>But I'm asking you about the proof of the labor theory of value in fact. I didn't thought that there exist people who take it seriously after marginal revolution.
The proof is "in the pudding" as it were; there are a few theorists (either heterodox economists or philosophers of economics) who argue that Marx himself did enough to "prove" the theory, either logical-deductively, or otherwise; see Elena Lange[0], Patrick Murray[1], Guido Starosta[2], Andrew Kliman[3], Chris Arthur[4] and a few others - though they approach the matter from different angles. Martha Campbell defends the objectivity of value in capitalist society as opposed to marginalist accounts and Veblen's "habitual action" account[5]. In general, those that hold to Marx's exposition with the "third thing" argument argue that the theory cannot apply to each commodity individually, though it would apply to an aliquot as taken as a sample of the lot of them.
>Business shows exactly the opposite, the most risky (volatile) domains have the highest gains and highest losses: pharma, construction, fintech.
These are not businesses, but fields of businesses, within them it is possible to find the greatest variation in risk. It is also not clear whether the risk is taken by the owner of the capital, or by the labourers themselves - in construction, a major risk falls on the safety of the workers. To say that they have the highest gains and the highest losses implies risk is a mere tautology (of course! that's what risk means, you win big or you lose big), but it says nothing about profitability.
>When you pay for a Intel x86 processor, you also pay for failed Intel iAPX 432 which never appeared in the market.
Again, offsetting the effects of failed developments and theft is what capitalists do with profit, it is not an explanation as to the origin of profit.
>Goods have value, labor has value as a good evaluated by an employer, but it does not "create value".
What you're saying is absolutely true, but it's an equivocation on "value". When you speak of the value to someone, from someone's perspective, that's not what Marx means by "value". Marginalist accounts of value are semi-compatible with the labour theory of value, so long as we're talking about different things when we say "value"; for example, it's clear that what the LTV means by "value" is not "artistic value" or "moral value" or any of a huge range of values. In the same way, it does not mean value as a subjective preference for one thing over another. That concept gets a look-in with the Marxist concept of use-value - but not exchange-value.
>If you make a chair, you apply labor, but if nobody values it and nobody buys it, it has no value, hence your labor has no value.
Only use-values count as values, because according to Marx, a commodity is a complex of a use-value and value (expressed in a given magnitude of exchange-value). Therefore it's meaningless to talk of something usunable and undesirable as having value. Even Ricardo knew this was the case. Wine is a more interesting matter; depending on how one looks at it, either the very act of storage is (objectively) highly valued, or the good is not entirely freely reproducible (i.e my wine aged for ten years will never sell as well as a brand name aged for five years), or along with Murray, the theory does not apply to this individual commodity, but if you were to take a sample of all capitalist commodities, you'd find that the identity of total value = total price holds in aggregate.
> They sell chairs for $1, which share of this $1 each of than created? How to measure that objectively?
There is no way to determine that; it is just as impossible as quantitatively determining "utility". Value is not sensible, it is a socially-determined supersensible aspect of commodities. In other words, the essence behind the appearance. See Murray on the neoclassical focus on capital's shadow forms[6]. In the same way, measuring skilled versus unskilled labour may not be possible quantitatively, but it clearly happens qualitatively - what the market rewards in wages on average to two groups of people with different skill sets means the abstraction and calculation is already quantitatively done for us in the real world. This is exactly the same with the neoclassical concept of utility, in which we can actually see prices, but not a drop of utility, no matter how we twist and turn an object.
[0] http://www.consecutio.org/2018/11/the-proof-is-in-the-puddin...
[1] https://philpapers.org/rec/PATIDO-2
[2] https://cicpint.org/wp-content/uploads/2017/03/2008_Starosta...
[3] Kliman, A. 2008. The Fourth Thing on the Third Thing: A response to James Furner and Patrick Murray.
[4] Arthur, Christopher J Source: Capital & Class 15-39 no. 73 (Spring 2001): p. 15-39 https://libcom.org/library/value-labour-negativity-christoph...
[5] Campbell M. (2004) The Objectivity of Value versus the Idea of Habitual Action. In: Bellofiore R., Taylor N. (eds) The Constitution of Capital.
[6] http://crisiscritique.org/political11/Dennis%20Badeen%20and%...