Capability Matrix

The table below summarises the verification and validation status of each solver capability in the package.

Stable solvers have been verified (convergence studies, manufactured solutions) and validated against published benchmarks. Suitable for publication-grade results.
Provisional solvers have automated verification but incomplete V&V coverage. Suitable for internal research and method development.
Tooling features (I/O, dashboards, checkpointing) support the research workflow but are not part of the solver V&V.
The "V&V Coverage" column lists the verification stages that must be present in the validation manifest for a feature to be considered fully verified.

Capability	Category	Maturity	Validation Status	V&V Method	Solver Family	V&V Coverage	Notes	Limitations
`amr`	`claim_bearing_solver`	`provisional`	`internal_research_only`	`convergence_verified`	`amr`	verification, benchmark, invariant	Block-structured AMR with smooth-transport convergence, adaptive reference tracking, and conservative regridding checks.	AMR remains provisional because shock-dominated AMR tutorials and broader nonlinear benchmark families are not yet promoted into the automated evidence ladder.; Current AMR claim scope is limited to the smooth transported-pulse and conservative regridding cases listed in the validation manifest.
`coupling`	`claim_bearing_solver`	`provisional`	`internal_research_only`	`convergence_verified`	`coupling`	verification, benchmark, invariant	Operator-split hyperbolic plus stiff-source coupling with identity verification, smooth reference tracking, and mass-momentum conservation checks.	Coupling remains provisional because the automated evidence currently covers operator-split hyperbolic plus local stiff-source cases, not broader multiphysics workflows.; Current claim scope is limited to the NullSource identity, smooth advection-cooling reference benchmark, and periodic mass-momentum conservation cases listed in the validation manifest.
`dashboard`	`research_support_tooling`	`experimental`	`reproducibility_infrastructure_only`	`smoke_tests`	`research_tooling`	n/a	Dashboard export and WebSocket monitoring utilities with compatibility and smoke tests.	Dashboard functionality is reproducibility infrastructure and does not constitute scientific solver validation.; Web UI behavior remains experimental and should not be treated as a stable research interface contract.
`hyperbolic`	`claim_bearing_solver`	`stable`	`publishable_scientific_claim`	`convergence_verified`	`hyperbolic`	verification, benchmark, invariant	1D and 2D cell-centered hyperbolic solvers with MMS convergence verification and analytical benchmarks.	Publication-grade claims are limited to solver configurations and benchmarks listed in the validation manifest.; Advanced reconstruction, stiff-source, and multidimensional options outside the evidence ladder remain configuration-sensitive.
`io_extensions`	`research_support_tooling`	`experimental`	`reproducibility_infrastructure_only`	`targeted_tests`	`research_tooling`	n/a	Optional JLD2 checkpointing and HDF5 solution I/O with round-trip integrity checks.	I/O extensions are treated as reproducibility tooling; they do not expand the package's scientific validation claims.; Optional extensions still require explicit dependency opt-in and should remain experimental until broader archival compatibility is exercised across more workflows.
`mhd_ct`	`claim_bearing_solver`	`stable`	`publishable_scientific_claim`	`convergence_verified`	`mhd_ct`	verification, benchmark, invariant	2D MHD with constrained transport and divergence-preservation checks.	Publication-grade claims are restricted to constrained-transport configurations covered by automated evidence.; Resistive, Hall, and other extended MHD variants require additional feature-specific validation before strong claims.
`parabolic`	`claim_bearing_solver`	`stable`	`publishable_scientific_claim`	`convergence_verified`	`parabolic`	verification, benchmark, invariant	Cell-vertex parabolic and elliptic solvers with executed tutorials and convergence checks.	Publication-grade claims are limited to cases explicitly covered by the validation manifest.; Reference evidence is established on CPU Float64 runs; other execution modes require separate parity checks.
`relativistic`	`claim_bearing_solver`	`stable`	`publishable_scientific_claim`	`convergence_verified`	`relativistic`	verification, benchmark, invariant	SR/GR hydro and MHD solvers verified with eigenmode convergence and asymptotic reduction tests.	Publication-grade claims are limited to relativistic cases explicitly listed in the validation manifest.; Metric choices, recovery procedures, and problem setups outside the evidence ladder remain research-use-only until separately validated.