmological inflation occurred.
14. The temperature of the Big Bang was not finite.
15. The temperature of the Big Bang can be exceeded in the universe at latter times.
16. There are (or were) primordial black holes for more than an instant.
17. There are substances in the universe with greater density than the most dense possible neutron star or the smallest possible stellar black hole.
18. Dark energy is a non-Standard Model substance of some kind (other than a gravity modification).
19. Massless gravitons do not exist.
20. Gravitational energy cannot be localized.
21. There are ever violations of mass-energy conservation involving gravity.
22. General relativity correctly models the self-interactions of gravitons.
23. The strong equivalence principle is not violated by an external field effect.
24. Lorenz violation is possible in detectable amounts for long distances (e.g. kilometers or more) in a time period comparable to the age of the universe.
25. Free glueballs (i.e confined composite structures made purely of gluons) exist.
At some point, I may want to make an additional list of the beyond the Standard Model physics theories which I do believe are possible given these constraints. But, not today.
I believe that these principles would be a better and more fruitful guiding force for hypothesis generation in theoretical physics than many of those those commonly in use today such as (1) "naturalness", (2) the "hierarchy problem", (3) the "strong CP problem", (4) the hypothesis that at at t=0 plus an infinitesimal amount the aggregate baryon number of the universe was zero and the aggregate lepton number of the universe was zero, (5) the anthropic principle, and (6) multiverse reasoning.
Footnotes and Clarifications
* To be clear, I don't claim to have the answer to the source of neutrino mass, I simply think that all of the above statements are not true and that some other mechanism than those set forth is the actual source of neutrino mass.
** This is subject to the caveat that there could be more fundamental fermions or bosons that can only combined to, or interact to give rise to dynamically, the Standard Model particles. For example, I do not rule out the possibility that the Higgs boson is a composite particle made up of a W+ boson, a W- boson, a Z boson and a photon, or that all Standard Model fundamental particles are vibration modes of a fundamental string.
*** Dimensionality might, however, be an emergent property of space-time and not fundamental.
**** I do not rule out the possibility that there are microscopic non-local connections at approximately the Planck length scale that could connection to profoundly distant points in space-time that are not traversable.