Solvers & preconditioners

Solvers & preconditioners · 159

Iterative, direct, eigen, optimization, and time-integration solvers with determinism goldens and failure taxonomies. Method shown on hover; tolerance is the pass gate. back to QA

Case	Tier	Reference	Gate
`solvers.eigen-checked-boundary.v1`	physics-gate	independent 2x2 symmetric eigenvalues and checked malformed-input admissions	finite valid result; malformed dimension and non-finite input rejected
`solvers.iterative-contracts.v1`	smoke	known-system residual and cross-solver agreement	1e-6 to 1e-8, case-defined
`solvers.nonlinear-generated-residual.v1`	solver-gate	canonical NewtonError NumericalError and SolverFailure metadata	5/5 generated-output cases report NumericalError and NotChecked accuracy, including one malformed trial shape and two Jacobian matvec failures
`solvers.optimization-contracts.v1`	smoke	analytic sphere/Rosenbrock minima and unit-circle equality	8/8 contracts pass: objective, distance-to-optimum, feasibility, and cross-solver consistency
`solvers.optimization-status.v1`	smoke	shared SolverStatus and AccuracyStatus vocabulary	16/16 canonical status/accuracy/generated-callback contract cases pass
`solvers.optimization-epsilon-kkt.v1`	solver-gate	every converged epsilon subproblem carries a finite original-problem KKT report	pareto_points=5; kkt_report_cases=5; missing_kkt_reports=0; finite_objective_values=1; maximum KKT norm <= 1e-3
`solvers.optimization-bobyqa.v1`	solver-gate	analytic quadratic minimizers and typed OptimError::NumericalError	coordinate error <= 2e-4; objective <= 1e-7; converged_status_contract=3; deterministic gaps = 0; generated_nonfinite_rejections >= 1
`solvers.optimization-line-search-boundary.v1`	solver-gate	canonical SolverStatus::NumericalError result contract	9/9 invalid-input cases report NumericalError with zero evaluations
`solvers.optimization-line-search-generated-output.v1`	solver-gate	canonical SolverStatus::NumericalError and AccuracyStatus::NotChecked	3/3 generated-output cases report NumericalError before a later trial can be accepted
`solvers.optimization-ipm-state.v1`	smoke	independent primal/dual/complementarity/KKT recomputation	3/3 IPM state diagnostics cases pass, including typed infeasible restoration failure with finite diagnostics; native multiplier errors < 1e-6
`solvers.direct-contracts.v1`	smoke	analytical SPD/indefinite solutions and typed singular rejection	direct errors <= 1e-12; dimension/non-finite/configuration rejection and checked ILU identity application counts >= 1
`solvers.direct-scalar-execution.v1`	smoke	analytic solutions [1, 2] for real and complex32 fixtures	f32 and Complex32 solution/residual errors <= 2e-5
`solvers.robustness-metamorphic.v1`	smoke	complex inner-product identities, true residuals, block-vs-column solution parity, warm-vs-cold block-GMRES residual parity, numeric replay seed, checked plan rejection, typed scalar/block/GMRES-DR/recycled/mixed-precisi	all identity and metamorphic solution errors <= 1e-10; residuals <= 1e-8; block-vs-column checks = 2; warm-vs-cold checks = 2; replay_seed = 20260819; eight plan formats reject invalid inputs; scalar/
`solvers.time-integration-contracts.v1`	smoke	analytic displacement cos(t) and velocity -sin(t)	Newmark and explicit displacement errors <= 2e-4; finite and non-finite adjoint statuses; initial, callback-panic, at least two generated-output, four implicit callback-attribution, and at least two m
`solvers.preconditioner-contracts.v1`	smoke	exact identity application and typed checked-boundary rejection plus self-adjoint AMG forward/Hermitian parity	three constructions/applications, three checked rejection categories, two AMG adjoint capability checks, one exact Hermitian action, residual <= 1e-10
`solvers.amg-diagonal-adjoint.v1`	solver-gate	exact capability metadata, forward/transpose/Hermitian action parity, and independently recomputed Hermitian inner-product identity	2 exact capability checks; action and inner-product errors <= 1e-12
`solvers.preconditioner-setup-diagnostics.v1`	solver-gate	aggregate pivot/non-finite diagnostics, checked-constructor rejection, and finite spectral-bound admission	minimum pivot finite positive; ILUT and block generated non-finite count >= 1; checked rejection, GenEO fallback, typed checked GenEO rejection, and Chebyshev/host/backend AMG generated-value rejectio
`solvers.preconditioner-runtime-diagnostics.v1`	solver-gate	runtime call counters, coarse correction count, setup provenance, and typed failure counters	exact deterministic counters; zero coarse-solve failures; non-finite checked inputs rejected
`solvers.preconditioner-partition-boundary-matrix.v1`	solver-gate	independent partition ownership and coverage oracle	five plain and five ORAS malformed cases reject; valid plain and ORAS cases accept
`solvers.convergence-spectrum.v1`	smoke	known manufactured solutions and solver status semantics	1e-10
`solvers.eigen-laplacian-reference.v1`	smoke	closed-form eigenvalues 4 h^-2 sin^2(k pi / (2(n+1)))	eigenvalue error <= 1e-6; residual norm <= 1e-8
`solvers.eigen-complex-generalized-reference.v1`	smoke	known diagonal ratios of an independent complex generalized pencil	eigenvalue error <= 1e-7; relative residual <= 1e-7; dimension_rejection = 1
`solvers.eigen-generalized-reference.v1`	smoke	known diagonal ratios of an independent SPD generalized pencil	eigenvalue error <= 1e-9; relative residual <= 1e-9
`solvers.iterative-independent-reference.v1`	physics-gate	independent dense Gaussian-elimination reference	reference and independent residual errors <= 1e-10
`solvers.iterative-family-reference.v1`	physics-gate	independent dense Gaussian-elimination and diagonal MINRES references	all solution and independently recomputed residual errors <= 1e-10
`solvers.iterative-extended-reference.v1`	physics-gate	independent dense partial-pivot references for TFQMR and CA-CG	all independently recomputed errors and residuals <= 1e-10
`solvers.iterative-failure-matrix.v1`	smoke	independent checked iterative failure/status matrix	all 60 failure fixtures reject or return a non-converged checked status
`solvers.iterative-breakdown-matrix.v1`	smoke	independent checked iterative breakdown/non-convergence matrix	all 24 fixtures reject or return finite non-converged checked status
`solvers.iterative-breakdown-matrix.v2`	smoke	independent typed failure-exit oracle	all 10 methods return typed non-converged status; breakdown statuses reported separately; panic_free=1
`solvers.adaptive-failure-matrix.v1`	solver-gate	independent typed failure and serialized caller-state oracle	all five failure metrics, state_unchanged, and panic_free equal one
`solvers.preconditioner-failure-contract.v1`	smoke	shared SolverFailure status and accuracy vocabulary	all seven mappings match NumericalError and NotChecked
`solvers.iterative-result-contract.v1`	smoke	checked scalar/block and adaptive/recycled/deflated wrapper result status and accuracy contract	all status/accuracy and family-contract metrics equal one
`solvers.iterative-block-result-contract.v1`	solver-gate	independent block GMRES/FGMRES numerical-error contract fixtures	all block result-contract metrics equal one; negative-diagnostic rejections = 3
`solvers.facade-result-contract.v1`	physics-gate	identity solve and typed public facade rejection matrix	ten result/error/status/accuracy checks pass
`solvers.extended-result-contract.v1`	smoke	checked cross-family solver result and failure-taxonomy contract	all extended result-contract metrics equal one
`solvers.optimization-result-contract.v1`	smoke	checked line-search, Pareto, and QP result contracts	all optimization result-contract metrics equal one
`solvers.optimization-differential-reference.v1`	physics-gate	independent translated diagonal quadratic minimizer and objective recomputation	both optimizers converge; coordinate error <= 1e-7; independently recomputed objective <= 1e-12
`solvers.iterative-scalar-contract.v1`	smoke	independent scalar-family iterative result-contract fixtures	all scalar-family status, accuracy, and numerical-error metrics equal one
`solvers.iterative-scalar-execution.v1`	physics-gate	independent partial-pivot dense solve from deterministic known-solution fixtures	all scalar-family reference errors and independently recomputed relative residuals remain within f32/Complex32 1e-4 or f64/Complex64 1e-12
`solvers.compatibility-scalar-execution.v1`	physics-gate	independent partial-pivot dense references and CSR residuals	f32/Complex32 <= 1e-4; f64/Complex64 <= 1e-12
`solvers.checked-dense-constructor.v1`	smoke	independent checked dense-to-CSR admission and thresholding	three constructor checks non-finite admission pass
`solvers.compatibility-failure-matrix.v1`	smoke	independent typed dimension/non-finite/configuration failure classification	24 typed failure classifications pass before iteration
`solvers.direct-compatibility-normalization.v1`	physics-gate	known-solution CSR residuals, dimension/input rejection, status normalization, and transactional destination preservation	eighteen direct normalization and failure-boundary checks pass
`solvers.direct-result-contract.v1`	physics-gate	finite direct result status/iteration metadata plus dense backward-error gate	all result-contract checks pass; real and complex solution errors <= 1e-12; backward error <= 1e-12
`solvers.lu-transpose-transactional.v1`	physics-gate	typed numerical-breakdown attribution and unchanged caller destinations	typed transpose/adjoint failures and destination preservation equal one
`solvers.cholesky-transactional.v1`	physics-gate	typed numerical-breakdown attribution and unchanged caller destination	typed failure and destination preservation equal one
`solvers.operator-combinator-boundaries.v1`	physics-gate	typed shape/scratch rejection, valid composed matvec, callback panic containment, finite-output and adjoint admission	all boundary metrics equal one; valid composition output is exact
`solvers.saddle-point-contract.v1`	physics-gate	independent dense partial-pivot solution, residual, assumption metadata, and failure classification	reference and residual <= 1e-8; five contract checks
`solvers.compatibility-cg-execution.v1`	physics-gate	independent partial-pivot dense reference and CSR residual	f32/Complex32 <= 1e-3; f64/Complex64 <= 1e-11
`solvers.iterative-block-workload-reference.v1`	solver-gate	independent partial-pivot dense solve and residual; scalar GMRES differential	solution error <= 5e-8; independently recomputed relative residual <= 5e-10
`solvers.direct-scalar-method-reference.v1`	smoke	analytic solutions [1, 2], [1+0i, 2+0i], and [2, -1] least-squares fixture	all six solution/residual metrics <= 1e-12
`solvers.multifrontal-ldlt-reference.v1`	smoke	analytic exchange-system solution, independently constructed Hermitian RHS/solution, independently recomputed residuals, and typed malformed-input/non-finite-RHS rejection	real/complex solution and residual errors <= 1e-12; 2x2 pivot and two typed rejection checks >= 1
`solvers.multifrontal-blr-config.v1`	solver-gate	independently recomputed CSR residuals for BLR and LDLT across scalar families and a seeded SPD matrix bank, plus typed InvalidConfiguration for finite f64 values that overflow selected f32 configuration fields	4 scalar-family checks; 16 matrix-bank checks; 4 overflow rejections; maximum relative residual <= 3e-5
`solvers.conformance-matrix.v1`	smoke	checked-in conformance records with independent or cross-checked evidence for every row	at least 35 unique rows; zero incomplete or documented-only rows
`solvers.factor-solve-reference.v1`	smoke	analytic/deterministic-fixture:solvers-factor-solve-v1	all reported errors <= 1e-12; finite-RHS numerical failure preserves the destination and reports transactional_block_failure=1
`solvers.differential-reference.v1`	smoke	independent/deterministic-fixture:solver-differential-reference-v1	dense/sparse reference error <= 1e-11; GMRES reference error <= 1e-9; independent residual <= 1e-10
`solvers.factor-solve-properties.v1`	smoke	analytic/deterministic-fixture:factor-solve-properties-v1	f32 final residual <= initial + 1e-6 and <= 1e-5; permutation error <= 1e-11; Complex32 errors <= 1e-5; Complex64 HPD/indefinite errors <= 1e-12
`solvers.direct-breakdown-matrix.v1`	smoke	independent/deterministic-fixture:direct-breakdown-matrix-v1	dense/sparse singular LU, rank-deficient dense QR, and non-SPD Cholesky all reject; panic_free=1
`solvers.eigen-breakdown-matrix.v1`	smoke	independent/deterministic-fixture:eigen-breakdown-matrix-v1	one-step result is non-converged or typed failure; result contract valid; panic_free=1
`solvers.differentiable-checkpoint-replay.v1`	smoke	independent/deterministic-fixture:differentiable-checkpoint-replay-v1	all determinism/cancellation metrics equal one; every checkpoint payload non-empty
`solvers.sparse-lu-parallel.v1`	solver-gate	analytic/deterministic-fixture:sparse-lu-parallel-v1	maximum solution error and residual <= 1e-10
`solvers.sparse-lu-permutation-parallel.v1`	solver-gate	analytic/deterministic-fixture:sparse-lu-permutation-parallel-v1	maximum solution errors and residual <= 1e-10
`solvers.sparse-lu-adjoint-block.v1`	solver-gate	independent dense transpose/Hermitian action and known-solution residual oracle	two factor classes; maximum solution/residual error <= 1e-10; two non-finite rejections and two preserved destinations
`solvers.sparse-lu-adjoint.v1`	solver-gate	analytic/deterministic-fixture:sparse-lu-adjoint-v1	maximum solution error and residual <= 1e-10
`solvers.sparse-cholesky-adjoint.v1`	solver-gate	analytic/deterministic-fixture:sparse-cholesky-adjoint-v1	maximum solution error, residual, and real adjoint error <= 1e-10
`solvers.factor-solve-complex-permutation.v1`	smoke	analytic/deterministic-fixture:solvers-factor-solve-complex-permutation-v1	all six solution and residual errors <= 1e-11
`solvers.validation-corpus.v2`	smoke	checked-in sonium-solvers validation corpus and property suite	at least 12 fixtures, at least 6 adversarial, zero invalid/missing rows
`solvers.optimization-kkt-reference.v1`	smoke	analytic/deterministic-fixture:solvers-optimization-kkt-v1	feasibility <= 1e-4; stationarity and KKT norm <= 1e-3; one active upper bound
`solvers.optimization-kkt-matrix.v1`	solver-gate	independent recomputation of primal feasibility, dual feasibility, stationarity, complementarity, and active-set classification	ten runs; independent and reported KKT norms <= 2e-5; active-set classifications exact
`solvers.optimization-kkt-gate-family.v1`	solver-gate	each converged result must carry a finite independently recomputed KKT report within the public success gate	seven reports; missing_kkt_reports=0; nongated_successes=0; maximum KKT norm <= 1e-2
`solvers.optimization-scaled-kkt.v1`	solver-gate	independent gradient, active-set, multiplier, and stationarity oracle	twelve converged cases including seeded_case_count=8; exact active sets; overall and seeded KKT/stationarity <= 3e-5
`solvers.validation-corpus-reference.v2`	smoke	analytic/deterministic-fixture:solver-corpus-reference-v2	direct and block metrics <= 1e-12; real and complex ILU-preconditioned metrics <= 1e-10; rank-deficient rejection equals one; positive factor workload metrics
`solvers.validation-corpus-workloads.v1`	solver-gate	analytic known-solution vectors with independently recomputed true residuals	solution and true residual errors <= 1e-10; exact 16-dof/46-nnz admission
`solvers.matrix-market-parser.v1`	solver-gate	independent known solution and canonical CSR action	solution/residual/action errors <= 1e-10; exact symmetry/pattern/Hermitian counts; malformed rejection equals one; shared contract error <= 1e-12
`solvers.failure-exit-matrix.v1`	smoke	typed rejection contract and failure taxonomy	8/8 rejection cases; zero unexpected successes
`solvers.external-differential-reference.v1`	solver-gate	PETSc 3.x live residual and iteration record	both residuals <= 1e-8; residual gap <= 1e-8; iteration deltas are diagnostic only
`solvers.compatibility-method-matrix.v1`	solver-gate	known solution vectors and typed wrong-guess rejection	f64 solution/residual/backward error <= 1e-10; f32/Complex32 residual <= 1e-5; 15 contract checks
`solvers.fem-bem-workload.v1`	solver-gate	production assembly paths with independently recomputed true residuals	all true relative residuals <= 1e-7; FEM nodal plane-wave error <= 1e-2; timing metrics non-negative
`solvers.optimization-scipy-reference.v1`	solver-gate	live SciPy 1.x optimization result on identical objective and analytic gradient	both external methods converge; Sonium/SciPy coordinate errors <= 1e-7; cross-method gap <= 1e-6
`solvers.gmres-checkpoint-reference.v1`	solver-gate	analytic 3x3 SPD matrix with two independent known RHS solutions	solution, round-trip, and independent residual errors <= 1e-10; serialized size and iteration metrics finite
`solvers.gmres-basis-checkpoint.v1`	solver-gate	analytic 4x4 tridiagonal SPD matrix and independent matvec	solution, round-trip, and independent residual errors <= 1e-9; checkpoint and iteration metrics finite
`solvers.gmres-basis-checkpoint-scalars.v1`	solver-gate	analytic 4x4 tridiagonal SPD matrix with independent scalar-family replay	solution/residual errors <= 1e-3; two cross-family restores rejected
`solvers.gmres-basis-checkpoint-adaptive.v1`	solver-gate	analytic 4x4 tridiagonal SPD matrix with deterministic adaptive-restart replay	solution/residual errors <= 1e-9; restart bounds and iteration metrics finite
`solvers.gmres-basis-operator-boundary.v1`	solver-gate	analytic 4x4 SPD matrix with deterministic callback-counted failure	operator failure is GMRES basis replay operator and final-residual callback count is exactly four
`solvers.differentiable-block-adjoint.v1`	solver-gate	analytic symmetric 3x3 matrix with independent forward/adjoint block solutions	solution errors and true residuals <= 1e-9; continuation iteration counts = 0; continuation_contract >= 1
`solvers.differentiable-continuation.v1`	solver-gate	analytic symmetric 3x3 matrix scalar differentiable continuation	residuals and solution deltas <= 1e-9; continuation iteration counts = 0
`solvers.differentiable-lifecycle-contract.v1`	solver-gate	analytic deterministic callback lifecycle with independent family and dimension checks	error metrics <= 1e-12; replay evaluations equal two; cancellation rejections equal four; scalar mid-iteration cancellation equals one; block mid-iteration cancellation equals one; generated-output/re
`solvers.differentiable-taylor-replay.v1`	solver-gate	analytic quadratic and exact-affine Taylor remainder and deterministic replay	real/complex observed order >= 1.9; exact-affine order = +infinity; replay evaluations = 2
`solvers.differentiable-native-eigen.v1`	solver-gate	native eigen result contract shape/status validation and deterministic replay	two replay evaluations; malformed state rejected; complex native dimension 3
`solvers.sparse-lu-refinement-many.v1`	solver-gate	independent analytic SPD solutions with same-pattern numeric value update	all solution errors and independent residuals <= 1e-10; three columns converge
`solvers.sparse-lu-pivot-reuse.v1`	solver-gate	independent analytic solution and true residual recomputation	solution errors and true residual <= 1e-10
`solvers.sparse-lu-preconditioner-scalar.v1`	solver-gate	scaled ComplexField reciprocal and independently checked relative solution error	4 scalar checks; maximum relative error <= 3e-6
`solvers.sparse-lu-preprocessing.v1`	solver-gate	independent analytic solution and true residual recomputation	solution and true residual <= 1e-10; two malformed CSR cases rejected; tiny-pivot solution error <= 1e-12
`solvers.csr-index-width.v1`	solver-gate	independent known solution and true residual recomputation	solution errors and true residuals <= 1e-12; two malformed-input rejections
`solvers.bsr-generated-nonfinite.v1`	solver-gate	independent duplicate-sum action and typed construction error	finite action error <= 1e-12; one generated-nonfinite construction rejection
`solvers.csr-generated-nonfinite.v1`	solver-gate	independent duplicate-sum action and checked TripletMatrix admission errors	finite action/matmul errors <= 1e-12; one CSR and three TripletMatrix boundary rejections
`solvers.csr-mutation-generated-nonfinite.v1`	solver-gate	independent finite mutation parity and typed generated-value rejection	finite scale and diagonal errors <= 1e-12; one rejection at each boundary
`solvers.csr-spmv-transactional.v1`	solver-gate	independent finite action oracle and typed transactional rejection	finite action error <= 1e-12; four CSR and three compact-CSR rejection gates
`solvers.spd-scalable-certificate.v1`	solver-gate	independent true residual and assumption provenance	certified residual <= 1e-7; uncertified SPD rejected
`solvers.hpd-scalable-certificate.v1`	solver-gate	independent true residual, solution error, assumption provenance, and non-Hermitian rejection	certified residual and solution error <= 1e-7; non-Hermitian HPD rejection required
`solvers.spd-duplicate-csr.v1`	solver-gate	independent coalesced dense solution and true residual; non-positive aggregate diagonal rejection	solution error and residual <= 1e-10; non-positive aggregate diagonal rejected
`solvers.factor-solve-complex-cholesky.v1`	solver-gate	independent true residual and solution error against known Complex64 solution	solution error and true residual <= 1e-12
`solvers.preconditioner-adjoint-matrix.v1`	solver-gate	independent complex Hermitian inner-product recomputation	both Hermitian adjoint errors <= 1e-10
`solvers.preconditioner-adjoint-randomized.v1`	solver-gate	independent transpose and Hermitian inner-product recomputation including mixed-precision cast path	both maximum identity errors <= 1e-6; 128 checks
`solvers.operator-adjoint-randomized.v1`	solver-gate	independent transpose/Hermitian inner-product recomputation and per-column block oracle	both maximum scaled identity errors <= 1e-10; 576 identity checks, 54 block checks, 4 rejection checks
`solvers.preconditioner-adjoint-capability-matrix.v1`	solver-gate	independent exact-adjoint inner-product recomputation and capability metadata	transpose/Hermitian errors <= 1e-10; 3 exact capability cases; unsupported transpose and Hermitian actions reject; forward AMG remains available
`solvers.preconditioner-hilu-coupled-adjoint.v1`	solver-gate	independent complex bilinear and Hermitian inner-product recomputation	transpose/Hermitian errors <= 1e-10; in-place Hermitian parity <= 1e-12; 16 vector-pair cases
`solvers.preconditioner-mixed-block-adjoint.v1`	solver-gate	column-by-column scalar adjoint actions	both maximum errors <= 1e-5; 12 checks
`solvers.preconditioner-mixed-hilu-adjoint.v1`	solver-gate	independent bilinear and Hermitian inner-product recomputation over eight deterministic vector pairs	both maximum errors <= 3e-5; 16 identity checks
`solvers.sparse-lu-checkpoint.v1`	solver-gate	independent dense partial-pivot solve and restored-factor residual	restored solution error and independent residual <= 1e-10
`solvers.ilu-checkpoint.v1`	solver-gate	analytic deterministic CSR ILU(0) factor round-trip	restored solution error and independent residual <= 1e-12
`solvers.chebyshev-checkpoint.v1`	solver-gate	analytic deterministic source/restored Chebyshev action comparison	action errors <= 1e-12; five malformed packets rejected
`solvers.schwarz-checkpoint.v2`	solver-gate	analytic deterministic source/restored action comparison with nested-factor and CSR corruption rejection	all action errors <= 1e-12; one-level malformed rejections >= 5; nested coarse rejection >= 1
`solvers.amg-checkpoint.v1`	solver-gate	analytic deterministic source/restored host and backend AMG action comparison	host action errors <= 1e-12; backend action error <= 1e-9; seven host and two backend malformed packets rejected; exactly one backend apply
`solvers.saddle-point-checkpoint.v1`	solver-gate	analytic deterministic source/restored action comparison	action errors <= 1e-12; six malformed packets rejected
`solvers.ilut-checkpoint.v1`	solver-gate	analytic deterministic CSR residual and source-factor application	restored solution error and independent residual <= 1e-11
`solvers.parilut-checkpoint.v1`	solver-gate	analytic deterministic factor-action and setup-metadata comparison	source/restored action and residual-history errors <= 1e-12
`solvers.parallel-ilu-checkpoint.v1`	solver-gate	analytic deterministic source/restored preconditioner action and metadata comparison	colored and fixed-point action errors <= 1e-12
`solvers.block-jacobi-checkpoint.v1`	solver-gate	analytic deterministic source/restored Block-Jacobi action comparison	restored action error <= 1e-11
`solvers.hilu-checkpoint.v1`	solver-gate	analytic deterministic source/restored HILU action comparison	action errors <= 1e-11; five malformed packets rejected
`solvers.mixed-precision-checkpoint.v1`	solver-gate	independent analytic SPD solutions and true residual recomputation	solution error and independent residual <= 1e-10
`solvers.mixed-precision-adjoint-continuation.v1`	solver-gate	independent adjoint action residual and cold/resumed iterate parity	residual/delta <= 1e-10; continuation and rejection contracts = 1
`solvers.mixed-precision-adjoint-capability.v1`	solver-gate	unsupported transpose/Hermitian actions reject before Krylov iteration	unsupported actions reject; operator and low-precision application counts = 0
`solvers.mixed-precision-checkpoint-portable.v1`	solver-gate	independent analytic SPD solution and strict packet validation	round-trip delta/residual <= 1e-11; metadata/cumulative/rejection contracts = 1
`solvers.mixed-precision-block-checkpoint.v1`	solver-gate	independent analytic SPD block solutions and true block residual recomputation	solution error and independent residual <= 1e-9
`solvers.mixed-precision-block-checkpoint-portable.v1`	solver-gate	independent analytic block solution and strict packet validation	round-trip/iterate delta/residual <= 1e-10; metadata/cumulative/rejection contracts = 1
`solvers.block-fgmres-checkpoint-scalars.v1`	solver-gate	independent typed packet round-trip and metadata parity oracles	round-trip = 1; coordinate errors <= 1e-12; block-GMRES = 1; cross-family = 1; corruption/non-finite = 2
`solvers.distributed-checkpoint-manifest.v1`	solver-gate	typed mixed-precision bundle sharding/repartition with checked decode, ILU/Sparse-LU/Sparse-Cholesky action replay, and independent checksum validation	round-trip delta <= 1e-12; metadata and rejection contracts = 1
`solvers.gcro-dr-checkpoint.v1`	solver-gate	independent analytic tridiagonal solution and true residual recomputation	solution error and independent residual <= 1e-9; malformed_empty_dimension_rejection = 1
`solvers.gcro-dr-checkpoint-scalars.v1`	solver-gate	independent analytic tridiagonal solutions and true residual recomputation	three scalar-family cases; solution delta and independent residual <= 1e-4; cross_family_rejection = 1
`solvers.gcro-dr-transactional.v1`	solver-gate	independent identity/zero-operator callback-failure fixture	state_unchanged = 1 and failure_typed = 1
`solvers.gmres-deflated-operator-boundary.v1`	solver-gate	independent typed attribution of final operator callback failure	operator_failure_typed = 1; final_residual_operator_calls = 3
`solvers.deflated-checkpoint.v1`	solver-gate	independent analytic diagonal solution and true residual recomputation	f64 solution/residual errors <= 1e-10; continuation and malformed-guess contracts = 1; malformed_empty_dimension_rejection = 1; scalar-family solution delta/residual <= 1e-5; scalar_family_case_count
`solvers.recycled-checkpoint.v1`	solver-gate	independent fresh recycled-GMRES solve and true residual recomputation across scalar families	f64 checkpoint/solution/residual errors <= 1e-9; three scalar-family cases with delta/residual <= 1e-5 and non-empty packets
`solvers.eigen-continuation-predictor.v1`	solver-gate	independent analytic affine branch lambda(p) = 1 + p	all analytic errors <= 1e-12
`solvers.transient-checkpoint.v1`	solver-gate	independent deterministic forward-state replay and reverse-order contract	round-trip and corruption errors exactly zero
`solvers.saddle-point-adjoint.v1`	solver-gate	independent diagonal inverse and coupled triangular bilinear/Hermitian identities	adjoint action errors <= 1e-12; exact contract flag exactly one
`solvers.mixed-precision-failure-diagnostics.v1`	solver-gate	independent deterministic failure injection	low_precision_failure_count >= 2
`solvers.mixed-precision-block-failure-diagnostics.v1`	solver-gate	typed block preconditioner failure with fail-before-operator provenance	low_precision_failure_count >= 1; operator_calls_before_failure <= 2
`solvers.mixed-precision-promoted-residual.v1`	solver-gate	independent high-precision residual recomputation and midpoint tolerance	projected estimate < midpoint tolerance < true residual; block projected residual below tolerance while true residual exceeds it
`solvers.mixed-precision-recycled-deflated.v1`	solver-gate	independent analytic diagonal solution and exact residual recomputation	exact candidate checks >= 1; continuation residual <= 1e-14; typed solver status contract
`solvers.factor-solve-near-singular.v1`	solver-gate	independent A*x reconstruction from known solutions	all residuals <= 1e-8; 12 finite variant cases; 12 non-finite rejections and 12 preserved destinations
`solvers.factor-solve-seeded-matrix.v1`	solver-gate	independent generated-solution reconstruction	all solution errors <= 1e-10
`solvers.preconditioner-coarse-adjoint.v1`	solver-gate	independent complex bilinear and Hermitian inner-product recomputation	both coarse adjoint errors <= 1e-10; unsupported calls return typed errors
`solvers.numa-partitioning-report.v1`	solver-gate	independent partition-count, total-nnz, finite imbalance, policy-action parity, and positive runtime-rate invariants	finite non-negative imbalance and positive finite runtime rates; nonzero imbalance <= 1; exact admission/clamp counts; exact-budget flags and policy action errors satisfy one and <= 1e-10
`solvers.sparse-cholesky-checkpoint.v1`	solver-gate	analytic/deterministic-fixture known solutions plus restored-factor residual	all solution errors and independent residuals <= 1e-10
`solvers.sparse-lu-refinement-variants.v1`	solver-gate	analytic/deterministic-fixture known solutions and independent CSR residuals	all solution errors and residuals <= 1e-10; 16 malformed-input rejections
`solvers.recycled-resume.v1`	solver-gate	analytic/deterministic-fixture known solution and independent CSR residual	all solution errors and residuals <= 1e-10; resumed iterations = 0; both contract checks pass
`solvers.block-gmres-rank-deficiency.v1`	solver-gate	zero-RHS solution, linearity of the scaled-dependent pair, and recomputed true residuals	all solution/residual errors <= 1e-9; converged flag set
`solvers.eigen-pseudo-arclength.v1`	solver-gate	analytic continuation branch (-1,1) -> (0,2) -> (-0.5,3)	all five metrics <= 1e-12
`solvers.optimization-risk-aggregation.v1`	solver-gate	independent deterministic risk/aggregation oracle	all fifteen metrics <= 1e-12
`solvers.optimization-risk-bfgs.v1`	solver-gate	analytic minimizer x=1 with independently known CVaR/KS value and gradient	all nine metrics <= 1e-8
`solvers.optimization-gcmma.v1`	solver-gate	analytic minimum x=y=0.5 for x+y>=1	all five metrics <= 2e-3
`solvers.chebyshev-finite-setup.v1`	solver-gate	typed ChebyshevError::NonFiniteEntries and finite lambda_max	one NaN rejection, one infinity rejection, finite setup admitted
`solvers.sparse-submatrix-checked.v1`	solver-gate	canonical local columns, duplicate accumulation, and typed rejection of invalid boundaries	all six contract metrics must be one
`solvers.direct-configured-diagnostics.v1`	solver-gate	analytic matrix 4 1; 2 3 with one-norm condition estimate 3 and solution [1, 2]	condition, solution, residual, backward error <= 1e-12; invalid tolerance rejection = 1
`solvers.sparse-configured-diagnostics.v1`	solver-gate	analytic known-solution sparse LU fixture with retained-operator backward-error diagnostics	solution and backward-error diagnostics <= 1e-12; invalid options and budget reject
`solvers.boundary-fuzz.v1`	contract-gate	all malformed cases reject with typed errors; valid fixtures are accepted; no boundary panic; checkpoint fixture round-trips	at least 200 typed rejections per sparse/option/checkpoint family, at least 400 dense/sparse factorization rejections, one checkpoint round-trip, and zero panics
`solvers.nonlinear-independent-accuracy.v1`	solver-gate	((1 +/- sqrt(7))/2, (-1 +/- sqrt(7))/2)	true residual <=1e-9; root error <=1e-9; two converged solves required