Can a writing instrument affect problem solving ability?

Background story

After years of studying math auto-didactically, with artefacts shared in my previous linkedin posts, I decided it was time to start 'phase 3' of my mathematical adventure. The topic of this adventure is that I have, in 'phase 2', explored and demystified every single element that itched me about mathematics during 'phase 0', which is described here: https://sites.google.com/site/77neuronsprojectperelman/jad/theplan.

Phase 2 was a long undertaking. It spanned a wide range of topics all the way from the top of differential geometry, down to mathematical logic, not ignoring computability.

The 1269-entry long literature collection I visited during this phase is shared here: https://github.com/jadnohra/tag_export

Phase 3

Phase 3 is about filling all the gaps present in my swiss-chees-like (even if comprehensive) knowledge of mathematics. In particular, a thorough focus on proving. I had attempted 'cracking' mathematical proving several times, with several strange and less-strange methods before with not much success.

But the concentrated learning of mathematical, formal and symbolic logic allowed me to see why these attempts were doomed to fail. I decided that the best way to execute phase 3 is to enroll for a master's degree in mathematics. Luckily, I found Emporia State University to be a serious university that offered such a degree by distance education. Looking at the curriculum, I expected to be able to use my years of studying such that the time spent mostly goes into polishing and solidifying. If this turned out to be true, it would validate my belief of having demystified all itchy spots.

Writing Instrument

I am now preparing for the final exam of the first course. It is a proof writing course which hijacks a basic topology course for material. My grade so far is 99%. Given this is working as expected, I do spend time polishing my thinking about proof writing. Within this activity, I think I stumbled upon a strange phenomenon. Some months ago, I was working on fixing my handwriting. This included trying many kinds of pens and pencils. After passing through a stage of using a a calligraphic pen (Tombow WS-BH 150), also using it for solving the exercises of the math course. I slowly moved back to the much finely pointed Staedler triplus fineliner.

Looking back, my handwriting has degraded again, but I have produced lots of proofs in the meantime. Having a bit of time, I decided to pickup the Tombow again. Doing this today, I had the feeling that it deteriorated my ability to think. Seeing my proof develop with this thick point made me feel clumsy, and lacking oversight of the proof's structure. Maybe it is because I could see more of the proof at once when it took a smaller area on paper. On the other hand, maybe it is simply habit. All mathematics I did in the previous phases were written using a 0.7, then 0.5, then 0.3 mechanical pencil in that order, and that's half a decade of doing that.

I will be researching this, but if anyone has any ideas, explanations, or similar experiences, I would very much like to discuss them!