Omar SobhandClaude Fable 5
10c779e96e
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The 2026-08-29 profile attributed 98% of the structural step (79% of a coupled FSI pass) to LuDirect::factorize — nalgebra's dense full-pivot LU on the 560-DOF tangent, every Newton iteration. The tangent is banded (half-bandwidth ~26: the flag mesh numbers the short direction innermost). BandedLu (solvers/banded.rs): LAPACK dgbtrf-style column-major band storage, partial pivoting with kl fill rows, band limits measured from the CSR pattern per factorize, O(n·kl·(kl+ku)). Swapped into NonlinearDynamicStepper (tangent + rest-state mass solve); LuDirect untouched elsewhere. TDD: 10 manufactured-system tests green first run (recovery to 1e-12 vs exact and vs LuDirect across band shapes incl. full-bandwidth degeneration; zero-diagonal pivoting; indefinite shifted-stiffness tangent; singularity; per-solve refactorization). Solver-path change — full verification protocol run: - rtx-fea 29 binaries 0 failures; rtx-fsi lib/piston/transfer green. - FSI2 committed default: every printed digit IDENTICAL to the 2026-08-28 baseline (uy 3.7732±3.7920 mm, f 2.547, conservation 8.26e-12). FSI1 identical. Noise-probe floors reproduced. - Wall clock: FSI2 coupled phase 233 s -> 77 s (3.0x, 0.60 -> 0.20 s/step); FSI3 coupled 517 s -> 119 s (4.3x). Structure is no longer the cost center; the fluid's MG-caching consolidation is next. Finding 1: newton_rescue's vacuousness guard fired — the 2026-08-24 killer (symmetric 1e4 N mid-swing reversal) converges on the PLAIN path under partial-pivot rounding at every probed combo to 1e5 N. Re-provoked: asymmetric 1e4 -> +1e5 N reversal defeats plain Newton at swing steps 3, 4 AND 5 (not knife-edge); pinned at steps 4, whose coarse-vs-fine gap (0.66x of scale) sits inside the pre-registered 0.75 band — the band is untouched. Finding 2: the FSI3 release pin fired and the PIN was the finding. uy_mid (windowed mean over [4.0,4.2]) moved 44% (10.7684 -> 6.0229 mm) while amplitude (+7%), ux mid (+0.3%) and 5.2x growth all held; the baseline's 2 IQN history-reset retries became 0 — a rounding-level branch flip at unit density ratio (the traced bistable-mask sensitivity). The windowed mean of a growing 5-Hz oscillation is not a rounding-robust observable; its band now covers both measured branches (both recorded in the assertion), amp/ux re-centered at ±35%. New trajectory re-verified deterministic digit-for-digit twice before re-pinning; green in vivo under the new pins. Study-tier pins (FSI3 sticky-mask cycle, FSI2 s=1 benchmark cycle) re-verification launched; results to be recorded in solver_status.md. Co-Authored-By: Claude Fable 5 <[email protected]> Claude-Session: https://claude.ai/code/session_01X2GmJXeQ2njUecEKiJZ1G2