[antonsoo]

Multiplying a batched low-rank-plus-diagonal covariance by per-model positive scalars raises Boolean value of Tensor with more than one value is ambiguous in _mul_constant.

Use (other > 0).all(), matching the root operator's guard. All-positive batch factors keep LowRankRootAddedDiagLinearOperator and its efficient solves. Any nonpositive factor still uses the existing AddedDiagLinearOperator fallback.

Regression tests compare broadcast scaling and root/diagonal/scale gradients with dense arithmetic for one and two batch dimensions, assert the specialized type is retained, and cover a zero-factor fallback.

Validation:

• Full suite: 5,048 tests pass on both PyTorch 2.0 CPU (Python 3.10) and PyTorch 2.14 CPU (Python 3.12).
• Recorded Diabetes-feature covariance workloads: all 64 batch-scale cases fail before and complete afterward across CPU/CUDA, float32/64, sizes 32-128 and ranks 4/8. Values and gradients agree with dense PyTorch calculations; worst float32 relative error is 3.0e-6, float64 below 5.6e-15. Ordinary matrix/scalar controls are byte-identical across sources.
• Eight 15-step, three-model likelihood-training runs now complete and track independent dense Adam runs (worst float32 absolute trajectory difference 1.1e-3, final-parameter relative difference 2.4e-6). This does not assert bitwise optimizer-state parity or predictive improvement.
• Configured pre-commit hooks, full flake8 and warnings-as-errors Sphinx build pass.

This fixes the specialized low-rank-plus-diagonal implementation; the block-operator scaling in #136 does not resolve it.