check_out broke out of the key loop at totaltimeref, so keys appended
after it (e.g. by a case-local check_extra.py) were never compared.
Change the break to a continue (totaltimeref is only skipped, never
compared) and run check_extra.py (when present) right after
catch_properties.sh, appending its stdout to result.out / result.ref.

No existing cases ship a check_extra.py, so this only enables the
hook for the new T4-T7 cases that follow.

- T4 240_NO_KP_15_SO_FD: SOC nonlocal force finite-difference (GaAs,
  nspin=4, multi-k). check_extra.py compares the analytic force with a
  central finite difference (delta=1e-3 Bohr, threshold 1e-4 eV/Bohr)
  and the acoustic sum rule. Measured max_dev ~5.8e-5 eV/Bohr.
- T4 260_NO_DJ_PK_PU_SO_4K: sign-sensitive Fe DFT+U case (4x1x1 grid
  with non-TRIM k points) with the reference regenerated for the
  e^{-ikR} fix (etot -6791.4650419973 eV). Flipping the sign back to
  +sinp shifts etot by 0.44 eV and the Fe1 force by ~4 eV/Ang, so the
  case turns red under the wrong sign.
- T5 18_NO_hyb_TDDFT: current physics checks via check_extra.py
  (zero-field current ~5e-17, full-k vs per-k DMR path deviation
  ~3e-18, +/-k cancellation 0).
- T6 260_NO_DJ_PK_PU_SO_4K_MUL: nspin=4 multi-k Mulliken calibration.
  Cross-checks Mulliken charge/magnetization against the rho cell
  magnetization (max |dev| 0.044 uB < 0.1 uB). No anomalous m_y
  deviation is present, so the B-class gemm (S^T -> S^dagger) is not
  applied.
- T7 260_NO_DJ_PK_PU_AFM_URAMPING_MUL: nspin=2 AFM spin-channel
  checks (opposite-sign Fe moments +1.92/-3.73 uB, spin1+spin2 equals
  total charge 44, small O moments, Mulliken sum vs rho cell
  magnetization).

All cases converge (SCF CONVERGED; guarded by *_converged_pass keys).
Verified with OMP_NUM_THREADS=1, mpirun -np 1: full CASES_CPU.txt run
passes 27/27 keys and T5 passes 6/6.

docs/nao_lcao_force_stress_derivation.md was added by the DMK->DMR
sign fix in Chinese; translate it to English and drop the references
to the internal Chinese planning/investigation documents (kept out of
the repo). Point the code comments in density_matrix.h and the
T1/T2/T3/T8 unit tests at the English derivation sections (Sec. 3 for
the Fourier sign, Sec. 5 for the closed-trace protection).

Comment-only changes; no behavior change.

…r-sign

Conflict resolutions (build fixes required by the merged tree):
- module_operator_lcao/test/CMakeLists.txt: ORB_atomic_lm.cpp ->
  orb_atomic_lm.cpp, matching develop's filename normalization (deepmodeling#7797)
  in the dm_trace test target sources.
- module_lr/utils/exciton_plotter.cpp: add missing 'template' keyword
  for the dependent-template call eval_wfc_bloch<T> (upstream BSE
  module, deepmodeling#7718) that fails to compile with the standard C++11 rule.

Remove docs/nao_lcao_force_stress_derivation.md and the code-comment
references that pointed at it. The conventions it documented (DMK =
(C f C†)^T storage, e^{-ikR} inverse Fourier sign, closed-trace
protection for force/stress) are already stated inline in
density_matrix.h/.cpp and the T1/T2/T3/T8 unit tests.

… doc

The check_extra.py scripts of the T4-T7 integration cases referenced
docs/dm_dmk_dmr_action_plan.md, which is intentionally kept out of the
repository. Replace those pointers with self-contained text; no behavior
change (verified with python3 -m py_compile).