docs: fix spelling in src/lpp.c and add GEMINI.md for AI context

GEMINI.md

@@ -0,0 +1,77 @@
+# GEMINI.md - WEEKS Microstrip Calculator
+
+This file provides context and instructions for AI assistants working on the `weeks` project.
+
+## Project Overview
+
+`weeks` is a C-based command-line tool that implements the **Partial Element Equivalent Circuit (PEEC)** method (Weeks et al., IBM, 1979) to calculate the resistance and inductance of rectangular conductors on PCB substrates.
+
+### Key Capabilities
+- **R/L Matrices**: Computes frequency-dependent series resistance (Ω/m) and inductance (H/m) matrices for multi-conductor systems.
+- **Transmission-Line Parameters**: Derives per-line quasi-TEM parameters including characteristic impedance ($Z_0$), capacitance ($C$), effective permittivity ($\varepsilon_{eff}$), and attenuation.
+- **Dielectric Support**: Supports materials like FR4 and Rogers substrates (affects transmission-line parameters only).
+- **Validation**: Includes Python-based harnesses to cross-check results against FastHenry (field solver) and Hammerstad-Jensen closed-form solutions.
+
+## Architecture & Data Flow
+
+1.  **Input Phase (`src/input.c`)**: Parses a YAML configuration file (hardcoded as `test.yaml`) using `libyaml`. Populates the `conductor[]` array and sets the `global_frequency`.
+2.  **Meshing Phase (`src/build.c`)**: Discretizes each conductor into rectangular mesh elements based on user-defined divisions (`nw`, `nh`) and density (`b`).
+3.  **Matrix Phase (`src/calcl.c`)**: Builds a large complex impedance matrix $Z$ for all filaments. Self-inductance is calculated in `src/lpp.c` using the Neumann partial inductance formula.
+4.  **Aggregation Phase (`src/weeks.c`)**: Inverts the $Z$ matrix (using Meschach), aggregates filament-level admittances back to per-conductor quantities, and inverts again to get the final $N \times N$ R/L matrices.
+5.  **Output Phase**: Prints the R, L, and $|Z|$ matrices. Calls `calc_line_params()` to print transmission-line results.
+
+## Build and Run
+
+### Requirements
+- **GCC**: C compiler.
+- **libmeschach-dev**: Matrix/vector operations library.
+- **libyaml-dev**: YAML parsing library.
+
+### Key Commands
+```bash
+# Check if libraries are installed
+make check-deps
+
+# Build the 'weeks' executable
+make
+
+# Run the tool (reads from test.yaml)
+./weeks
+
+# Run with material examples
+make test-fr4      # FR4 substrate
+make test-air      # Air baseline
+make test-rogers   # Rogers RO4003C
+
+# Validation
+make check-fasthenry  # Cross-check R/L vs FastHenry (needs fasthenry on PATH)
+make check-z0         # Sanity-check Z0 vs Hammerstad-Jensen closed form
+
+# Cleaning
+make clean
+```
+
+## Development Conventions
+
+- **Input Filename**: The C program hardcodes `test.yaml` as the input. To run a specific case, copy it to `test.yaml`.
+- **Conductor 0**: The first conductor (`line0`) in the YAML file MUST be the ground plane.
+- **Substrate Height**: Not a direct input. It is derived as the gap between the signal trace's bottom (`y`) and the ground plane's top (`y + h`).
+- **Dielectric Parameters**:
+    - `er` and `tan_delta` are material properties.
+    - They **do not** affect the series R/L/|Z| matrices (which are dielectric-independent for $\mu_r \approx 1$).
+    - They **do** affect the separate "TRANSMISSION-LINE PARAMETERS" section.
+- **Units**: All dimensions in the YAML file MUST be in **meters** (e.g., `1.6e-3` for 1.6 mm).
+- **Matrix Library**: Uses `libmeschach`. Key types: `ZMAT` (complex matrix), `ZVEC` (complex vector).
+- **Testing**:
+    - The C code lacks an internal unit test suite.
+    - Use the Python harnesses in `tools/` for numerical validation.
+    - FastHenry validation requires `fasthenry` to be installed manually (see `docs/fasthenry-crosscheck.md`).
+
+## Directory Structure
+
+- `src/`: C source files.
+- `include/`: C header files.
+- `examples/`: Sample YAML configurations.
+- `tools/`: Python validation harnesses.
+- `docs/`: Technical documentation and cross-check details.
+- `build/`: Temporary build artifacts.

src/lpp.c

@@ -7,7 +7,7 @@
  * It is assumed that the permeability is equal to that of free space
  * (4 * PI * 1e-7).
  *
- * No attempt have been made to optimize the calculations. The
+ * No attempt has been made to optimize the calculations. The
  * calculations can be speeded up a bit by "writing out" the function
  * 'F' and combining terms.
  *