So what it misses is that the ADM formalism is a subset of GR, in that it can only simulate a subset of the full equations for GR. It also gives a lot of reason

So what it misses is that the ADM formalism is a subset of GR, in that it can only simulate a subset of the full equations for GR. It also gives a lot of reasoning there that is quite faulty with respect to answer the question of if its strictly equivalent >Wait, does this decomposition change the physics? Or is it just a different mathematical approach? I think it's the latter This for example is faulty reasoning, because its not an either or situation >I should check if there are any subtleties, like constraints or boundary conditions that might affect equivalence This is also faulty reasoning, because it assumes that non equivalence must mean that they produce difference physics >Another point is the initial value problem. ADM is used for that, which suggests it's a way to set up initial data consistent with GR. If the equivalence wasn't strict, then initial data in ADM wouldn't correspond properly to GR solutions. But I think they do, as long as the constraints are met. Notice how its trying to sneak a fast one past you. Its saying that because ADM with valid initial conditions maps to GR, therefore GR maps to ADM - which is a logical fallacy! It makes this mistake several times in its chain of reasoning The issue is its not doing any real reasoning, and isn't capable of actually making deductions. Its about as productive as just.. throwing all the pieces of information on the floor, and picking them up in a random order This isn't really getting into the weeds with astrophysics, its ADM 101, and deepseek is just.. lying right to your face with confidence, presented under the guise of a chain of reasoning