[wangyinz]

Fixes #852

Summary

• mark the theta == pi downward-axis shortcut non-cardinal and orthogonal after applying its sample/matrix transform
• allow rotate_to_standard to execute the inverse orthogonal transform instead of returning early
• add Release-safe native and Python binding regressions for theta 0, pi/2, and pi plus complete pi round-trip restoration

Validation

• Release full build: passed
• CTest: 13/13 passed
• rebuilt utility/seismic bindings, confirmed loaded from the isolated review tree: 7/7 related tests passed
• baseline-red proof: temporarily removing the two state assignments makes both native and binding tests fail at the pi cardinal assertion
• clang-format, Black, py_compile, and git diff --check: passed

Independent agent review

A different agent re-read #852, independently rebuilt Release and bindings, inspected samples/matrix/flags and the full restored object state, performed the remove-and-restore red proof, and returned REVIEW PASS with no blocker. No merge was performed.

[codecov]

Codecov Report

❌ Patch coverage is 86.25000% with 11 lines in your changes missing coverage. Please review.
✅ Project coverage is 71.33%. Comparing base (431f962) to head (00cca0c).

Files with missing lines	Patch %	Lines
cxx/test/tcs/test_rotation_state.cc	85.89%	6 Missing and 5 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #895      +/-   ##
==========================================
+ Coverage   71.28%   71.33%   +0.04%     
==========================================
  Files         180      181       +1     
  Lines       35475    35554      +79     
  Branches     2510     2523      +13     
==========================================
+ Hits        25289    25362      +73     
- Misses       9286     9288       +2     
- Partials      900      904       +4     

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