fix: address issues

- add to docs for plan name skipping with respect to what is returned
- fix typo in Doc
- replace `mulmod` with `mul` in `make_transcript`

Author: iajoiner

solidity/src/proof_exprs/ProofExpr.pre.sol

@@ -31,7 +31,7 @@ library ProofExpr {
     ///   length equal to the columns in the expression
     /// ##### Return Values
     /// * `expr_ptr_out` - pointer to the remaining expression after consuming the proof expression
-    /// * `eval` - the evaluation of the result of this expression. Cirically, this resulting evaluation must be guarenteed to be
+    /// * `eval` - the evaluation of the result of this expression. Critically, this resulting evaluation must be guarenteed to be
     ///   the correct evaluation of a column with the same length as the columns in the expression. Every column has implicit infinite length
     ///   but is padded with zeros. This is guarenteed to match the length of the chi column, and varients must be designed to handle this.
     /// ##### Proof Plan Encoding

solidity/src/verifier/PlanUtil.sol

@@ -25,7 +25,7 @@ library PlanUtil {
     /// @dev     * length of output column name (uint64)
     /// @dev     * output column name (variable length)
     /// @param __plan The calldata pointer to the plan.
-    /// @return __planOut The updated pointer after skipping names.
+    /// @return __planOut The updated pointer after skipping names which points to the actual plan itself. i.e., the AST without any names.
     function __skipPlanNames(bytes calldata __plan) external pure returns (bytes calldata __planOut) {
         assembly {
             function skip_plan_names(plan_ptr) -> plan_ptr_out {

solidity/src/verifier/Verifier.pre.sol

@@ -454,7 +454,7 @@ library Verifier {
                 append_array(transcript_ptr, table_lengths_ptr)
 
                 let commitment_len := mload(commitments_ptr)
-                mstore(commitments_ptr, mulmod(commitment_len, 2, MODULUS))
+                mstore(commitments_ptr, mul(commitment_len, 2))
                 append_array(transcript_ptr, commitments_ptr)
                 mstore(commitments_ptr, commitment_len)
 

solidity/test/verifier/Verifier.t.pre.sol

@@ -4,7 +4,6 @@ pragma solidity ^0.8.28;
 
 import {Test} from "forge-std/Test.sol";
 import "../../src/base/Constants.sol";
-import {Errors} from "../../src/base/Errors.sol";
 import {Verifier} from "../../src/verifier/Verifier.pre.sol";
 
 contract VerifierTest is Test {