In what follows, J&J and Astrazeneca are considered identical. The eventual explanation may fork into separate ones for each vaccine, but nothing’s showing now.

Let’s define some terms. The scientific method names two classes of explanation:

• Theory –an explanation that has a test, and can be proven false.
• Hypothesis — a good idea, with clues that point in a direction, with plenty of imagined glue to tie it together.

(BioSpace) COVID-19 Brief: Theories on the COVID-19 Blood Clotting and More Top Stories blurbs an incomplete theory, first described for  AstraZeneca  in this paper: Thrombosis and Thrombocytopenia after ChAdOx1 nCoV-19 Vaccination. It’s  better than a hypothesis but not a complete explanation either. Quoting from the blurb:

The leading theory appears to be an unusual and rare immune response similar to heparin-induced thrombocytopenia (HIT), where the immune system makes antibodies to a complex of heparin and a protein known as platelet factor 4 (PF4). This causes platelets to form dangerous clots throughout the body. Some research has found that patients with clots had antibodies to PF4.

Antibodies were observed. They were created by the immune system in response to antigen which mimics portions of PF4 with pathological features. This antigen remains unidentified.

It was almost a complete theory. If part of the spike antigen made by these vaccines were shown to be the antigen by cross-reaction with PF4, it would be complete. An unreviewed preprint with good methodology, (ResearchSquare, pdf) Anti-SARS-CoV-2 Spike Protein and Anti-Platelet Factor 4 Antibody Responses Induced by COVID-19 Disease and ChAdOx1 nCov-19 vaccination, shows that it does not cross-react.

So to be complete,  this “leading theory” requires that some other antigen, made by some other action of the vaccine, reacts with PF4. The BioSpace blurb offers this:

A research team out of the University of Griefswal…Their theory is that there are about 50 billion virus particles in each dose of the vaccine, and some might break apart and release their DNA. Like heparin, DNA has a negative charge that might help bind it to PF4, which has a positive charge. That bound complex might trigger antibodies’ production, which could signal the body to increase blood coagulation.

This is not a theory. It’s a completely legitimate hypothesis.  To describe it as a theory in a specialty website does no service to the subject. It erodes clear thinking.

Next: A few more hypotheses, which you may elaborate with your own imaginative, well-founded logic.