Currently access and refresh token i'm getting are opaque. i'm unable to verify them locally. only id token is a JWT. is there any request parameter to make google return access token in a JWT form signed with a asymmetric key? the endpoint i'm using: /oauth2/v4/token and params: code: req.query.code, client_id: clientId, client_secret: clientSecret, redirect_uri: 'http://localhost:8080/login/oauth2/code/google', grant_type: 'authorization_code', access_type: 'offline', approval_prompt:'force'
How can I verify a Google authentication access token?  I need to somehow query Google and ask: Is [given access token] valid for the [example@example.com] Google account?  Short version: It's clear how an access token supplied through the  can be used to then request data from a range of Google services. It is not clear how to check if a given access token is valid for a given Google account. I'd like to know how.  Long version: I'm developing an API that uses token-based authentication. A token will be returned upon provision of a valid username+password or upon provision of a third-party token from any one of N verifiable services.  One of the third-party services will be Google, allowing a user to authenticate against my service using their Google account. This will later be extended to include Yahoo accounts, trusted OpenID providers and so on.  Schematic example of Google-based access:    The 'API' entity is under my full control. The 'public interface' entity is any web- or desktop-based app. Some public interfaces are under my control, others will not be and others still I may never even know about.  Therefore I cannot trust the token supplied to the API in step 3. This will be supplied along with the corresponding Google account email address.  I need to somehow query Google and ask: Is this access token valid for example@example.com?  In this case, example@example.com is the Google account unique identifier - the email address someone uses to log in to their Google account. This cannot be assumed to be a Gmail address - someone can have a Google account without having a Gmail account.  The Google documentation clearly states how, with an access token, data can be retrieved from a number of Google services. Nothing seems to state how you can check if a given access token is valid in the first place.  Update The token is valid for N Google services. I can't try a token against a Google service as means of verifying it as I won't know which subset of all Google's services a given user actually uses.  Furthermore, I'll never be using the Google authentication access token to access any Google services, merely as a means of verifying a supposed Google user actually is who they say they are. If there is another way of doing this I'm happy to try.
How do I put big brackets under different parts of an equation so that I can write, e.g., text specific to these parts? For example: f =  x^3 +  2     |___|  |__|        |     |    text 1  text 2 I'm a little confused as to when to use  for my physics class. For example, I'm asked to find the average speed of a race car that travels around a circular track with a radius of $500~\mathrm{m}$ in $50~\mathrm{s}$.  Would I need to apply the rules of significant figures to this step of the problem? $$ C = 2\pi (1000~\mathrm{m}) = 6283.19 $$  Or do I just need to apply significant figures at this step? $$ \text{Average speed} = \frac{6283.19~\mathrm{m}}{50~\mathrm{s}} = 125.664~\mathrm{m}/\mathrm{s} $$  Should I round $125.664~\mathrm{m}/\mathrm{s}$  to  $130~\mathrm{m}/\mathrm{s}$ since the number with the least amount of significant figures is two? How do I skip specific tests when building an rpm? I am building an RPM of git version 2.13.0. The build has gone ok but one of the tests are failing:  Config variable ${LIB_HTTPD_SVN} is not defined Config variable ${LIB_HTTPD_SVN_PATH} is not defined   I cannot find any info about these variables so I was going to just skip the tests. How can I do that? From what I understood, cardinal numbers are defined as:  $\aleph_0$ = the cardinality of $\mathbb{N}$ $\aleph_{n+1}$ = is the least cardinal number greater than $\aleph_n$  The continuum hypothesis states that the cardinality of $\mathbb{R}$ is  $\aleph_1$. I more or less understand this cannot be proven (does not follow from ZFC).  However, can it be proven dat there in fact is a 'least cardinal number' greater than $\aleph_0$?  Is it possible that there are sets with cardinality $\aleph_{1/2}$, $\aleph_{1/3}$, et cetera, so to speak?  Or expressed differently: is it possible that for every set A with cardinality CA > $\aleph_0$, there exists another set B with cardinality CB where CA > CB > $\aleph_0$? Render looks darker than Look Dev mode I have been texture painting in look dev mode. But when i try to render it, everything looks very dark. I have 3 sun lights in my scene, ambient turned on in Eevee settings. What am i missing? I really like the look of my scene in Look Dev mode, how can i achieve the same look when my scene is rendered too? Given the sentence:     Most people who live and work near Washington, DC, would have trouble      imagining dinosaurs walking around the area.   Grammatically, what would ‘imaging’ be called in this case? Present participle or gerund or something?  I mean, if it is a present participle, ‘imagining~’ might be a description of the subject. And if it is a gerund, ‘imagining~’ might be an object of the verb phrase of ‘have trouble’. How do they explain this ‘imagining’ after ‘have trouble’? Why is the order of $\mathbb{Z}[i]/\langle 3+i\rangle$ equal to 10? The reasoning my book uses is as follows:   Since $(3+i)(3-i) = 10$, $10 + \langle 3+i\rangle = 0 + \langle 3+i\rangle $. Also, $i + \langle 3+i\rangle = -3 + \langle 3+i\rangle = 7 + \langle 3+i\rangle$. So, $\mathbb{Z}[i]/\langle 3+i\rangle = \{k + \langle 3+i\rangle \mid k = 0,1,\ldots ,9\}$, since $1 + \langle3+i\rangle$ has additive order $10$.   I do not understand why the additive order of $1 + \langle 3+i\rangle$ is $10$, or why the fact that $(3+i)(3-i) = 10$, shows the additive order or $1 + \langle 3+i\rangle$  is $10$. If someone could please explain this I would greatly appreciate it.   Note: I apologize for not using MathJax to write this post. I intend to learn it over the coming weekend. These are my current disk partitions. /yedek is for some personal backup files. As you can see there is only Ubuntu on my PC. I will install Windows, too. Because of this I want to shrink /dev/sda3 . It currently 546GB and I want to split it: 300GB for / and 246GB for Windows (NTFS) is OK for me.  I'm using GParted for the first time. How can I shrink /?  I don't want to lose any datas from Ubuntu. How can I get around giving my mobile phone number to Google? let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then Why is the B field of a solenoid equal to $\mu_0 i n$ while that of a loop is $\frac{\mu_0 i R^2}{2(R^2+z^2)^{3/2}}$? Can you upgrade the RAM of an Android device? I'm sure many people like me are aware and annoyed by the extremely limited amount of RAM in Nexus S (512MB but only 300+ is usable), I have searched all over google for a solution to increase the amount of RAM available and came up empty (I tried swap file applications but they just broke my system's SD card partitions causing a complete reset).  I wonder if there is any hardware solution to this problem. Is it possible to swap the chip out for a bigger capacity one? I realize that it is not as simple as swapping out PC RAM from a dimm but I haven't seen any schematics for the chip layout on the ARM boards in the smartphones so I really hope that it is somewhat possible to increase the amount of RAM on the board. How do I create a file of size 10M, format it with ext3 filesystem and then mount it in /media/fuse?  I tried with  mkfs -t ext3 file   then to mount it  mount -t ext3 file /media/fuse   It didn't work because it said that file wasn't a block device. Can anybody help me? Difference between "git add -A" and "git add ." The command git add [--all|-A] appears to be identical to git add .. Is this correct? If not, how do they differ? What is the full "for" loop syntax in C? Can I reposition AdSense ads with Javascript (for responsive purposes)? I have a responsive blog where ads are displayed in the sidebar. On mobile devices however, the sidebar is pushed to the bottom below the posts.   So what I'd like to do is move the ads from the sidebar and insert them into the post itself on mobile devices   I do this using javascript:  &lt;div id="main"&gt;     &lt;div id="article"&gt;         &lt;div class="post"&gt;             &lt;p class="intro"&gt;&lt;/p&gt;             &lt;p class="text"&gt;&lt;/p&gt;         &lt;/div&gt;     &lt;/div&gt;     &lt;div id="sidebar"&gt;         &lt;div class="adbox-1"&gt;&lt;/div&gt;     &lt;/div&gt;     &lt;/div&gt;  &lt;script&gt;     jQuery(document).ready(function(){          // AD REPOSITION         if ($(window).width() &lt; 769) {             $('.ad-box1').insertAfter($('.intro'));                    }      }); &lt;/script&gt;   The ads are always loaded in the sidebar, but if the screen width is below 768px, they will be moved somewhere else.  I wonder if this would violate AdSense terms of service? Statement: $[a, b] \cap \mathbb{Q}$ in $\mathbb{Q}$ is not compact. Thus the interior of all compact subsets of $\mathbb{Q}$ is $\emptyset$.   I am trying to understand the first sentence. I read that a closed subspace of a compact space is compact, so for example, consider the unit interval $[0, 1]$ which is a compact space. Take a closed subspace $[0, 1] \cap \mathbb{Q}$ of $[0, 1]$. This set is closed since it just consists of all the rational numbers in between $0$ and $1$, including $0$ and $1$. So it is a closed subspace of a compact space. But why isn't this compact? The usage of singular and plural has always been confusing for me.   I often see sentences like these         People are using cell phones.   People are using a cell phone.      Does the first sentence mean everyone has a phone and they are all using their own?  Does the second sentence mean they are sharing one cell phone?   If I see a group of people holding a cell phone in their hand(s), &lt;- even this is confusing for me, should I use the first sentence then?   Another example: you see two men, and both of them are carrying a bag. Which sentence should I say/use?        They are carrying backpacks          They are carrying a backpack      Could you please make it clear for me? How do I rename a directory via the command line? I have got the directory /home/user/oldname and I want to rename it to /home/user/newname. How can I do this in a terminal? Are features that allow −5 to attack to get +10 to damage mathematically sound? Some class features, monster traits, and feats allow you to take a −5 to your attack roll in order to gain a +10 to your damage roll. At first glance this looks really good, but when will it deal more damage than not using it on average?  For instance if you have a total attack bonus of +8 and you deal 1d12 damage. You have to roll a 7 to hit an AC of 15. If you take the −5 that makes it where you have to roll a 12. That's going to reduce your average damage by a lot.