[Bug]: extract() resolves the same paths ~24k times and the call tie-break re-parses candidate paths on every site #4194

Pre-flight checks

• I have checked the Troubleshooting section in the README

What happened?

Profiling a no-change graphify update on graphify's own repo shows two pieces of repeated path work that do not depend on anything that changes during the run:

1. extract()'s id remap calls Path.resolve() on the same file paths once per input, once per target_file-stamped edge (_raw_tp.resolve(), stem_forms.get(Path(tf).resolve())) and once per node (prefix_remap.get(Path(sf).resolve())): 23,819 calls from extract() itself for ~1k distinct files.
2. paths._path_proximity_winner (the Cross-file calls edges dropped for any symbol with 2+ same-named definitions (test-mock stubs erase the real call graph) #1553 god-node tie-break) builds a PurePosixPath for every candidate's parent directory, twice (same-directory tier and common-prefix tier), on every ambiguous call site. A common name brings the same candidate files back on every site: 226,809 Path objects per update.

Expected: each distinct path resolved/parsed once; same graph.

Steps to reproduce

git clone https://github.com/Graphify-Labs/graphify && cd graphify
graphify update . --force                      # first build
python -c "import cProfile,sys; from graphify.__main__ import main; sys.argv=['graphify','update','.','--force']; cProfile.run('main()','u.prof')"
python -c "import pstats; p=pstats.Stats('u.prof'); p.sort_stats('cumulative'); p.print_callers('pathlib.py.*\\(resolve\\)'); p.print_callees('_path_proximity_winner')"

Error output or graph output

Path.resolve <- extract()            23,819 calls
_path_proximity_winner  1,649 calls -> PurePosixPath.__new__ 226,809 calls

Wall time of the whole update (not profiled), graphify's repo, 18,830 nodes: cold ~28 s, no-change ~21-25 s.

Graphify version

0.9.79 (f765dcb)

Operating System

Windows

Python Version

3.12

Installation Method

built from source (git clone)

Additional Environment Details

No provider keys set. Reproduces on a clean checkout of graphify itself.

Additional context

#3500 memoized path resolution inside the symbol-resolution passes; this is extract()'s own remap and the paths.py tie-break, which it did not cover. A fix with before/after numbers and identical-output checks is ready; PR right after this.