feat(#162): use exponential action for relaxation trajectories

[marcohost33-maker]

Summary

Stacked on PR #174, which establishes the fail-closed trajectory-domain contract. This PR changes only the propagation method and adds backend/audit evidence.

SciPy documents scipy.sparse.linalg.expm_multiply as computing the action exp(tA) B directly, with an interval API for evenly spaced times. LiouScope now uses that action instead of materialising the full dense expm(tL) matrix.

Backend contract

• exact NumPy-linspace grids -> one expm_multiply(..., start, stop, num) interval call;
• arbitrary/non-uniform/two-scale grids -> independent actions from the same initial state, avoiding stepwise error accumulation;
• exact t=0 state is restored explicitly;
• low-level propagation accepts both dense and SciPy sparse matrices;
• top-level diagnose() remains dense-only: this PR does not claim sparse-native orchestration or sparse steady-state solving.

Fail-closed preservation

PR #174 remains the prerequisite. Before entering the action algorithm LiouScope checks that L*t and its 1-norm are representable. Runtime failures or non-finite action outputs raise UnrepresentableTrajectoryError. The astronomical #156 fixture is therefore still a domain refusal rather than a hang/NaN.

No physics cutoff is introduced: the preflight refuses only non-finite represented entries or an unrepresentable mathematical 1-norm.

Numerical audit

RelaxationResult gains additive/defaulted fields:

• trajectory_backend;
• trajectory_max_trace_error;
• trajectory_max_hermiticity_defect;
• trajectory_min_eigenvalue.

These are measurements, not repair operations. Negative positivity drift is recorded; no eigenvalue clipping is performed.

Discrimination

• dense action vs former scipy.linalg.expm(L*t) @ rho0 reference on uniform and non-uniform grids;
• sparse vs dense propagation;
• exact linspace interval-path selection and exact t=0;
• non-uniform pointwise-path selection;
• rate-unit metamorphism L -> cL, t -> t/c;
• trace/Hermiticity/min-eigenvalue trajectory audit;
• inherited fix(#127): handle zero-resolution and unrepresentable propagation limits #156 non-representability tests under the action backend;
• manual benchmark benchmarks/issue162_expm_action.py runs full dense expm and action in separate processes, reporting elapsed time, peak RSS and relative error.

Scientific / release impact

This is a numerical methodology change, not a mathematical-model change. Floating-point trajectories can move at round-off level relative to full dense expm, so README / CHANGELOG / CITATION are updated. No D1-D24 definition, classifier threshold, manifest field or schema changes.

Dependency

Must not merge before #174. Once #174 is integrated, this stack should be rebuilt/rebased non-destructively from then-current main if required by base movement.

Test plan

• focused Trajectory backend: use matrix-exponential action instead of materialising expm #162 tests
• inherited fix(#127): handle zero-resolution and unrepresentable propagation limits #156 representability tests
• anchors
• ruff
• mypy
• full pytest Python 3.10-3.14 proposed-merge + exact-head
• QuTiP proposed-merge + exact-head
• Quality Contract
• CodeQL
• reusable CI
• zero unresolved review threads

Refs #156. Closes #162 when merged after #174.