diff --git a/.gitignore b/.gitignore
index bd3e442..aaf460a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -79,3 +79,4 @@ __pycache__
 logs
 scratch
 notes
+.cache
diff --git a/README.md b/README.md
index a32b36c..356574f 100644
--- a/README.md
+++ b/README.md
@@ -1,24 +1,18 @@
 # Summary
 
 # TODOs
-- [ ] Figure out the tranpose non-sense or support both
-- [ ] Clean up `apply_batch` we shouldn't need to pass a coeff
 - [ ] Add docstrings
   - [X] Pauli
   - [X] PauliString
   - [ ] PauliOp
   - [ ] SummedPauliOp
+- [ ] Figure out the tranpose non-sense or support both (some functions take the transpose of the states and others don't)
+- [ ] Clean up `apply_batch` we shouldn't need to pass a coeff
 - [ ] Clean up tests
-- [X] Clean up test utils
-- [X] Add type aliases and factory functions to utils for fast_pauli
-- [X] Seach the names and make sure we don't have any overlap with other projects
-- [ ] Build out pauli decomposer
-- [X] Remove the weights argument and rename to data
-- [X] Add namespace
 - [ ] Add apply method to SummedPauliOp that takes precomputed weighted data
-- [ ] Writeup for docs
 - [ ] Add pybind11 interface and python examples
-- [ ] Change functions names over to default to parallel impl and use `_serial` for the serial implementation
+- [ ] Change functions that may run in parallel to take [`std::execution_policy`](https://en.cppreference.com/w/cpp/algorithm/execution_policy_tag_t)
+- [ ] Possibly add levels to methods like BLAS to group methods by scaling
 - [ ] Migrate `PauliOp` and `SummedPauliOp` to only store mdspans rather than copies of the data itself
 
 ## Requirements
@@ -32,7 +26,7 @@
 ## Build and Test
 
 ```bash
-cmake -B build -DCMAKE_CXX_COMPILER=<your_favorite_c++_compiler>
+cmake -B build -DCMAKE_CXX_COMPILER=clang++
 cmake --build build
 ctest --test-dir build
 ```
@@ -42,3 +36,4 @@ ctest --test-dir build
 The C++ portion of this library relies heavily on spans and views.
 These lightweight accessors are helpful and performant, but can lead to dangling spans or accessing bad memory if used improperly.
 Developers should familiarize themselves with these dangers by reviewing [this post](https://hackingcpp.com/cpp/std/span.html).
+
diff --git a/docs/planning.md b/docs/planning.md
new file mode 100644
index 0000000..246cc42
--- /dev/null
+++ b/docs/planning.md
@@ -0,0 +1,22 @@
+# General
+
+
+## Notation
+
+- Pauli Matrix $\sigma_i \in \{ I,X,Y,Z \}$
+- Pauli String $\mathcal{\hat{P}} = \bigotimes_i \sigma_i$
+- Sum of weighted Pauli strings (currently called `PauliOp`) $A_k = \sum_i h_i \mathcal{\hat{P_i}}$
+- Sum of summed weighted Pauli strings (currently called `SummedPauliOp`) $B = \sum_k \sum_i h_{ik} \mathcal{\hat{P_i}}$
+
+# List of Operations
+
+Here's a terse list of the type of operations we want to support in `fast_pauli` (this list will grow over time):
+
+1. Pauli String to sparse matrix (Pauli Composer)
+2. $\mathcal{\hat{P}} \ket{\psi}$
+3. $\mathcal{\hat{P}} \ket{\psi_t}$
+4. $\big( \sum_i h_i \mathcal{\hat{P}}_i \big) \ket{\psi_t}$
+5. $\big(\sum_k \sum_i h_{ik} \mathcal{\hat{P}}_i \big) \ket{\psi_t}$
+6. $\big(\sum_k x_{tk} \sum_i h_{ik} \mathcal{\hat{P}}_i \big) \ket{\psi_t}$
+7. $\bigg(\sum_k \big( \sum_i h_{ik} \mathcal{\hat{P}}_i \big)^2 \bigg) \ket{\psi_t}$
+8. Calculate $\bra{\psi_t} \{ \mathcal{\hat{P_i}}, \hat{A_k} \} \ket{\psi}$ and $\bra{\psi} \mathcal{\hat{P_i}} \ket{\psi}$
diff --git a/include/__pauli_string.hpp b/include/__pauli_string.hpp
index 4f59038..9060b4d 100644
--- a/include/__pauli_string.hpp
+++ b/include/__pauli_string.hpp
@@ -39,7 +39,7 @@ struct PauliString {
    * calculates the weight.
    *
    */
-  constexpr PauliString(std::span<fast_pauli::Pauli> const &paulis)
+  constexpr PauliString(std::span<fast_pauli::Pauli> const paulis)
       : weight(0), paulis(paulis.begin(), paulis.end()) {
     for (auto const &pauli : paulis) {
       weight += pauli.code > 0;
diff --git a/src/fast_pauli.cpp b/src/fast_pauli.cpp
new file mode 100644
index 0000000..22db19a
--- /dev/null
+++ b/src/fast_pauli.cpp
@@ -0,0 +1,33 @@
+#include "fast_pauli.hpp"
+
+#include <experimental/mdspan>
+#include <pybind11/numpy.h>
+#include <pybind11/pybind11.h>
+#include <pybind11/stl.h>
+
+namespace py = pybind11;
+
+void scale_tensor_3d(py::array_t<double> array, double scale) {
+  auto arr = array.mutable_unchecked<>();
+  std::mdspan tensor(arr.mutable_data(), arr.shape(0), arr.shape(1),
+                     arr.shape(2));
+
+#pragma omp parallel for collapse(3)
+  for (size_t i = 0; i < tensor.extent(0); i++) {
+    for (size_t j = 0; j < tensor.extent(1); j++) {
+      for (size_t k = 0; k < tensor.extent(2); k++) {
+        tensor(i, j, k) *= scale;
+      }
+    }
+  }
+}
+
+PYBIND11_MODULE(py_fast_pauli, m) {
+  m.doc() = "Example NumPy/C++ Interface Using std::mdspan"; // optional module
+                                                             // docstring
+  m.def("scale_tensor_3d", &scale_tensor_3d, "Scale a 3D tensor by a scalar.",
+        py::arg().noconvert(), py::arg("scale"));
+
+  py::class_<fast_pauli::SummedPauliOp<double>>(m, "SummedPauliOp")
+      .def(py::init<>());
+}
\ No newline at end of file