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Co-authored-by: Raphael <[email protected]>
Co-authored-by: Tolik Zinovyev <[email protected]>

docs/rustdoc/centralized_telescope/main.md

@@ -16,8 +16,8 @@ This generalized construction uses the same key parameters as prehashed construc
 - Retries with index $v$: 
   - The prover retries the proof generation process up to $r$ times.
   - Each retry uses a different retry counter $v$, where $v \in \[1, r\]$, to diversify the search process.
-- Hash-based binning:
-  - Elements in $S_p$ are prehashed into bins using $H_0(v, \cdot) where v \in \[1,r\]$, grouping elements based on their hash values. We prehashed using the retry counter to get different bins for each repetition, reducing the risk of badly distributed bins.
+- Seeded binning:
+  - Elements in $S_p$ are prehashed into bins using $H_0(v, \cdot)$ where $v \in \[1,r\]$, grouping elements based on their hash values. We prehashed using the retry counter to get different bins for each repetition, reducing the risk of badly distributed bins.
   - This process limits the search space for DFS, making it more efficient.
 - Bounded DFS:
   - A depth-first search explores valid proof sequences of size $u$, using the bins for efficient lookup.
@@ -37,7 +37,7 @@ This generalized construction uses the same key parameters as prehashed construc
 4. **Bounded DFS**:
    - A bounded DFS search is used to construct the sequence $(t, s_1, ..., s_u)$, with a shared step limit $B$ applied across all starting points $t$.
    - At each step of DFS:
-     - The algorithm search a new element for the current sequence $(t, s_1, ..., s_k)$ in bin numbered $H_1(v, t, s_1, ..., s_k)$.
+     - The algorithm searches a new element for the current sequence $(t, s_1, ..., s_k)$ in bin numbered $H_1(v, t, s_1, ..., s_k)$.
      - If the step limit $B$ is reached or no valid extension exists, the DFS backtracks and explores another retry $r$, restarting the process with a new partitioning of elements. 
      - Otherwise, the DFS updates the step limit and then recursively calls itself with the extended tuple.
 5. **Validation**: