| /* | |
| * jordan.h — Jordan Spectral Transformer | |
| * Stage 4: Eigendecomposition and stable attractor identification | |
| * | |
| * Mathematical framework: | |
| * | |
| * Density-matrix evolution: ρ' = φ⁻¹ U ρ U† + φ⁻² ρ | |
| * φ = (1+√5)/2 (golden ratio) | |
| * Fixed points: [U, ρ*] = 0 (commutation) | |
| * Stable attractors: e ∘ e = e (idempotents) | |
| * Routing decisiveness: λ₊ - λ₋ (spectral gap) | |
| */ | |
| extern "C" { | |
| typedef enum { | |
| HK_OK = 0, | |
| HK_ERR_NULL = 1, | |
| HK_ERR_ALLOC = 2, | |
| } hk_status; | |
| typedef struct { | |
| double spectral_radius; /* max |λ| */ | |
| double stability_score; /* [0,1]: how quickly system decays */ | |
| int jordan_blocks; /* Number of Jordan blocks */ | |
| double gershgorin_radius; /* Upper bound on eigenvalue magnitudes */ | |
| double spectral_gap; /* λ₊ - λ₋: routing decisiveness */ | |
| double convergence_tolerance; /* Tolerance for fixed-point detection */ | |
| hk_status status; | |
| } hk_jordan_features; | |
| /** | |
| * hk_jordan_transform — Compute spectral features of routing graph | |
| * | |
| * Eigendecomposes the adjacency matrix and extracts: | |
| * - Spectral radius (largest |λ|) | |
| * - Stability score (measure of decay) | |
| * - Jordan block structure | |
| * - Gershgorin circle radius | |
| * - Spectral gap (λ₊ - λ₋) | |
| * | |
| * @param adj_matrix Adjacency matrix [dim x dim] | |
| * @param dim Matrix dimension | |
| * @return Features with status code | |
| */ | |
| hk_jordan_features hk_jordan_transform(double **adj_matrix, int dim); | |
| /** | |
| * hk_jordan_detect_fixed_point — Check if matrix is a fixed point | |
| * | |
| * A fixed point ρ* satisfies [U, ρ*] = 0 (commutes with evolution). | |
| * | |
| * @param matrix Input matrix [dim x dim] | |
| * @param dim Matrix dimension | |
| * @param tolerance Tolerance for commutation check | |
| * @return 1 if fixed point detected, 0 otherwise | |
| */ | |
| int hk_jordan_detect_fixed_point(double **matrix, int dim, | |
| double tolerance); | |
| /** | |
| * hk_jordan_converge_idempotent — Iterate to idempotent | |
| * | |
| * Repeatedly squares the matrix A until A² = A (idempotent). | |
| * Stable routing attractors satisfy e ∘ e = e. | |
| * | |
| * @param matrix Input matrix [dim x dim] | |
| * @param dim Matrix dimension | |
| * @param max_iter Maximum iteration count | |
| * @param tolerance Convergence tolerance | |
| * @return Number of iterations to convergence, -1 if failed | |
| */ | |
| int hk_jordan_converge_idempotent(double **matrix, int dim, | |
| int max_iterations, | |
| double tolerance); | |
| /** | |
| * hk_jordan_print_features — Debug output | |
| */ | |
| void hk_jordan_print_features(hk_jordan_features feat); | |
| } | |