Here is the comprehensive report consolidating the findings and suggested resolutions for the `ries-rs` codebase. 

You’ve built an exceptionally rigorous, mathematically sound, and well-documented system. It successfully modernizes a historical algorithm while adhering to high engineering standards. The following report outlines a few architectural, performance, and UX refinements to help push this engine even further.

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### Executive Summary of Strengths
Before diving into the critiques, it is worth highlighting what this codebase does exceptionally well:
* **Zero-Allocation Hot Paths:** Using `SmallVec<[Symbol; 21]>` ensures that expressions remain on the stack, preventing heap allocation overhead during intense search loops.
* **Memory-Aware Architecture:** The adaptive and streaming generation modes gracefully prevent out-of-memory (OOM) errors by falling back to `O(depth)` memory processing when the expression space grows too large.
* **Reproducibility:** The implementation of `--deterministic` alongside JSON run manifests (`--emit-manifest`) is a massive win for academic rigor.

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### Detailed Findings & Suggested Resolutions

#### 1. UI Thread Blocking in WASM Frontend
* **The Issue:** In the browser interface (`web/index.html`), the WASM `search` function is called synchronously within the `performSearch` handler.
* **The Impact:** Deep searches (e.g., Level 4 or 5) require significant compute time. Because the call is synchronous, it entirely blocks the browser's main JavaScript thread, freezing the UI (including the loading spinner) until the search completes.
* **Suggested Resolution:** Offload the WASM search execution to a Web Worker. You can pass the target and search configuration to the worker via `postMessage`, allowing the main thread to keep the UI responsive and animate the loading states smoothly.

#### 2. Aggressive Quantization Collisions in Generation
* **The Issue:** During expression generation, `src/gen.rs` deduplicates left-hand side (LHS) expressions using a quantized key: `(quantize_value(expr.value), quantize_value(expr.derivative))`. The `quantize_value` function scales `f64` values by `1e8` before rounding them to an `i64`.
* **The Impact:** This scaling only preserves about 8 significant digits. Consequently, two mathematically distinct expressions that evaluate to very similar values and derivatives at a specific target `x` will produce a hash collision. The system will overwrite one with the other, potentially discarding a valid or more elegant equation before Newton-Raphson refinement occurs.
* **Suggested Resolution:** Replace the `i64` quantization key with `ordered_float::OrderedFloat<f64>`, which you already utilize elsewhere in the codebase. This preserves full `f64` precision for deduplication and prevents accidental collisions of distinct expressions.

#### 3. PSLQ Precision Ceiling
* **The Issue:** The PSLQ integer relation algorithm in `src/pslq.rs` is implemented using standard `f64` arithmetic. 
* **The Impact:** Standard double-precision floats only preserve 53 bits of mantissa. As the matrix entries grow during the PSLQ loop, the floating-point state loses exactness, forcing the algorithm to abort early to avoid untrustworthy results.
* **Suggested Resolution:** Since you have already built the `HighPrec` abstraction (backed by the `rug` crate) for arbitrary-precision verification, refactor the PSLQ module to use `HighPrec`. This will allow the engine to discover significantly deeper and more complex integer relations without succumbing to floating-point noise.

#### 4. Python API Streaming Limitations
* **The Issue:** The Python bindings in `ries-py/src/lib.rs` compute the entire result set in Rust before returning a `Vec<PyMatch>`, which PyO3 translates into a complete Python list.
* **The Impact:** Python users must wait for the entire search to finish before they can inspect the first match.
* **Suggested Resolution:** Expose a Python generator (iterator) interface. Since the Rust core already supports a streaming architecture via callbacks (`generate_streaming`), you can yield `PyMatch` objects back to Python as they are discovered. This is highly idiomatic for Python data science workflows.

#### 5. Infix Formatting Boilerplate
* **The Issue:** There is heavy code duplication in `src/expr.rs` across the `try_to_infix`, `to_infix_mathematica`, and `to_infix_sympy` methods. 
* **The Impact:** Each method rewrites the exact same stack-based parsing loop, `needs_paren` checks, and operator precedence logic, making the file unnecessarily long and harder to maintain.
* **Suggested Resolution:** Abstract the stack traversal and parenthesization logic into a single internal function. You can pass a formatting trait or a set of closures into this function that maps `Symbol` variants to their respective string representations (e.g., mapping `Symbol::Sqrt` to `"sqrt()"` or `"Sqrt[]"`).

#### 6. Thread-Local Storage Overhead
* **The Issue:** In `src/eval.rs`, `evaluate_fast_with_context` relies on a `thread_local!` static `EvalWorkspace` to achieve zero-allocation evaluation. 
* **The Impact:** While highly optimized, thread-local lookups are not entirely free. Furthermore, as noted in your documentation, this global state prevents safe recursive calls if different contexts (like user constants or functions) are required.
* **Suggested Resolution:** For parallel generation, consider using Rayon's `map_init` or `ThreadLocal` types to explicitly instantiate an `EvalWorkspace` per worker thread. Passing `&mut EvalWorkspace` explicitly down the call stack is often slightly faster than global TLS lookups in tight loops and entirely removes the hidden global state.

#### 7. Symbol Enum Boilerplate
* **The Issue:** The `Symbol` enum in `src/symbol.rs` manually unrolls `UserConstant0` through `UserConstant15` and `UserFunction0` through `UserFunction15` to maintain a 1-byte footprint. 
* **The Impact:** It creates significant visual noise across pattern matching blocks in `symbol.rs` and `symbol_table.rs`.
* **Suggested Resolution:** Implement a simple declarative macro to generate the `Symbol` enum, its `from_byte` implementation, and the `default_weight` matches. This will drastically clean up the codebase while preserving the strict `repr(u8)` memory layout.