Fix transverse refinement and transition-state acceptance

[spraharsh]

Transition-state refinement can step along its excluded reaction mode after the projection changes because transverse L-BFGS retains history from the old plane. It can also accept stationary points with additional downhill directions.

Preserve L-BFGS history when the normalized excluded direction stays the same, including sign flips. Reset it when the plane changes, restoring the caller's configured initial H0. Global L-BFGS reset behavior and optimizer implementations are unchanged.

Before accepting a candidate, require a converged negative primary eigenpair and screen the remaining physical space with two iterative searches. Use an independent private generator that advances between screens; index_seed makes its starts reproducible without consuming the global NumPy stream used by the primary search. Keep the two searches, fixed history and linear workspace. A passing screen is probabilistic and can still miss a negative mode; it is not an exhaustive index-one certificate. No dense Hessian or growing spectral basis is added.

For unit eigenvectors, the old fixed RMS stopping threshold becomes increasingly permissive with dimension. The default secondary-search RMS tolerance is now 1e-5 / sqrt(ndof), giving a dimension-independent gradient-norm threshold. An explicit lowestEigenvectorQuenchParams["tol"] retains its existing RMS meaning. Force and test-comparison tolerances are unchanged. Cold secondary searches retain the eigenvector solver's existing 500-step default; explicit budgets and the warm primary search's default are preserved.

When the screen finds a second negative physical mode, displace downhill along it and continue within the existing outer budget. Unconverged or ambiguous checks return failure. Central gradient differences check the primary curvature and the detected negative pair; all evaluations and returned state remain consistent.

Accounting tests refine a physically perturbed existing LJ18 saddle instead of assuming arbitrary random starts always converge. Transition-state and connection tests explicitly seed both their legacy initialization and private probe starts. The generalized-dimer tests retain their own initialization seed. All success, evaluation-count and iteration assertions remain intact. Deployment notes document arithmetic differences; the solver documentation describes the probabilistic screen.

Validation:

• Review-fix local non-GUI Python suite: 609 passed, 9 skipped, 2 subtests passed, using existing compiled extensions. The single-threaded run used a guard that stops at 88% system memory use; no local native build was needed.
• New regressions first reproduced the four-dimensional mode missed by the old fixed guesses, premature positive convergence on a seeded 4,096-dimensional weak-curvature problem, trajectory changes on unchanged/sign-flipped planes, and loss of configured H0. After the fixes all passed. Existing tests cover index-two rejection/recovery, constraints, one dimension, a stiff index-one candidate, exact evaluation counts and independent physical Hessians for stored connection saddles.
• Seeded gradient-only quadratics retain O(n) workspace. At 262,144 dimensions the old RMS rule missed two negative modes among 16 cases; the scaled rule detected all 16. At 4,096 dimensions with weaker curvature the old rule missed four of eight; the scaled rule detected all eight. Across the 72 sampled models the scaled rule detected every negative mode, without non-convergence. These examples support the stopping correction; they do not establish a per-million failure rate.
• Earlier macOS traces reproduced the added 100-step verification cap rejecting valid saddles: fixed-coordinate replays needed 103 steps on Apple Silicon and up to 117 on Intel. The added cap was removed in favor of the existing 500-step default.
• The Intel Python 3.12 trajectory trace recorded 44 searches and 1,064 primary snapshots with no curvature-sign misclassification and exact counts. Four searches correctly returned failure. The older CI failure's exact coordinates were not logged, so this reproduced its abort pattern rather than its exact trajectory.
• The separate Intel alignment probe showed byte-identical projected vectors producing norms one ULP apart at different memory addresses, propagating into curvature and gradient results. NumPy reports Accelerate; PELE separately loads OpenBLAS. Temporary probes stay outside this PR.
• Review-fix native CI passed all six jobs on b2ea75df: Linux and macOS source suites each passed 618 tests / 4 skipped / 2 subtests; installed-package suites each passed 609 tests / 13 skipped / 2 subtests; both C++ suites passed.
• The full portable-wheel matrix passed on b2ea75df: all 12 Linux x86_64, macOS Intel and macOS Apple Silicon wheels for Python 3.11–3.14 each passed 609 tests / 9 skipped / 2 subtests. The source distribution passed, all artifacts uploaded, and PyPI/TestPyPI publishing was skipped.
• The subsequent f97d6667 commit changes only RELEASING.md; implementation and tests are byte-identical to b2ea75df. Its native CI passed all six jobs. GitHub automatically started another wheel run, which remains in progress.

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[spraharsh]

Adding tracers to make CI run. because there's that strange bug that pops up only on MacOSX and I can only debug via the CI runners

[spraharsh]

@codex review

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Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-10-12T00:31:55.382339Z	800e5ec	Manual request

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