ORIGINAL:
Links: the pictures are for those interested but short of the 10K threshold.
interesting how the deleted posts appear as https: and so on, while the undeleted appear as an underlined question title.
https://mathoverflow.net/questions/353146/does-this-inequality-on-these-symmetric-matrices-hold
https://math.stackexchange.com/questions/3553446/in-this-always-true
https://math.stackexchange.com/questions/3557059/would-this-inequality-be-true
https://math.stackexchange.com/questions/3558299/is-this-on-symmetric-matrix-true
https://math.stackexchange.com/questions/3559339/does-this-hold-or-not
https://mathoverflow.net/questions/354446/any-counter-example-matrix
https://math.stackexchange.com/questions/3590234/on-matrix-with-det-0 The current version of the question is still open, as I write this. I now think this is a single OP crowdsourcing, well, something. There may or may not be a visible programming contest involved.