[Zanthoxylum]

Summary

Unconstrained linear-response self-consistency violates the translational
acoustic sum rule on the Gamma dynamical matrix, and the Born effective
charges violate sum_a Z*_a = 0 similarly. This PR adds the standard
post-processing remedy as a new INPUT parameter dfpt_asr (default no),
applied to the RAW Gamma matrix before the LO-TO nonanalytic term, together
with the Z* sum rule, so the LO-TO term consumes the corrected charges (the
QE dynmat set_asr order). Two modes:

• simple — the legacy fix translated to our mass-reduced storage:
  D(a,a) = -sum_{b!=a} sqrt(m_b/m_a) D(a,b).
• crystal — the optimized minimal-norm fix: the symmetric projection
  D -> (1-P) D (1-P) with the orthonormal translation vectors
  w_i(3a+alpha) = sqrt(m_a) delta(alpha,i)/sqrt(sum m); zeroes every
  physical row AND column sum exactly, preserves Hermiticity and keeps
  symmetry-equivalent atoms equivalent.

Diagnostics: per-stage audit lines (raw / asr / loto) print per-atom
PHYSICAL row sums (sum_jb sqrt(m_jb) D) with the worst relative to the
matrix scale, plus an explicit correction report (worst physical rowsum before -> after | max |sum_a Z*_a| -> 0).

Tests (MODULE_DFPT_phon_serial 12 -> 17): simple and crystal zero the
physical row sums; crystal keeps Hermiticity, maps the acoustic triplet to
machine zero, and keeps symmetry-equivalent atoms equivalent (mass-equal
species); Born charges shift by the per-component mean; regression: unequal
masses + violating matrix + eps and unbalanced Z* -> after crystal + LO-TO
the acoustic triplet stays at zero.

[mohanchen]

LGTM

[ABACUS-PR-BOT]

Static review of f7c9bd39e2cd0166fd55a7664321fc0f6154d775 with independent verification: two correctness issues and two nonblocking suggestions inline. git diff --check passed; the trusted governance checker reported documentation warnings only. No build or runtime tests were run; CI diagnostics were unavailable.

Non-blocking: Please add the exact commands, configuration, and observed results behind the test claims (or explicitly mark them not run), plus a short note that the INPUT pages are generated from the updated C++ metadata by the existing documentation pipeline.

[Zanthoxylum]

Both P2 findings are fixed in 64fcadf:
P2: directional cancellation — The audit and the apply_asr report now compute per-direction residuals R(a,α,β) = Σ_b √m_b D(3a+α, 3b+β) at a fixed translation direction β, then combine norms. The cancellation pattern [[1,-1,0],[-1,1,0]] is detected by the new AsrDirectionalCancellationDetected regression.
P2: Hermitian re-symmetrization breaks simple — Root cause: the onsite dump can write complex values on the diagonal (the j > i symmetrization loop leaves the diagonal untouched), producing a non-Hermitian input to the crystal projection whose result is then non-Hermitian; the shared re-symmetrization halves the correction back (the review's ±δ/2 example). Fix: (1) take the real part of the diagonal after the onsite dump, making the input genuinely Hermitian; (2) finish with the crystal projection, which now gives an exact Hermitian matrix satisfying all three translation constraints. New regression AsrSimpleCrossCartesianRegression checks translations exact + Hermiticity + real diagonal with cross-Cartesian coupling and unequal masses.
The two non-blocking notes are also addressed: the header doc now states the translation vectors as √m_a·δ(α,i)/√(Σm) and describes simple as an onsite-block correction with a projection finish; run_assemble performs a single eigensolve after any applicable correction instead of diagonalizing non-Gamma matrices twice.