I would argue that the whole concept of a "jump" is contrary to the need of quantitative evidence.
The idea that everything needs to be proven with evidence is what an LLM excels at. If you give it a task such as "analyze this massive dataset and demonstrate that is proves or disproves this concept" or "find a counter argument to this theory", it will dutifully run through the information and give an answer. If you give it the task of "invent a new style of music", it will do poorly.
It will not do poorly from of lack of ability, nor lack of originality, it will do poorly as "style of music" is a human concept, "new" is a human concept and "invent" is a human concept. Being human concepts, these are things without quantitative value. There is no truth or certainty to what is "invented", as others may call it "discovered" or "developed" (developed in the sense of progressing from a previous work). While a trained ear my call a song "Breakcore" and not "Gabber", another would clump it into "EDM".
The only solution to this is to have human origin. As humans will tell the tale of how an idea came about, inspiring similar thought patterns in peers and earning the title of "new". This to me seems to happen more often with art than science or engineering. Although, it is hard to tell if it is due to increased creativity, or ability to convey thoughts.
All of this is impossible for a non-human to do, as they will give evidence to support the conclusion rather than the tale. This will turn into a possible addition to the knowledge of humanity, but can never earn acceptance as a "jump", as humans care little for evidence. Humans are inherently social beings and, as a side effect, will never acknowledge a non-human contribution.
An easy way to put this is a literal jump. The humans at Merriam-Webster define it in part as "to spring into the air". However, a quick peruse of the comments on a video about the "World's Highest Jumping Robot" will find disagreements about the definition of "jumping" and "robot". The device does spring into the air, but it does so without human legs, human movement, or human consideration for safety. Should you instead look at a video on the highest jumping bipedal robot, you will instead find nearly full acceptance that what happened was a "jump" (it should be noted that there is much disagreement in comments about if such videos are AI generated). By my understanding of the world, this is due to human ability to excite brain paths of an action when viewing another entity preforming the action. So if the viewer's brain does not fire the signal of a jump motion happening, the viewer will seek any rationale to explain the action as not being a jump.
TL;DR: It is all based on vibes, and LLMs give the wrong vibe.