T25 — Split factorization: tiled SYRK, chunked TRSM, split regime-C fronts #25

Task T25 of TASKS.md — milestone M11 — Performance. (Rescoped on 2026-10-09: the former "performance pass" is split into T22, T24, T25 and T26, see STATE.md §8.)

Depends on: #24 (T24) must be merged first; tasks are strictly sequential.

Summary (from TASKS.md): adopt bench/fact_split.jl (PR #107): for fronts with m > 64 the fused regime-B kernel's SYRK and TRSM become separate many-block kernels (tiled 32×32 SYRK with disjoint writes, bit-identical; chunked TRSM); regime-C fronts narrower than 64 run the regular assembly kernels plus the split factor kernels batched per level, vendor potrf only above width 64; longest-first regime-A launches; regime_c_rows re-measured together with T24's solve. LDLᵀ must not regress. Report: refactorization table vs cuDSS with the per-class split.

Scope and deliverables: the section T25 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 T25: … from branch task/T25-<slug> with Closes #25 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).