L0 character-subspace weight energies by unlabeled ICA axis
0 [('query', [(13, np.float64(1.04)), (0, np.float64(0.472)), (4, np.float64(0.429)), (11, np.float64(0.37)), (23, np.float64(0.358)), (20, np.float64(0.301)), (1, np.float64(0.288))]), ('key', [(13, np.float64(2.241)), (0, np.float64(1.236)), (9, np.float64(1.114)), (5, np.float64(0.896)), (18, np.float64(0.868)), (22, np.float64(0.861)), (16, np.float64(0.834))]), ('value', [(13, np.float64(1.22)), (0, np.float64(0.899)), (25, np.float64(0.705)), (2, np.float64(0.624)), (15, np.float64(0.576)), (1, np.float64(0.574)), (26, np.float64(0.571))])]
1 [('query', [(12, np.float64(11.063)), (21, np.float64(6.311)), (24, np.float64(4.53)), (18, np.float64(4.412)), (3, np.float64(4.007)), (8, np.float64(3.83)), (0, np.float64(3.495))]), ('key', [(12, np.float64(11.364)), (21, np.float64(6.31)), (24, np.float64(4.572)), (18, np.float64(4.199)), (3, np.float64(4.061)), (8, np.float64(3.909)), (0, np.float64(3.878))]), ('value', [(20, np.float64(1.882)), (1, np.float64(1.813)), (27, np.float64(1.79)), (14, np.float64(1.783)), (10, np.float64(1.773)), (9, np.float64(1.77)), (0, np.float64(1.762))])]
2 [('query', [(26, np.float64(2.172)), (2, np.float64(2.047)), (17, np.float64(1.848)), (21, np.float64(1.558)), (7, np.float64(1.558)), (24, np.float64(1.553)), (18, np.float64(1.211))]), ('key', [(0, np.float64(2.229)), (7, np.float64(2.029)), (26, np.float64(1.936)), (17, np.float64(1.57)), (19, np.float64(1.564)), (25, np.float64(1.556)), (2, np.float64(1.482))]), ('value', [(0, np.float64(1.798)), (25, np.float64(1.437)), (23, np.float64(1.396)), (27, np.float64(1.293)), (15, np.float64(1.142)), (14, np.float64(1.101)), (26, np.float64(1.101))])]
3 [('query', [(13, np.float64(1.841)), (0, np.float64(1.837)), (21, np.float64(1.177)), (15, np.float64(1.097)), (23, np.float64(1.069)), (24, np.float64(0.991)), (14, np.float64(0.924))]), ('key', [(13, np.float64(3.116)), (20, np.float64(2.433)), (17, np.float64(2.094)), (7, np.float64(1.987)), (1, np.float64(1.798)), (24, np.float64(1.586)), (5, np.float64(1.558))]), ('value', [(15, np.float64(0.865)), (20, np.float64(0.835)), (17, np.float64(0.834)), (13, np.float64(0.817)), (24, np.float64(0.8)), (21, np.float64(0.771)), (14, np.float64(0.768))])]
4 [('query', [(12, np.float64(0.053)), (24, np.float64(0.05)), (0, np.float64(0.046)), (21, np.float64(0.043)), (18, np.float64(0.042)), (25, np.float64(0.04)), (2, np.float64(0.035))]), ('key', [(24, np.float64(0.076)), (21, np.float64(0.072)), (23, np.float64(0.067)), (17, np.float64(0.063)), (18, np.float64(0.06)), (12, np.float64(0.06)), (15, np.float64(0.057))]), ('value', [(13, np.float64(1.792)), (4, np.float64(1.095)), (16, np.float64(1.085)), (22, np.float64(1.037)), (5, np.float64(1.034)), (1, np.float64(0.977)), (11, np.float64(0.954))])]
5 [('query', [(12, np.float64(5.833)), (21, np.float64(4.149)), (24, np.float64(3.958)), (17, np.float64(3.514)), (0, np.float64(3.37)), (15, np.float64(3.37)), (2, np.float64(2.768))]), ('key', [(12, np.float64(6.123)), (21, np.float64(4.609)), (24, np.float64(4.561)), (17, np.float64(4.545)), (15, np.float64(3.239)), (0, np.float64(3.224)), (2, np.float64(2.897))]), ('value', [(9, np.float64(2.033)), (1, np.float64(2.003)), (5, np.float64(1.981)), (10, np.float64(1.977)), (8, np.float64(1.901)), (18, np.float64(1.832)), (11, np.float64(1.823))])]

L0H4 top value-input singular vectors: overlap with content and QK5 row spaces
0 4.101 0.051 0.759
1 3.34 0.136 0.621
2 2.538 0.116 0.532
3 2.115 0.605 0.448
4 1.785 0.813 0.214
5 1.547 0.731 0.581

Relative rotation geometry of L0H1 and L0H5
Weight-matrix powers only; no sequence or attention computation.
rank 16 H5 singular values [1.063 0.059] H1 versus H5 polar powers [(-4, np.float64(0.231)), (-3, np.float64(-0.37)), (-2, np.float64(-0.09)), (-1, np.float64(0.167)), (0, np.float64(-0.278)), (1, np.float64(0.028)), (2, np.float64(0.623)), (3, np.float64(0.043)), (4, np.float64(-0.384)), (5, np.float64(0.131)), (6, np.float64(0.082))]
rank 24 H5 singular values [1.272 0.037] H1 versus H5 polar powers [(-4, np.float64(0.24)), (-3, np.float64(-0.43)), (-2, np.float64(-0.111)), (-1, np.float64(0.29)), (0, np.float64(-0.29)), (1, np.float64(-0.031)), (2, np.float64(0.647)), (3, np.float64(-0.016)), (4, np.float64(-0.335)), (5, np.float64(0.197)), (6, np.float64(-0.036))]
rank 32 H5 singular values [1.518 0.041] H1 versus H5 polar powers [(-4, np.float64(0.066)), (-3, np.float64(-0.104)), (-2, np.float64(-0.159)), (-1, np.float64(0.326)), (0, np.float64(-0.292)), (1, np.float64(0.093)), (2, np.float64(0.36)), (3, np.float64(0.057)), (4, np.float64(-0.195)), (5, np.float64(0.13)), (6, np.float64(-0.031))]
rank 40 H5 singular values [1.614 0.013] H1 versus H5 polar powers [(-4, np.float64(-0.038)), (-3, np.float64(-0.036)), (-2, np.float64(-0.15)), (-1, np.float64(0.245)), (0, np.float64(-0.26)), (1, np.float64(0.135)), (2, np.float64(0.211)), (3, np.float64(0.061)), (4, np.float64(-0.173)), (5, np.float64(0.185)), (6, np.float64(-0.096))]
