Fix gtfs io discrepancy

[Hussein-Mahfouz]

Problem:

We identified a discrepancy between how the GTFS is read/encoded in prepare_gtfs.py and how it is written/decoded in gtfs.py. Previously, the optimization pipeline was generating a deflated service level.

This issue was traced to extract_route_templates in the GTFS writer. When a route had multiple templates, the legacy code attempted to find the template of the last trip for a given headsign/direction. If that specific template did not exist or failed to map cleanly, the script would silently fail to write the trip. As a result, large chunks of optimized trips were simply dropped during the final GTFS construction.

Changes in this PR:

• Spatial Grouping & Direction Inference: Replaced previous "splitting factor" logic with spatial grouping. The code now infers route directions by analyzing trip origins and destinations, efficiently grouping all disparate headsigns into two spatially-defined directions and mapping each headsign accordingly (extract_route_templates, gtfs.py).
• Proportional Round-Robin Template Handling: For routes with multiple headsigns (branches), the code now analyzes historical trip frequencies and populates a weighted template list in proportion to each branch's frequency. (extract_route_templates, gtfs.py).
• Round-Robin Trip Generation: When generating trips, the function now cycles through the list of templates for each direction. This ensures that generated trips are distributed according to real-world service ratios, and that the aggregate service frequency matches the optimized headway precisely without dropping trips (generate_trips_and_stop_times, gtfs.py).
• Validation Notebook: Introduced 4_validate_gtfs_io.ipynb to mathematically show read/write pipeline discrepancies across the network. It isolates actual headway snapping (e.g. boundary constraints dropping/adding trips at the 5-min or 60-min marks) from unintentional bugs, showing the I/O pipeline now has minimal discrepancy