What does الحج سهر معلومات mean?

What is your justification for reading this verse: الحج سهر معلومات As الحج أشهر معلومات When الحج إشهار معلومات is perfectly consistent with what the word “حج” means in every other instance it is used in The Quran. In fact, this is the verse that defines it as the meaning we give it everywhere else in The Quran. If you, for whatever reason, can justify why أشهر is the plural of of شهر “month” despite the 8:36 verse:

إن عدة الشهور عند الله إثنا عشر شهرا

Which you interpret as:
The number of months according to God is twelve months. Which would make شهور the plural of months not أشهر like we see in 2:197, and somehow also justify معلومات to mean “known” months, not INFORMATION, then you have no justification for what حج means for all the other times you interpret as “proof”. Besides, why would God say “The Hajj is known months” instead of telling us what these months are?? How are they known!??

And what reasoning can you provide not to interpret Hajj to mean “the unveiling/revealing of information” as in to make information known publicaly. Making معلومات consistent with its root word علم meaning knowledge, so “bits of knowledge” or “information” as we would say today. And just like a famous person is مشهور because he’s well know to the public. Or when use the verb form like it’s found in the verse when we say an angry animal “showed” teeth or a warrior “unsheathed” his sword. And as an added bonus, remove the “mystery” surrounding what “The Hajj Al-akabar” means which becomes simply “The Great Proof” or “Proving” since the Arabic version refers to the process of conducting a proof of something.