T24 — Partitioned-inverse fused solve (solve_alg = "algo1", issue #82 solve half) #24

Task T24 of TASKS.md — milestone M11 — Performance. (Renamed on 2026-10-09: the ND partition-tree task moved to T30, see STATE.md §8.)

Depends on: #23 (T23) must be merged first; tasks are strictly sequential.

Summary (from TASKS.md): adopt the PR #107 solve prototype (bench/solve_proto_*.jl): per-front L₁₁ inverses turning every TRSV into a GEMV, one fused dependency-counter kernel per direction for fronts of width ≤ 256 (atomic-free variant kept), strategy chosen per schedule (it regresses on lap3d_40 and apache2), Cholesky and LDLᵀ, nrhs > 1; every solve suite repeated under "algo1" with a residual gate; Report: solve table vs the cuDSS baseline. Refs #82.

Scope and deliverables: the section T24 of TASKS.md on main is the single source of truth; it is not copied here so it cannot drift.

Definition of done:

• Every test listed in the task passes on the KA CPU backend and on the CUDA self-hosted runner (Run tests and Aqua 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 T24: … from branch task/T24-<slug> with Closes #24 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).