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The RPC (currently delphinet), allows you to query a contract's storage and big map key at a particular block id.

GET ../<block_id>/context/big_maps/<big_map_id>/<script_expr>

GET ../<block_id>/context/contracts/<contract_id>/storage

My intuition is that if you query a contract at block X, the storage and big map values you get back for block X include the changes from the operations of block X. Is this correct?

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Yes, the context queried in the RPC is the context resulting from the operations in that block. This can be demonstrated thus:

Consider the contract store_string.tz:

parameter string ;
storage (option string);
code { CAR;
       SOME;
       NIL operation;
       PAIR;
     };

It takes a string as a parameter and stores it. We originate the contract in a local sandbox:

$ tezos-client originate contract store_string transferring 0 from bootstrap1 \ 
                         running ~/store_string.tz  --init None --burn-cap 1

and bake in another terminal:

$ tezos-client bake for bootstrap2

Here is my receipt, abbreviated:

Operation found in block: BMAvJZqXQGmHhBybem2iRWfvZuK5d2i5ZbK4aj59DZ4gzcp6KwP (pass: 3, offset: 0)
This sequence of operations was run:
   ...
New contract KT1PcdVdbupFbMscwLmxEe1DEKPbwobCpnqk originated.
The operation has only been included 0 blocks ago.
We recommend to wait more.
Use command
  tezos-client wait for ooQ3bo5ncArZnR5fBSzeon5nSmf5brvW7DnHtH81xf5DKrEYn9J to be included --confirmations 30 --branch BL6LcKc7fm6PKV8V7Rn2hzWesZGfWQe9DJp47tUzPEnHZx273oh
and/or an external block explorer.
Contract memorized as store_string.

Thus the contract was originated in block BMAvJZqXQGmHhBybem2iRWfvZuK5d2i5ZbK4aj59DZ4gzcp6KwP with address KT1PcdVdbupFbMscwLmxEe1DEKPbwobCpnqk.

Let's inspect the storage of the contract in the block where it was originated:

$ tezos-client rpc get /chains/main/blocks/BMAvJZqXQGmHhBybem2iRWfvZuK5d2i5ZbK4aj59DZ4gzcp6KwP/context/contracts/KT1PcdVdbupFbMscwLmxEe1DEKPbwobCpnqk/storage
{ "prim": "None" }

The storage is None, as expected.

Now, let's update its storage with a transaction:

$ tezos-client transfer 0 from bootstrap1 to store_string --arg '"test!"' --burn-cap 1

and bake in another terminal:

$ tezos-client bake for bootstrap2

From the abbreviated receipt :

Operation found in block: BM3rZ6CzSxZ7XHqsHnbJAP3bUd8Ey5zzE3bxt3u2v9GRSdesUgU (pass: 3, offset: 0)
...

we see that the transaction was included in block BM3rZ6CzSxZ7XHqsHnbJAP3bUd8Ey5zzE3bxt3u2v9GRSdesUgU. Let's inspect the storage of our contract at that very block:

$ tezos-client rpc get /chains/main/blocks/BM3rZ6CzSxZ7XHqsHnbJAP3bUd8Ey5zzE3bxt3u2v9GRSdesUgU/context/contracts/KT1PcdVdbupFbMscwLmxEe1DEKPbwobCpnqk/storage
{ "prim": "Some", "args": [ { "string": "test!" } ] }

We see that the storage is updated.

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