In reality, these are just are opinions you and I have. We'll find out in the next 18 months what the fate (and the value) of Yahoo is.

It's not an opinion that $4.8 billion in sales and one of the largest Web properties, is worth more than zero. That's easily backed up by comps such as AOL, Yahoo's nearly 20 years of being public along with how the markets treated it, and how they were valued prior to the Alibaba stake becoming valuable (hint: they never received a negative valuation, even in the absolute worst of times post dotcom bubble when their business was falling apart rapidly).

Fair value on stand-alone Yahoo is a lot closer to $5 to $10 billion than not. Verizon just paid $4.4 billion for AOL, which has a fraction of the business that Yahoo does.

I could claim that Microsoft being worth more than $1 is merely an opinion. Does that mean Microsoft's market value is subject to such whims? No, there's a vast historical basis to go on, and a well understood approach for valuing such companies and their businesses. The opinion of Microsoft being only worth $1 is wrong, and easily proven so. The same is true regarding Yahoo's core business being worthless, and for the same conceptual reasons. The only valid room for opinion in the matter, is in how much it's worth. Anything else has no historical example to back it up (there is not a single example in modern history of a public corporation of Yahoo's sales size, with a positive balance sheet and earnings, that isn't collapsing due to some scandal, that is worth less than zero; not one example exists).

Well you should buy some shares because Wall Street currently think Core Yahoo is worthless.

That's incorrect. Wall Street thinks the Alibaba stake, Yahoo Japan stake and its cash holdings are worth less than their face value - as is always the case (see: how EMC's VMWare stake has always been discounted historically). For numerous reasons, the most obvious of which is: investors can never realize the entire face value of those holdings, so they never give a $1 to $1 value to them.

We can simplify this really fast: give me one example of a public company of even remotely similar financials trading with a negative market cap in the last ~30 years in the US equity markets.

Tons always have. Look up the valuation of Macy's real estate; it is about 2x the market cap. Even adjusting for the full EV value its at a discount. They would realize more value by shutting down the retail business and selling off the real estate. But investors feel the chances of that happening are slim to none which leads to the low valuation. Yahoo is a tech company but revenue, growth rates, net income and free cash flow are common to all companies.