1.6.0 release qualification

This report qualifies only the 1.6 typed dense decomposition and direct-solver milestone. It does not claim any 1.7 modelling/optimisation or deferred sparse, iterative, or advanced spectral family.

Supported targets and configurations

The repository CI runs the complete public API test suite on Linux x86-64, Windows x86-64, and Windows i386, compiles/runs every example, checks/builds documentation, compiles benchmarks, builds both Lazarus package targets, and tests the archived quick starts. Local qualification results and CI coverage are distinguished: the table records the completion run on the qualification host; the workflow is the cross-platform evidence executed for each pushed commit.

Algorithm-specific acceptance budgets

| Householder QR | `2e-12` complex, `2e-13` real | `2e-5` | `||A-QR||F/||A||F`, `||Q^H Q-I||F`, solve residual |

| Column-pivoted QR | `2e-11` badly scaled permutation fixture | `2e-5` | `||AP-QR||F/||A||F`, permutation identity, rank decision |

| Compact SVD | `2e-11` complex, `2e-12` real | `2e-5` | `||A-U S V^H||F/||A||F`, descending singular values, unit vectors |

| Minimum-norm solve | `2e-12` | `2e-5` | RHS residual and independent Moore-Penrose reference solution |

| Symmetric/Hermitian eigen | `2e-12` | `2e-5` | `||A v-lambda v||`, `||V^H V-I||`, ascending eigenvalues |

Budgets are attached to the named deterministic fixtures; they are not universal forward-error promises for arbitrarily ill-conditioned input. Tolerance decisions scale with scalar epsilon, dimensions, and the relevant pivot/diagonal/singular value.

Reference, structural, and adversarial evidence

• QR uses an independently checkable four-observation straight-line fit with coefficients (3.5, 1.4), plus reconstruction and orthogonality identities.
• CPQR checks A*P=Q*R, largest-trailing-column selection, exact rank deficiency, a caller-controlled near-rank threshold, and a useful basic rank-deficient solve.
• SVD checks diagonal reference singular values (3,2), tall/wide and complex reconstruction, descending ordering, and the underdetermined reference solution (2/3,2/3,4/3).
• Real eigen checks analytic eigenvalues (1,3,5); Hermitian complex eigen checks (1,3). Both check every eigenpair residual. Repeated spectra and a 1e-200 scale fixture check basis freedom and scale-relative convergence.
• Empty factors, empty output arrays, multiple right-hand sides, source mutation after factorisation, invalid wide QR, nonsymmetric/non-Hermitian input, non-finite SVD input, singularity, indefiniteness, and unchanged caller storage after validation failure are permanent tests.
• Existing 1.5 LU/Cholesky reconstruction, complex Hermitian, tiny positive-definite, singular, ill-conditioned, and multiple-RHS tests remain in the full suite.

The test corpus is checked into the repository and needs no network or external numerical runtime.

Deterministic performance and allocation evidence

BenchmarkRunner uses deterministic trigonometric and structured inputs and reports:

• a 96 x 32 QR factor plus 20 reused four-RHS solves;
• five allocating least-squares convenience calls on the same shape;
• a 48 x 16 compact SVD plus two-RHS minimum-norm solve; and
• a 24 x 24 full symmetric eigensystem.

Output includes elapsed milliseconds, checksums, convergence sweeps/rank, factor-build counts, result-allocation counts, and scalar working-storage estimates. Factor reuse performs one factor build; the convenience path performs one factor build per call. A solve returns a fresh result by contract. The benchmark does not claim parallel, SIMD, external-BLAS, or cross-library performance.

On the Windows x86-64 FPC 3.2.2 -O3 qualification host, the completion run recorded:

The same run reported QR checksum 2.786934, SVD checksum 2.917959, and eigen checksum 4.230000. Timings are host-specific reproducibility data.

Ownership, compatibility, dependencies, and licence

Factor snapshot and copied-accessor tests prove that source mutation cannot alter an existing factor. No factor stores a last result or shared public workspace. All validation occurs before a caller-visible result is returned.

The source-compatible IMatrix, TMatrixKit, and IVector public surface is unchanged. The new tests import both compatibility and typed units in the same runner. The migration guide names every compatibility bridge as a deep copy and does not imply contract equivalence.

The stable units import only Free Pascal RTL units and existing MIT-licensed mathlib-fp source. A dependency scan checks for foreign declarations, dynamic library loading, process execution, sockets, HTTP, and external commands. Normal build, test, documentation, examples, and runtime use need no network, DLL, service, licence key, or third-party package.

Deferred families

The capability inventory records sparse/structured storage, LDLT, iterative and matrix-free solves, advanced nonsymmetric/generalized/partial spectral families, factor updates, destructive/public-workspace APIs, automatic dispatch, parallel/SIMD/GPU kernels, and external BLAS/LAPACK as unsupported. No deferred family counts toward the 1.6 completeness claim.