fix a few typos and escape sequences in specs

Co-authored-by: Simon Shine <simon@neptune.cash>

specification/src/copy-constraints.md

@@ -21,7 +21,7 @@ To establish that the product is correctly computed, the Prover needs to supply
 
 **Protocol Permutation**
  - Verifier is already in possession of polynomial oracles $[t(X)]$ and $[s(X)]$ that agree with $T$ and $S$ on a subgroup $H$ of order $2^k$.
- - Verifier samples $\beta \xleftarrow{\$} \mathbb{F}$ and sends it to Prover.
+ - Verifier samples $\beta \xleftarrow{\\$} \mathbb{F}$ and sends it to Prover.
  - Prover computes running product polynomials, $t_ p(X)$ and $s_ p(X)$ of degree at most $|H|-1$ and sends them to Verifier.
  - Prover and Verifier run an AIR sub-protocol to establish that the AIR is satisfied for $(t(X), s(X), t_ p(X), s_ p(X))$.
 
@@ -56,7 +56,7 @@ Likewise, we can re-write the AIR for the running product to avoid accumulating
 **Protocol Subset**
  - Prover computes $R \leftarrow \mathsf{sort}(T)$ and $M \leftarrow \{[ [ S_{[i]} \in \mathsf{set}(R) ] ] \, \vert \, i \in \{0, \ldots, 2^k-1\}\}$ and commits to them.
  - Prover and Verifier run a Permutation subprotocol on $(T,R)$.
- - Verifier samples $\beta \xleftarrow{\$} \mathbb{F}$ and sends it to Prover.
+ - Verifier samples $\beta \xleftarrow{\\$} \mathbb{F}$ and sends it to Prover.
  - Prover computes the running square-free product table $R_ p$ of $R$, and the running masked product table of $S_ p$ of $S$ masked by $M$.
  - Prover sends $R_ p$ and $S_ p$ to Verifier.
  - Verifier checks the AIR for $(R, R_ p)$ and the AIR for $(S_ p, M \circ S)$.

specification/src/instructions.md

@@ -61,7 +61,7 @@ the value `a` was supplied as a secret input.
 
 | Instruction      | Opcode | old OpStack     | new OpStack                   | Description                                                                                             |
 |:-----------------|-------:|:----------------|:------------------------------|:--------------------------------------------------------------------------------------------------------|
-| `hash`           |     28 | `_jihgfedcba`   | `_yxwvu00000`                 | Overwrites the stack's 10 top-most elements with their hash digest (length 6) and 6 zeros.              |
+| `hash`           |     28 | `_jihgfedcba`   | `_yxwvu00000`                 | Overwrites the stack's 10 top-most elements with their hash digest (length 5) and 5 zeros.              |
 | `divine_sibling` |     32 | `_ i*****edcba` | e.g., `_ (i div 2)edcbazyxwv` | Helps traversing a Merkle tree during authentication path verification. See extended description below. |
 | `assert_vector`  |     36 | `_`             | `_`                           | Assert equality of `st(i)` to `st(i+5)` for `0 <= i < 4`. Crashes the VM if any pair is unequal.        |