openid connect – Should we include the “at_hash” (access token hash) claim in the id token of the authorization response when the response type is “code id_token”?

Should we include the “at_hash” (access token hash) claim in the id token when the response type is “code id_token”? According to this article by Takahiko Kawasaki, when the response type is “code id_token” an access token should not be returned from the authorization server. As I understand it, if a token is not returned, an “at_hash” should not be present in the id_token. Is my understanding correct?

Also in this OpenID specification description I cannot get a full understanding on whether we should or should not include the “at_hash” in the id_token of the authorization response when the response type is “code id_token”.

calculus – Is this claim true about the probability that \$;cos x;\$ is positive for a randomly chosen value of \$x\$?

Is is correct that the probability that the function $$;cos x;$$
for a randomly chosen value of $$xin(0,infty)$$ is positive (or negative) is equal to $$frac 12$$?

If the above claim is correct, can we say something similar about the probability that the function $$;cos (ax)+2cos (b x);$$ with $$frac ab notinmathbb{Q}$$ is positive (or negative) for a randomly chosen value of $$xin(0,infty)$$?

Why color-wheel websites (Adobe…) claim these colors are complementary

I just learn about the different color harmony styles models, and I was playing with Adobe color wheel website using the complementary style, but I’m realizing that the proposed colors are not really on the other side of the Hue circle:

Here, you see that the blueish line has hue 174° and the brown color has hue 19°, and 174°-19°=155°, while I would expect their distance to be 180° since they are complementary. And if I ask to Krita, they are indeed not on opposite parts of the Hue circle:

So what’s wrong with Adobe color wheel? I also tried with https://paletton.com, and the Paletton gives similar results compared to Adobe color. Are all color wheels crazy, or am I missing something? I also tried to check how footage was behaving, and they seem to agree with my definition, for instance this photo uses colors #27AB9E (Hue=174°) and #ff4473 (hue=344°), which are much more aligned, and we have 344-174 = 170° which is way closer to 180°.

security – Why do people claim that governments cannot confiscate Bitcoins?

Let’s say that I have taken the utmost precautions, fit only for a computer nerd like myself — definitely not the average person. I’ve used Bitcoin Core on a dedicated, secure computer and created an encrypted wallet.dat, then put that on a series of self-encrypted USB sticks/hard disks, storing them around my house and in my fireproof safe. The decryption phrases are very strong and I haven’t stored them anywhere on paper or on physical metal thingies that can be seized. (It’s all in my head or in a series of text documents on encrypted disks which only I know how to get to.)

What does that help me if the government comes with their cops and beat me up until I decrypt the devices and wallets? Or even “just” lock me up until I do so, without physically hurting me? I was once held hostage by them for only 24 hours, and it felt like 24 years. It was a living nightmare. I would never be able to endure that perpetually, and who knows what they actually do to my devices while I’m in there? They might decide to destroy them if I never tell them how to get to them, thus making them gone for me as well.

Maybe your answer will be that they cannot know about all my copies, if perhaps I have hidden one USB stick inside a wall or dug it down at a specific tree in the woods which only I know about. Sure. That’s a good argument. But still, if they physically beat me up, or otherwise know that I have the coins and just won’t let me go until I give it to them, how am I going to get out of that? You think that BS about having had a “boating accident” works in the real world? Nobody who goes through this kind of trouble would actually lose their coins in some “accident”. They are not stupid.

You don’t need to bring up seed phrases. For one thing, I don’t have any such, but even if I did, I could never memorize all that in my head, and I doubt that almost anyone who claims to have memorized theirs will ever be able to get their coins back when “it all hits the fan”. Also, they probably will have the seed phrase backed up somewhere, such as on a piece of paper or metal thingie. Guess what happens then when the cops come looking through your stuff?

Finally, I would guess that 99% of Bitcoin owners either have their coins on an exchange (thus they have zero ability to prevent direct deposits by the government) or using a hardware wallet, which, if you have one, make it obvious that you own some crypto coins, and all of the above applies even more to that situation.

To me, it all sounds like some kind of fantasy that people keep telling themselves. Please explain how having Bitcoin is any different in practice from having a bunch of gold bars that they can just steal?

Why color-wheel websites (Adobe…) claim these colors are complementary while they are not?

I just learn about the different color harmony styles models, and I was playing with Adobe color wheel website using the complementary style, but I’m realizing that the proposed colors are not really on the other side of the Hue circle:

Here, you see that the blueish line has hue 174° and the brown color has hue 19°, and 174°-19°=155°, while I would expect their distance to be 180° since they are complementary. And if I ask to Krita, they are indeed not on opposite parts of the Hue circle:

So what’s wrong with Adobe color wheel? I also tried with https://paletton.com, and the Paletton gives similar results compared to Adobe color. Are all color wheels crazy, or am I missing something? I also tried to check how footage was behaving, and they seem to agree with my definition, for instance this photo uses colors #27AB9E (Hue=174°) and #ff4473 (hue=344°), which are much more aligned, and we have 344-174 = 170° which is way closer to 180°.

legal – Copyright claim to Bitcoin Whitepaper

legal – Copyright claim to Bitcoin Whitepaper – Bitcoin Stack Exchange

algorithms – Prove the following claim on Hamilton Path?

I am trying to prove the following claim:

Given DAG graph, there is Hamilton path iff the following algorithm
returns true:

1. Do topologic sorting.
2. Move on the graph’s vertices one by one (from low to high). In case there is no edge connecting 2 vertices with adjacent values from the topologic sorting then return false.
if no false was returned after we check all vertices, return true.

I am stuck of proving one side which is: if there is Hamilton path then the algorithm returns true.

I tried using induction on number of vertices in the graph n:

So I said, let’s exclude the last vertex in the given Hamilton path (let’s call it a), and assume by contradiction that the algorithm returned false.

This means one of the 2:

1. Two vertices with adjacent values had no edge connecting them and both aren’t a.
this contradictc the assumtion that the claim hold for graph with n vertices.

2. One of the two vertices is a and the other isn’t a.

I am stuck on proving that case (2) will give us a contradiction, How may I continue?

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