nx_lowrank_attn.nx

nx_lowrank_attn.nx -- M3: low-rank KV through a REAL softmax-attention forward (end-to-end quality proof). module: nishi-core.ai.lowrank_attn capability: VRAM_REDUCTION (per-token low-rank KV, measured end-to-end) M0/M1 measured COVARIANCE fidelity (K^T K) of an FD sketch. But softmax attention needs PER-TOKEN scores Q.K[i], which an FD covariance sketch cannot give. The per-token low-rank compression that DOES work is Eigen-Attention / SVD-projection: find the top-r right singular basis V_r [r x d] of K (top-r eigenvectors of K^T K), store per-token coords[i] = K[i] @ V_r^T (n x r) + the shared basis (r x d), reconstruct K[i] ~= coords[i] @ V_r. This PRESERVES per-token identity -> usable in real attention. The eigen-extraction REUSES the M1 lesson: reorthogonalize (Gram-Schmidt twice) or the dominant direction leaks under f32. PROOF: compare the attention OUTPUT (after softmax + value mixing) full-KV vs compressed-KV. For genuinely rank-2 K/V, compressing to r>=2 reconstructs exactly -> output error ~0 (VRAM cut, quality kept end-to-end). Sovereign: nx_f32_hw (SSE arith) + nx_f32_sqrt + nx_f32_softmax (reused). no gcc. HONEST: reference-scale d=8.