T19 — General LU ("G"): CPU reference + GPU #19

Task T19 of TASKS.md — milestone M7 — General LU (LDU).

Depends on: #18 (T18) must be merged first; tasks are strictly sequential.

Summary (from TASKS.md): Symmetric-pattern multifrontal LU with U panels, in-block threshold partial pivoting (A/B) and getrf! + laswp! + post-check (C), perm_row/col, solve_mode 1/2, lu/lu!; ported CUDSS.jl unsymmetric tests and the uniform-batch LU tests pass; random_general residuals ≤ tol(T).

Scope and deliverables: the section T19 of TASKS.md on main is the single source of truth; it is not copied here so it cannot drift. Read it together with the PLAN.md sections it names and the Report blocks of the previous tasks.

Definition of done:

• Every test listed in the task passes on the KA CPU backend (GitHub runner) and on the CUDA/AMDGPU self-hosted runners (Run tests and Aqua checks green on the PR).
• The task's status marker in TASKS.md is set and its Report block is filled in honestly (CUDA counts come from CI).
• A PR titled T19: … from branch task/T19-<slug> with Closes #19 in its body, reviewed by the Claude reviewer with VERDICT: APPROVE.
• Out-of-scope bugs or follow-ups found on the way are opened as separate issues (label found-by-agent), not fixed silently.

How it starts: add the label claude:implement (the pipeline does this automatically after the previous task's PR merges; label on-hold to prevent that).

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