Determining Your "Magnus Number"

In maths, a researcher’s Erdos Number refers to the minimum number of shared coauthors needed to reach a joint paper with the beloved and prolific Paul Erdos. For example, my favorite professor as an undergrad was pretty proud to have an Erdos number of two—his PhD advisor wrote a joint paper with Erdos. Similar concepts have been extended to other disciplines as well (the six degrees of Kevin Bacon comes to mind).

Now chess is not transitive, but it is still an interesting question: what is the minimum number of connections needed for me to have beaten somebody who beat somebody who beat somebody….who beat the current World Champion (in any time format or venue). It should be noted that Carlsen does not frequently play on Chess.com given that he created his own platform Chess24, so I aim to show a connection to GM’s on chess.com who have beaten him in over the board play.

I am not sure of an efficient way to look at this question with the chess.com API, but to get a proof of concept, I just looked at my wins against masters (of which there are not many), by sorting my archive. From there my plan was just to keep searching on each players top rated victory.

Now I didn’t exactly pour through the possibilities, but at the very least I was able to find a four-path (see edit below-- 3-path found!): it turns out I was able to swindle a National Master from Boston, who in turn has beaten Ukrainian International Master Maly Alexey, who in turn has beaten Russian Grandmaster Vladamir Fedoseev, who himself has beaten Magnus Carlsen (in an OTB game). I would not be too surprised if my “Magnus Number” was actually 3 somehow, especially when considering other platforms that people play on. For example, the NM I beat also beat IM Mykola Bortnyk, who has beaten the top ranked player on chess.com, GM Hikaru Nakamura. That being said I am just about certain it is no lower than 3.

Below are the connections. Can anybody post a lower number? What do you think the minimum number of connections is for an arbitrary player (with say over 500 wins on chess.com) to be guaranteed a connection with Carlsen? My guess is 7, and I would be surprised if it was lower than 6.

Edit 9/2: Thanks to this tool https://sixdegreesofhikaru.com/ I found that I have a shorter path. I have beaten @OolonColluphid a player who has just rated 1320 when they beat Nakamura in a blitz game! Here is a link to their win: https://www.chess.com/game/live/3750068104?username=ooloncolluphid And here is a link to my win: https://www.chess.com/game/live/3950169421