Output files of the scripts, gathered in one file (Hexagon file-count limit). Each section is one original file. ==================================================================================================== ===== hadamardout.txt ==================================================================================================== 31 Oct 13:41 hadamard.py joint T6 dim Fix(G_H)(2),(3) = 2,5 joint k=4,5: [14, 42] H6^q, q=1 dim Fix(G_H)(2),(3) = 2,5 joint k=4,5: [14, 42] ==================================================================================================== ===== leveleight/resulta.txt ==================================================================================================== quadric span dimension mod p: 1154 eigenspace dimensions: [14, 5, 10, 5, 12, 5, 10, 5] total 66 span dimension by character: [134, 152, 135, 152, 142, 152, 135, 152] total 1154 initial gaps: {0: 602} (46s) 1: first (3, 0, 5, 1, 1) second (0, 5, 5, 1, 0): 448 cubics; gaps [574] (71s) 2: first (3, 0, 5, 1, 1) second (0, 3, 5, 1, 0): 448 cubics; gaps [546] (63s) 3: first (3, 0, 5, 1, 1) second (0, 4, 5, 1, 0): 448 cubics; gaps [518] (64s) 4: first (3, 0, 5, 1, 1) second (0, 0, 5, 0, 1): 448 cubics; gaps [498] (83s) 5: first (3, 0, 5, 1, 1) second (0, 5, 5, 0, 1): 448 cubics; gaps [478] (83s) 6: first (3, 0, 5, 1, 1) second (0, 2, 5, 0, 0): 71 cubics; gaps [470] (19s) 7: first (3, 0, 5, 1, 1) second (0, 2, 5, 0, 1): 448 cubics; gaps [462] (83s) 8: first (3, 0, 5, 1, 1) second (0, 3, 5, 0, 0): 71 cubics; gaps [462] (18s) 9: first (7, 6, 4, 0, 0) second (0, 7, 5, 0, 1): 448 cubics; gaps [435] (96s) 10: first (7, 6, 4, 0, 0) second (0, 2, 5, 0, 0): 71 cubics; gaps [427] (19s) 11: first (7, 6, 4, 0, 0) second (0, 3, 5, 0, 1): 448 cubics; gaps [427] (82s) 12: first (7, 6, 4, 0, 0) second (0, 4, 5, 1, 0): 448 cubics; gaps [407] (63s) 13: first (7, 6, 4, 0, 0) second (0, 0, 5, 1, 0): 448 cubics; gaps [407] (63s) 14: first (7, 6, 4, 0, 0) second (0, 2, 5, 1, 0): 448 cubics; gaps [407] (63s) 15: first (7, 6, 4, 0, 0) second (0, 7, 5, 1, 0): 448 cubics; gaps [388] (63s) 16: first (7, 6, 4, 0, 0) second (0, 1, 5, 1, 0): 448 cubics; gaps [388] (63s) 17: first (1, 3, 4, 0, 0) second (0, 4, 5, 1, 0): 448 cubics; gaps [360] (74s) 18: first (1, 3, 4, 0, 0) second (0, 5, 5, 1, 0): 448 cubics; gaps [334] (63s) 19: first (1, 3, 4, 0, 0) second (0, 3, 5, 1, 0): 448 cubics; gaps [334] (62s) 20: first (1, 3, 4, 0, 0) second (0, 2, 5, 0, 0): 71 cubics; gaps [334] (18s) 21: first (1, 3, 4, 0, 0) second (0, 5, 5, 0, 0): 71 cubics; gaps [334] (18s) 22: first (1, 3, 4, 0, 0) second (0, 3, 5, 0, 1): 448 cubics; gaps [316] (83s) 23: first (1, 3, 4, 0, 0) second (0, 2, 5, 0, 1): 448 cubics; gaps [298] (83s) 24: first (1, 3, 4, 0, 0) second (0, 4, 5, 0, 0): 71 cubics; gaps [298] (18s) 25: first (6, 6, 4, 0, 0) second (0, 2, 5, 0, 0): 71 cubics; gaps [298] (31s) 26: first (6, 6, 4, 0, 0) second (0, 0, 5, 1, 0): 448 cubics; gaps [298] (63s) 27: first (6, 6, 4, 0, 0) second (0, 4, 5, 0, 1): 448 cubics; gaps [298] (83s) 28: first (6, 6, 4, 0, 0) second (0, 4, 5, 1, 0): 448 cubics; gaps [298] (63s) 29: first (6, 6, 4, 0, 0) second (0, 3, 5, 0, 0): 71 cubics; gaps [298] (18s) 30: first (6, 6, 4, 0, 0) second (0, 7, 5, 1, 0): 448 cubics; gaps [298] (63s) 31: first (6, 6, 4, 0, 0) second (0, 1, 5, 0, 0): 71 cubics; gaps [298] (18s) 32: first (6, 6, 4, 0, 0) second (0, 3, 5, 0, 1): 448 cubics; gaps [298] (82s) 33: first (4, 2, 4, 0, 0) second (0, 4, 5, 0, 0): 71 cubics; gaps [298] (26s) 34: first (4, 2, 4, 0, 0) second (0, 7, 5, 1, 0): 448 cubics; gaps [298] (62s) 35: first (4, 2, 4, 0, 0) second (0, 2, 5, 0, 1): 448 cubics; gaps [298] (83s) 36: first (4, 2, 4, 0, 0) second (0, 4, 5, 0, 1): 448 cubics; gaps [298] (82s) 37: first (4, 2, 4, 0, 0) second (0, 0, 5, 1, 0): 448 cubics; gaps [298] (62s) 38: first (4, 2, 4, 0, 0) second (0, 7, 5, 0, 1): 448 cubics; gaps [298] (82s) 39: first (4, 2, 4, 0, 0) second (0, 6, 5, 1, 0): 448 cubics; gaps [298] (63s) 40: first (4, 2, 4, 0, 0) second (0, 0, 5, 0, 0): 71 cubics; gaps [298] (18s) 41: first (7, 3, 4, 0, 0) second (0, 2, 5, 0, 0): 71 cubics; gaps [298] (31s) 42: first (7, 3, 4, 0, 0) second (0, 5, 5, 1, 0): 448 cubics; gaps [298] (63s) 43: first (7, 3, 4, 0, 0) second (0, 1, 5, 0, 0): 71 cubics; gaps [298] (18s) 44: first (7, 3, 4, 0, 0) second (0, 3, 5, 1, 0): 448 cubics; gaps [298] (62s) 45: first (7, 3, 4, 0, 0) second (0, 0, 5, 0, 0): 71 cubics; gaps [298] (18s) 46: first (7, 3, 4, 0, 0) second (0, 6, 5, 1, 0): 448 cubics; gaps [298] (62s) 47: first (7, 3, 4, 0, 0) second (0, 6, 5, 0, 0): 71 cubics; gaps [298] (18s) 48: first (7, 3, 4, 0, 0) second (0, 6, 5, 0, 1): 448 cubics; gaps [298] (82s) 49: first (4, 1, 5, 1, 1) second (0, 6, 5, 0, 0): 71 cubics; gaps [298] (26s) 50: first (4, 1, 5, 1, 1) second (0, 1, 5, 0, 1): 448 cubics; gaps [298] (83s) 51: first (4, 1, 5, 1, 1) second (0, 0, 5, 0, 1): 448 cubics; gaps [298] (84s) 52: first (4, 1, 5, 1, 1) second (0, 4, 5, 0, 1): 448 cubics; gaps [298] (84s) 53: first (4, 1, 5, 1, 1) second (0, 1, 5, 1, 0): 448 cubics; gaps [298] (63s) 54: first (4, 1, 5, 1, 1) second (0, 2, 5, 1, 0): 448 cubics; gaps [298] (63s) 55: first (4, 1, 5, 1, 1) second (0, 0, 5, 1, 0): 448 cubics; gaps [298] (63s) 56: first (4, 1, 5, 1, 1) second (0, 7, 5, 0, 1): 448 cubics; gaps [298] (82s) 57: first (6, 3, 5, 1, 1) second (0, 7, 5, 0, 0): 71 cubics; gaps [298] (30s) ==================================================================================================== ===== leveleight/resulttest.txt ==================================================================================================== quadric span dimension mod p: 1154 eigenspace dimensions: [14, 5, 10, 5, 12, 5, 10, 5] total 66 span dimension by character: [134, 152, 135, 152, 142, 152, 135, 152] total 1154 initial gaps: {4: 548} (44s) 1: first (0, 4, 4, 0, 0) second (0, 2, 5, 0, 1): 448 cubics; gaps [520] (95s) 2: first (0, 4, 4, 0, 0) second (0, 2, 5, 0, 0): 71 cubics; gaps [520] (18s) 3: first (0, 4, 4, 0, 0) second (0, 0, 5, 1, 0): 448 cubics; gaps [492] (63s) 4: first (0, 4, 4, 0, 0) second (0, 6, 5, 0, 0): 71 cubics; gaps [492] (18s) 5: first (0, 4, 4, 0, 0) second (0, 6, 5, 0, 1): 448 cubics; gaps [492] (81s) 6: first (0, 4, 4, 0, 0) second (0, 2, 5, 1, 0): 448 cubics; gaps [488] (62s) 7: first (0, 4, 4, 0, 0) second (0, 5, 5, 0, 1): 448 cubics; gaps [461] (82s) 8: first (0, 4, 4, 0, 0) second (0, 4, 5, 0, 0): 71 cubics; gaps [461] (18s) final gaps: {4: 461} ==================================================================================================== ===== nineout/progress_a.txt ==================================================================================================== 31 Oct 13:13 === nine a: N in [19, 23], 4 workers, stops after 8.0 h === 31 Oct 13:13 N=19: kernel by rotation characters, start 31 Oct 13:15 N=19: kernel done (1.5 min) 31 Oct 13:15 N=19: quadrics, 4 workers, start 31 Oct 14:01 N=19: quadrics done (47.5 min) 31 Oct 14:01 N=19: certificates 31 Oct 14:01 N=19: files ['nineout/nineteen/nineforms_b.npz', 'nineout/nineteen/nineforms_c.npz', 'nineout/nineteen/nineforms_d.npz'], configurations done 67 of 90; blocks [37, 33, 33, 36, 33, 33, 36, 33, 33] 31 Oct 14:01 N=19: character 0: dim 37, restricted span 117 of 703; best min eigenvalue 1.177e-02 (max 4.687e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:01 N=19: character 1: dim 33, restricted span 117 of 561; best min eigenvalue 1.230e-02 (max 4.790e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:01 N=19: character 2: dim 33, restricted span 117 of 561; best min eigenvalue 1.432e-02 (max 4.186e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:01 N=19: character 3: dim 36, restricted span 117 of 666; best min eigenvalue 1.377e-02 (max 4.117e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:01 N=19: character 4: dim 33, restricted span 117 of 561; best min eigenvalue 1.635e-02 (max 4.343e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:01 N=19: character 5: dim 33, restricted span 117 of 561; best min eigenvalue 1.635e-02 (max 4.343e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:01 N=19: character 6: dim 36, restricted span 117 of 666; best min eigenvalue 1.377e-02 (max 4.117e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:01 N=19: character 7: dim 33, restricted span 117 of 561; best min eigenvalue 1.432e-02 (max 4.190e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:01 N=19: character 8: dim 33, restricted span 117 of 561; best min eigenvalue 1.230e-02 (max 4.790e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:01 N=19: ALL BLOCKS EXCLUDED BY POSITIVITY 31 Oct 14:01 N=23: kernel by rotation characters, start 31 Oct 14:03 N=23: kernel done (1.5 min) 31 Oct 14:03 N=23: quadrics, 4 workers, start 31 Oct 14:59 N=23: quadrics done (57.5 min) 31 Oct 14:59 N=23: certificates 31 Oct 14:59 N=23: files ['nineout/twentythree/nineforms_a.npz', 'nineout/twentythree/nineforms_b.npz', 'nineout/twentythree/nineforms_c.npz', 'nineout/twentythree/nineforms_d.npz'], configurations done 90 of 90; blocks [37, 33, 33, 36, 33, 33, 36, 33, 33] 31 Oct 14:59 N=23: character 0: dim 37, restricted span 117 of 703; best min eigenvalue 1.405e-02 (max 4.662e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:59 N=23: character 1: dim 33, restricted span 117 of 561; best min eigenvalue 1.414e-02 (max 4.830e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:59 N=23: character 2: dim 33, restricted span 117 of 561; best min eigenvalue 1.677e-02 (max 4.226e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:59 N=23: character 3: dim 36, restricted span 117 of 666; best min eigenvalue 1.579e-02 (max 4.175e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:59 N=23: character 4: dim 33, restricted span 117 of 561; best min eigenvalue 1.852e-02 (max 4.333e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:59 N=23: character 5: dim 33, restricted span 117 of 561; best min eigenvalue 1.852e-02 (max 4.333e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:59 N=23: character 6: dim 36, restricted span 117 of 666; best min eigenvalue 1.579e-02 (max 4.177e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:59 N=23: character 7: dim 33, restricted span 117 of 561; best min eigenvalue 1.677e-02 (max 4.225e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:59 N=23: character 8: dim 33, restricted span 117 of 561; best min eigenvalue 1.414e-02 (max 4.830e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:59 N=23: ALL BLOCKS EXCLUDED BY POSITIVITY 31 Oct 14:59 === nine a: done === ==================================================================================================== ===== nineout/progress_b.txt ==================================================================================================== 31 Oct 12:37 === nine b: N in [13, 17], 4 workers, stops after 8.0 h === 31 Oct 12:37 N=13: kernel by rotation characters, start 31 Oct 12:39 N=13: kernel done (1.5 min) 31 Oct 12:39 N=13: quadrics, 4 workers, start 31 Oct 13:36 N=13: quadrics done (58.5 min) 31 Oct 13:36 N=13: certificates 31 Oct 13:37 N=13: files ['nineout/thirteen/nineforms_a.npz', 'nineout/thirteen/nineforms_b.npz', 'nineout/thirteen/nineforms_c.npz', 'nineout/thirteen/nineforms_d.npz'], configurations done 90 of 90; blocks [37, 33, 33, 36, 33, 33, 36, 33, 33] 31 Oct 13:37 N=13: character 0: dim 37, restricted span 117 of 703; best min eigenvalue 5.869e-03 (max 4.703e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 13:37 N=13: character 1: dim 33, restricted span 117 of 561; best min eigenvalue 7.294e-03 (max 4.864e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 13:37 N=13: character 2: dim 33, restricted span 117 of 561; best min eigenvalue 8.237e-03 (max 4.010e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 13:37 N=13: character 3: dim 36, restricted span 117 of 666; best min eigenvalue 8.250e-03 (max 4.064e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 13:37 N=13: character 4: dim 33, restricted span 117 of 561; best min eigenvalue 1.019e-02 (max 4.279e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 13:37 N=13: character 5: dim 33, restricted span 117 of 561; best min eigenvalue 1.019e-02 (max 4.277e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 13:37 N=13: character 6: dim 36, restricted span 117 of 666; best min eigenvalue 8.250e-03 (max 4.065e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 13:37 N=13: character 7: dim 33, restricted span 117 of 561; best min eigenvalue 8.237e-03 (max 4.008e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 13:37 N=13: character 8: dim 33, restricted span 117 of 561; best min eigenvalue 7.298e-03 (max 4.835e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 13:37 N=13: ALL BLOCKS EXCLUDED BY POSITIVITY 31 Oct 13:37 N=17: kernel by rotation characters, start 31 Oct 13:38 N=17: kernel done (1.6 min) 31 Oct 13:38 N=17: quadrics, 4 workers, start 31 Oct 14:38 N=17: quadrics done (61.6 min) 31 Oct 14:38 N=17: certificates 31 Oct 14:39 N=17: files ['nineout/seventeen/nineforms_a.npz', 'nineout/seventeen/nineforms_b.npz', 'nineout/seventeen/nineforms_c.npz', 'nineout/seventeen/nineforms_d.npz'], configurations done 90 of 90; blocks [37, 33, 33, 36, 33, 33, 36, 33, 33] 31 Oct 14:39 N=17: character 0: dim 37, restricted span 117 of 703; best min eigenvalue 1.019e-02 (max 4.706e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:39 N=17: character 1: dim 33, restricted span 117 of 561; best min eigenvalue 1.104e-02 (max 4.791e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:39 N=17: character 2: dim 33, restricted span 117 of 561; best min eigenvalue 1.268e-02 (max 4.144e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:39 N=17: character 3: dim 36, restricted span 117 of 666; best min eigenvalue 1.236e-02 (max 4.099e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:39 N=17: character 4: dim 33, restricted span 117 of 561; best min eigenvalue 1.480e-02 (max 4.336e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:39 N=17: character 5: dim 33, restricted span 117 of 561; best min eigenvalue 1.480e-02 (max 4.336e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:39 N=17: character 6: dim 36, restricted span 117 of 666; best min eigenvalue 1.236e-02 (max 4.099e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:39 N=17: character 7: dim 33, restricted span 117 of 561; best min eigenvalue 1.268e-02 (max 4.150e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:39 N=17: character 8: dim 33, restricted span 117 of 561; best min eigenvalue 1.103e-02 (max 4.794e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 14:39 N=17: ALL BLOCKS EXCLUDED BY POSITIVITY 31 Oct 14:39 === nine b: done === ==================================================================================================== ===== nineout/progress_c.txt ==================================================================================================== 31 Oct 17:37 === nine c: N in [11, 12, 10, 9], 4 workers, stops after 8.0 h === 31 Oct 17:37 N=11: kernel by rotation characters, start 31 Oct 17:39 N=11: kernel done (1.5 min) 31 Oct 17:39 N=11: quadrics, 4 workers, start 31 Oct 18:35 N=11: quadrics done (57.5 min) 31 Oct 18:35 N=11: certificates 31 Oct 18:35 N=11: files ['nineout/eleven/nineforms_a.npz', 'nineout/eleven/nineforms_b.npz', 'nineout/eleven/nineforms_c.npz', 'nineout/eleven/nineforms_d.npz'], configurations done 90 of 90; blocks [37, 33, 33, 36, 33, 33, 36, 33, 33] 31 Oct 18:35 N=11: character 0: dim 37, restricted span 117 of 703; best min eigenvalue 3.134e-03 (max 4.888e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 18:35 N=11: character 1: dim 33, restricted span 117 of 561; best min eigenvalue 4.631e-03 (max 4.897e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 18:35 N=11: character 2: dim 33, restricted span 117 of 561; best min eigenvalue 5.297e-03 (max 4.033e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 18:35 N=11: character 3: dim 36, restricted span 117 of 666; best min eigenvalue 5.302e-03 (max 4.092e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 18:35 N=11: character 4: dim 33, restricted span 117 of 561; best min eigenvalue 6.783e-03 (max 4.277e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 18:35 N=11: character 5: dim 33, restricted span 117 of 561; best min eigenvalue 6.787e-03 (max 4.281e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 18:35 N=11: character 6: dim 36, restricted span 117 of 666; best min eigenvalue 5.301e-03 (max 4.090e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 18:35 N=11: character 7: dim 33, restricted span 117 of 561; best min eigenvalue 5.298e-03 (max 4.032e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 18:35 N=11: character 8: dim 33, restricted span 117 of 561; best min eigenvalue 4.632e-03 (max 4.899e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 18:35 N=11: ALL BLOCKS EXCLUDED BY POSITIVITY 31 Oct 18:35 N=12: kernel by rotation characters, start 31 Oct 18:37 N=12: kernel done (1.5 min) 31 Oct 18:37 N=12: quadrics, 4 workers, start 31 Oct 19:28 N=12: quadrics done (52.5 min) 31 Oct 19:28 N=12: certificates 31 Oct 19:28 N=12: files ['nineout/twelve/nineforms_a.npz', 'nineout/twelve/nineforms_b.npz', 'nineout/twelve/nineforms_c.npz', 'nineout/twelve/nineforms_d.npz'], configurations done 70 of 90; blocks [37, 33, 33, 36, 33, 33, 36, 33, 33] 31 Oct 19:28 N=12: character 0: dim 37, restricted span 117 of 703; best min eigenvalue 4.536e-03 (max 4.761e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 19:28 N=12: character 1: dim 33, restricted span 117 of 561; best min eigenvalue 6.035e-03 (max 4.880e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 19:28 N=12: character 2: dim 33, restricted span 117 of 561; best min eigenvalue 6.833e-03 (max 3.947e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 19:28 N=12: character 3: dim 36, restricted span 117 of 666; best min eigenvalue 6.859e-03 (max 4.059e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 19:28 N=12: character 4: dim 33, restricted span 117 of 561; best min eigenvalue 8.606e-03 (max 4.263e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 19:28 N=12: character 5: dim 33, restricted span 117 of 561; best min eigenvalue 8.602e-03 (max 4.258e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 19:28 N=12: character 6: dim 36, restricted span 117 of 666; best min eigenvalue 6.859e-03 (max 4.059e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 19:28 N=12: character 7: dim 33, restricted span 117 of 561; best min eigenvalue 6.832e-03 (max 3.956e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 19:28 N=12: character 8: dim 33, restricted span 117 of 561; best min eigenvalue 6.033e-03 (max 4.888e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 19:28 N=12: ALL BLOCKS EXCLUDED BY POSITIVITY 31 Oct 19:28 N=10: kernel by rotation characters, start 31 Oct 19:30 N=10: kernel done (1.4 min) 31 Oct 19:30 N=10: quadrics, 4 workers, start 31 Oct 21:25 N=10: quadrics done (116.9 min) 31 Oct 21:25 N=10: certificates 31 Oct 21:26 N=10: files ['nineout/ten/nineforms_a.npz', 'nineout/ten/nineforms_b.npz', 'nineout/ten/nineforms_c.npz', 'nineout/ten/nineforms_d.npz'], configurations done 90 of 90; blocks [37, 33, 33, 36, 33, 33, 36, 33, 33] 31 Oct 21:26 N=10: character 0: dim 37, restricted span 117 of 703; best min eigenvalue 1.747e-03 (max 4.993e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 21:26 N=10: character 1: dim 33, restricted span 117 of 561; best min eigenvalue 3.122e-03 (max 4.868e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 21:26 N=10: character 2: dim 33, restricted span 117 of 561; best min eigenvalue 3.654e-03 (max 4.259e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 21:26 N=10: character 3: dim 36, restricted span 117 of 666; best min eigenvalue 3.598e-03 (max 4.200e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 21:26 N=10: character 4: dim 33, restricted span 117 of 561; best min eigenvalue 4.742e-03 (max 4.347e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 21:26 N=10: character 5: dim 33, restricted span 117 of 561; best min eigenvalue 4.749e-03 (max 4.357e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 21:26 N=10: character 6: dim 36, restricted span 117 of 666; best min eigenvalue 3.597e-03 (max 4.198e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 21:26 N=10: character 7: dim 33, restricted span 117 of 561; best min eigenvalue 3.653e-03 (max 4.256e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 21:26 N=10: character 8: dim 33, restricted span 117 of 561; best min eigenvalue 3.121e-03 (max 4.880e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 21:26 N=10: ALL BLOCKS EXCLUDED BY POSITIVITY 31 Oct 21:26 N=9: kernel by rotation characters, start 31 Oct 21:27 N=9: kernel done (1.4 min) 31 Oct 21:27 N=9: quadrics, 4 workers, start 31 Oct 22:24 N=9: quadrics done (58.4 min) 31 Oct 22:24 N=9: certificates 31 Oct 22:25 N=9: files ['nineout/nine/nineforms_a.npz', 'nineout/nine/nineforms_b.npz', 'nineout/nine/nineforms_c.npz', 'nineout/nine/nineforms_d.npz'], configurations done 90 of 90; blocks [37, 33, 33, 36, 33, 33, 36, 33, 33] 31 Oct 22:25 N=9: character 0: dim 37, restricted span 117 of 703; best min eigenvalue 5.481e-04 (max 4.441e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 22:25 N=9: character 1: dim 33, restricted span 117 of 561; best min eigenvalue 1.612e-03 (max 4.708e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 22:25 N=9: character 2: dim 33, restricted span 117 of 561; best min eigenvalue 1.980e-03 (max 4.611e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 22:25 N=9: character 3: dim 36, restricted span 117 of 666; best min eigenvalue 1.867e-03 (max 4.344e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 22:25 N=9: character 4: dim 33, restricted span 117 of 561; best min eigenvalue 2.612e-03 (max 4.462e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 22:25 N=9: character 5: dim 33, restricted span 117 of 561; best min eigenvalue 2.615e-03 (max 4.465e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 22:25 N=9: character 6: dim 36, restricted span 117 of 666; best min eigenvalue 1.870e-03 (max 4.392e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 22:25 N=9: character 7: dim 33, restricted span 117 of 561; best min eigenvalue 1.978e-03 (max 4.627e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 22:25 N=9: character 8: dim 33, restricted span 117 of 561; best min eigenvalue 1.606e-03 (max 4.671e-01) -> POSITIVE DEFINITE: block excluded 31 Oct 22:25 N=9: ALL BLOCKS EXCLUDED BY POSITIVITY 31 Oct 22:25 === nine c: done === ==================================================================================================== ===== orthodualsout.txt ==================================================================================================== 31 Oct 12:45 orthoduals.py letters: 1 involution(s), 1 rotation pair(s), N = 3; span dims by level {2: (1, 1, 1), 4: (3, 2, 2), 6: (15, 6, 5), 8: (91, 23, 14)} (Brauer, half-liberated, Temperley-Lieb) 3328 tuples, 31 distinct law sets (4s) kinds: {'abelian': 6, 'half-abelian': 5, 'free-ish': 20}; law sets not easy over O_N: 0 (5s) letters: 2 involution(s), 0 rotation pair(s), N = 2; span dims by level {2: (1, 1, 1), 4: (3, 2, 2), 6: (10, 5, 5), 8: (35, 14, 14)} (Brauer, half-liberated, Temperley-Lieb) 424 tuples, 5 distinct law sets (0s) kinds: {'abelian': 2, 'half-abelian': 3}; law sets not easy over O_N: 0 (0s) letters: 2 involution(s), 1 rotation pair(s), N = 4; span dims by level {2: (1, 1, 1), 4: (3, 2, 2), 6: (15, 6, 5), 8: (105, 24, 14)} (Brauer, half-liberated, Temperley-Lieb) 10136 tuples, 595 distinct law sets (86s) kinds: {'abelian': 12, 'free-ish': 556, 'half-abelian': 27}; law sets not easy over O_N: 0 (121s) letters: 1 involution(s), 2 rotation pair(s), N = 5; span dims by level {2: (1, 1, 1), 4: (3, 2, 2), 6: (15, 6, 5)} (Brauer, half-liberated, Temperley-Lieb) 45008 tuples, 2339 distinct law sets (98s) kinds: {'abelian': 33, 'free-ish': 2278, 'half-abelian': 28}; law sets not easy over O_N: 0 (100s) letters: 3 involution(s), 1 rotation pair(s), N = 5; span dims by level {2: (1, 1, 1), 4: (3, 2, 2), 6: (15, 6, 5)} (Brauer, half-liberated, Temperley-Lieb) 7408 tuples, 917 distinct law sets (15s) kinds: {'abelian': 20, 'free-ish': 852, 'half-abelian': 45}; law sets not easy over O_N: 0 (16s) (paper: 31, 305, 595, 2339, 917 law sets, all easy over O_N) 31 Oct 12:50 orthoduals.py letters: 0 involution(s), 2 rotation pair(s), N = 4; span dims by level {2: (1, 1, 1), 4: (3, 2, 2), 6: (15, 6, 5), 8: (105, 24, 14)} (Brauer, half-liberated, Temperley-Lieb) 8902 tuples, 305 distinct law sets (84s) kinds: {'abelian': 22, 'half-abelian': 9, 'free-ish': 274}; law sets not easy over O_N: 0 (97s) (paper: 31, 305, 595, 2339, 917 law sets, all easy over O_N) ==================================================================================================== ===== orthotwistsout.txt ==================================================================================================== 31 Oct 13:02 orthotwists.py both N=3: 4 graphs, levels (4, 6, 8) expected dimensions {4: {'Br': 3, 'HL': 2, 'TL': 2}, 6: {'Br': 15, 'HL': 6, 'TL': 5}, 8: {'Br': 91, 'HL': 23, 'TL': 14}} eps = empty: O_N, joint dims {4: 3, 6: 15, 8: 91} ok eps = [(0, 1)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok eps = [(0, 1), (0, 2)]: O_N^*, joint dims {4: 2, 6: 6, 8: 23} ok eps = [(0, 1), (0, 2), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok N=3: 0 mismatches N=4: 11 graphs, levels (4, 6, 8) expected dimensions {4: {'Br': 3, 'HL': 2, 'TL': 2}, 6: {'Br': 15, 'HL': 6, 'TL': 5}, 8: {'Br': 105, 'HL': 24, 'TL': 14}} eps = empty: O_N, joint dims {4: 3, 6: 15, 8: 105} ok eps = [(0, 1)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok eps = [(0, 1), (0, 2)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok eps = [(0, 1), (0, 2), (0, 3)]: O_N^*, joint dims {4: 2, 6: 6, 8: 24} ok eps = [(0, 1), (0, 2), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok eps = [(0, 3), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok eps = [(0, 1), (0, 3), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok eps = [(0, 1), (0, 2), (0, 3), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok eps = [(0, 2), (0, 3), (1, 2), (1, 3)]: O_N^*, joint dims {4: 2, 6: 6, 8: 24} ok eps = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok eps = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5, 8: 14} ok N=4: 0 mismatches N=5: 34 graphs, levels (4, 6) expected dimensions {4: {'Br': 3, 'HL': 2, 'TL': 2}, 6: {'Br': 15, 'HL': 6, 'TL': 5}} eps = empty: O_N, joint dims {4: 3, 6: 15} ok eps = [(0, 1)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4)]: O_N^*, joint dims {4: 2, 6: 6} ok eps = [(0, 1), (0, 2), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 3), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 3), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 3), (0, 4), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 3), (0, 4), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 2), (0, 3), (1, 2), (1, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 2), (0, 4), (1, 2), (1, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 4), (1, 2), (1, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 2), (0, 3), (0, 4), (1, 2), (1, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4)]: O_N^*, joint dims {4: 2, 6: 6} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 4), (1, 2), (1, 3), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 4), (1, 2), (1, 3), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 4), (1, 2), (1, 3), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 4), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 3), (0, 4), (1, 2), (1, 4), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 3), (0, 4), (1, 2), (1, 4), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 4), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 3), (1, 4), (2, 3), (2, 4)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4)]: O_N^+, joint dims {4: 2, 6: 5} ok eps = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]: O_N^+, joint dims {4: 2, 6: 5} ok N=5: 0 mismatches N=4: levels (4, 6, 8), expected dimensions {4: {'Br': 3, 'HL': 2, 'TL': 2}, 6: {'Br': 15, 'HL': 6, 'TL': 5}, 8: {'Br': 105, 'HL': 24, 'TL': 14}} theta = 1/2: joint dims {4: 2, 6: 6, 8: 24} -> HL theta = 1/3: joint dims {4: 2, 6: 5, 8: 14} -> TL theta = 1/4: joint dims {4: 2, 6: 5, 8: 14} -> TL theta = 1/5: joint dims {4: 2, 6: 5, 8: 14} -> TL theta = 1/6: joint dims {4: 2, 6: 5, 8: 14} -> TL theta = 2/5: joint dims {4: 2, 6: 5, 8: 14} -> TL theta = sqrt2-1: joint dims {4: 2, 6: 5, 8: 14} -> TL theta = random: joint dims {4: 2, 6: 5, 8: 14} -> TL N=6: levels (4, 6), expected dimensions {4: {'Br': 3, 'HL': 2, 'TL': 2}, 6: {'Br': 15, 'HL': 6, 'TL': 5}} theta = 1/2: joint dims {4: 2, 6: 5} -> TL theta = 1/3: joint dims {4: 2, 6: 5} -> TL theta = 1/4: joint dims {4: 2, 6: 5} -> TL theta = 1/5: joint dims {4: 2, 6: 5} -> TL theta = 1/6: joint dims {4: 2, 6: 5} -> TL theta = 2/5: joint dims {4: 2, 6: 5} -> TL theta = sqrt2-1: joint dims {4: 2, 6: 5} -> TL theta = random: joint dims {4: 2, 6: 5} -> TL ==================================================================================================== ===== pairlevelsout.txt ==================================================================================================== 31 Oct 13:37 pairlevels.py eight level 8: |P_2^*(8)| = 24, |TL(8)| = 14 N=3: rank Cap = 22, dim ker = 2, h_+ = -8712, h_- = 0 N=4: rank Cap = 22, dim ker = 2, h_+ = -10108, h_- = -484/9 N=5: rank Cap = 22, dim ker = 2, h_+ = -134560/9, h_- = -14440/49 N=8: rank Cap = 22, dim ker = 2, h_+ = -443608/9, h_- = -4840 N=12: rank Cap = 22, dim ker = 2, h_+ = -172980, h_- = -1853388/49 rank of Cap(N) for N = 3..14: [22] (paper: 22 for N >= 2, so dim U(8) = 2) (N - 2)^2 h_+(N) = -12N + 20N^2 + 20N^3 - 20N^4 - 20N^5 - 4N^6 (N + 2)^2 h_-(N) = 12N + 20N^2 - 20N^3 - 20N^4 + 20N^5 - 4N^6 (paper: (N-2)^2 h_+ = -4N(N+3)(N^2+N-1)^2, (N+2)^2 h_- = -4N(N-3)(N^2-N-1)^2) expansion of the paper formula for +: -12N + 20N^2 + 20N^3 - 20N^4 - 20N^5 - 4N^6 31 Oct 13:37 pairlevels.py six level 6, Brauer: |P_2(6)| = 15, TL: 5 N=3: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.3727 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 1.166e+00 N=4: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.3330 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 1.905e+00 N=5: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.5381 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.321e+00 N=6: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6040 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.566e+00 N=7: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6292 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.722e+00 N=8: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6393 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.826e+00 N=10: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6433 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.955e+00 N=12: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6405 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 3.029e+00 (paper: dim U = 4 = 2 + 2; q has the zero lines h and y; y fails closure; the e^{+-2 pi i/3} block is excluded) 31 Oct 13:37 pairlevels.py ten level 10: |P_2^*(10)| = 120, crossing pairings at level 8: 10 N=5: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.02e-01, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 2.65e+00, exact LDL positive (3s) N=6: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 6.78e-02, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.11e+00, exact LDL positive (3s) N=7: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 2.78e-02, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.03e+00, exact LDL positive (3s) N=8: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.72e-02, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.13e+00, exact LDL positive (3s) N=9: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.27e-02, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.14e+00, exact LDL positive (3s) (paper: dim U(10) = 13 = 4 + 1 + 8 on rho = 1, rho = -1, Phi_5, nothing on Phi_10; all three blocks excluded for N >= 5) 31 Oct 13:38 pairlevels.py six level 6, Brauer: |P_2(6)| = 15, TL: 5 N=3: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.3727 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 1.166e+00 N=4: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.3330 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 1.905e+00 N=5: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.5381 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.321e+00 N=6: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6040 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.566e+00 N=7: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6292 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.722e+00 N=8: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6393 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.826e+00 N=9: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6428 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.900e+00 N=10: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6433 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 2.955e+00 N=12: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6405 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 3.029e+00 N=16: dim U = 4, rho-invariant block dim 2, other block real dim 2, zero lines of q: 2, one of them is the uncappable part h of xi_kappa: True; closure of y: |cos| = 0.6318 (1 would mean closure holds); other block: best positive combination (coefficients in {-1,0,1}) has smallest eigenvalue 3.108e+00 (paper: dim U = 4 = 2 + 2; q has the zero lines h and y; y fails closure; the e^{+-2 pi i/3} block is excluded) 31 Oct 13:38 pairlevels.py ten level 10: |P_2^*(10)| = 120, crossing pairings at level 8: 10 N=5: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.02e-01, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 2.65e+00, exact LDL positive (3s) N=6: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 6.78e-02, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.11e+00, exact LDL positive (3s) N=7: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 2.78e-02, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.03e+00, exact LDL positive (3s) N=8: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.72e-02, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.13e+00, exact LDL positive (3s) N=9: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.27e-02, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.14e+00, exact LDL positive (3s) N=10: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 6.49e-03, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.07e+00, exact LDL positive (3s) N=11: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 3.95e-03, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.64e+00, exact LDL positive (3s) N=12: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 2.92e-03, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.13e+00, exact LDL positive (3s) N=13: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 2.51e-03, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.38e+00, exact LDL positive (3s) N=14: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.64e-03, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 2.88e+00, exact LDL positive (3s) N=15: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.06e-03, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.50e+00, exact LDL positive (3s) N=16: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 8.89e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.10e+00, exact LDL positive (4s) N=17: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 6.80e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.40e+00, exact LDL positive (4s) N=18: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 6.00e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.49e+00, exact LDL positive (4s) N=19: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 4.77e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.36e+00, exact LDL positive (3s) N=20: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 3.32e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.30e+00, exact LDL positive (4s) N=21: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 3.61e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.49e+00, exact LDL positive (3s) N=22: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 2.28e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.22e+00, exact LDL positive (3s) N=23: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 2.01e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.41e+00, exact LDL positive (3s) N=24: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 2.00e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.29e+00, exact LDL positive (4s) N=25: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.72e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.18e+00, exact LDL positive (3s) N=26: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.23e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.60e+00, exact LDL positive (3s) N=27: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 1.16e-04, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.13e+00, exact LDL positive (3s) N=28: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 9.07e-05, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.38e+00, exact LDL positive (3s) N=29: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 6.97e-05, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.55e+00, exact LDL positive (3s) N=30: rank Cap = 107, dim U(10) = 13, blocks {'rho=1': np.int64(4), 'rho=-1': np.int64(1), 'Phi_5': np.int64(8), 'Phi_10': np.int64(0)}; rho=1: dim 4, 110 forms, margin 6.60e-05, exact LDL positive; rho=-1: dim 1, 110 forms, margin 1.05e+01, exact LDL positive; Phi_5: dim 8, 110 forms, margin 3.92e+00, exact LDL positive (3s) (paper: dim U(10) = 13 = 4 + 1 + 8 on rho = 1, rho = -1, Phi_5, nothing on Phi_10; all three blocks excluded for N >= 5) ==================================================================================================== ===== projectiveout.txt ==================================================================================================== 31 Oct 13:31 projective.py hyper N=3: dim C_(k) (and dim TL(k)) for k = 4, 6, 8: {4: (2, 2), 6: (5, 5), 8: (14, 14)} = O_N^+ N=4: dim C_(k) (and dim TL(k)) for k = 4, 6, 8: {4: (2, 2), 6: (5, 5), 8: (14, 14)} = O_N^+ 31 Oct 13:32 projective.py det U_4^2 at the color pattern of 8 white legs: 70 vectors eps_A (x) eps_B of rank 14, 1430 noncrossing vectors of rank 1430, joint rank 1444: intersection of dimension 0 (29s) N=3, generators in S_2..S_5; reference dims {4: {'Br': 3, 'HL': 2, 'TL': 2}, 6: {'Br': 15, 'HL': 6, 'TL': 5}, 8: {'Br': 91, 'HL': 23, 'TL': 14}}; positions M: ['I', 'random 1', 'random 2'] 103796 tuples, 119 distinct law sets (88s) classical PG: 30 law sets, non-classical: 89; unexpected outcomes: 0 (113s) 31 Oct 13:34 projective.py duals N=3, generators in S_2..S_5; reference dims {4: {'Br': 3, 'HL': 2, 'TL': 2}, 6: {'Br': 15, 'HL': 6, 'TL': 5}, 8: {'Br': 91, 'HL': 23, 'TL': 14}}; positions M: ['I', 'random 1', 'random 2'] 103796 tuples, 119 distinct law sets (84s) classical PG: 30 law sets, non-classical: 89; unexpected outcomes: 0 (108s) N=4, generators in S_2..S_4; reference dims {4: {'Br': 3, 'HL': 2, 'TL': 2}, 6: {'Br': 15, 'HL': 6, 'TL': 5}, 8: {'Br': 105, 'HL': 24, 'TL': 14}}; positions M: ['I', 'random 1', 'random 2'] 69784 tuples, 611 distinct law sets (402s) dualsfour run N=4, generators in S_2..S_4; reference dims {4: {'Br': 3, 'HL': 2, 'TL': 2}, 6: {'Br': 15, 'HL': 6, 'TL': 5}, 8: {'Br': 105, 'HL': 24, 'TL': 14}}; positions M: ['I', 'random 1', 'random 2'] 69784 tuples, 611 distinct law sets (391s) ==================================================================================================== ===== projlevelsout.txt ==================================================================================================== --- projlevels.py six 4 5 6 7 31 Oct 18:24 --- === level 6, projective: uncappable space of Br(6), rho^2 blocks, quadric, closure === |Br(6)| = 15, |TL(6)| = 5, |HL(6)| = 6 N = 4: dim U(6) = 4 eigenvalues of rho on U(6): -2.000/6, +0.000/6, +0.000/6, +2.000/6 (as k in e^{2 pi i k/6}) eigenvalues of rho^2 on U(6): -1.000/3, +0.000/3, +0.000/3, +1.000/3 rho-invariant block: dim 2; rho^2-invariant block: dim 2 quadric q on the invariant block (basis vectors in coordinates on Br(6)): ['-1/2', '1', '0', '1', '-3', '1', '0', '5/2', '-3', '1', '-3', '1', '-1/2', '1', '0'] ['-1/2', '0', '1', '0', '0', '0', '1', '-7/2', '0', '0', '0', '0', '-1/2', '0', '1'] q = [['-56', '28'], ['28', '0']] discriminant b^2 - ac = 784 zero line x = ['-1/2', '0', '1', '0', '0', '0', '1', '-7/2', '0', '0', '0', '0', '-1/2', '0', '1']: supported on HL(6): True; x o_3 x crossing part proportional to x: True (ratios ['2']) zero line x = ['-1', '1', '1', '1', '-3', '1', '1', '-1', '-3', '1', '-3', '1', '-1', '1', '1']: supported on HL(6): False; x o_3 x crossing part proportional to x: False (ratios ['-2/3', '-26/3', '-6', '14', '2']) N = 5: dim U(6) = 4 eigenvalues of rho on U(6): -2.000/6, +0.000/6, +0.000/6, +2.000/6 (as k in e^{2 pi i k/6}) eigenvalues of rho^2 on U(6): -1.000/3, +0.000/3, +0.000/3, +1.000/3 rho-invariant block: dim 2; rho^2-invariant block: dim 2 quadric q on the invariant block (basis vectors in coordinates on Br(6)): ['-2/5', '1', '0', '1', '-7/2', '1', '0', '29/10', '-7/2', '1', '-7/2', '1', '-2/5', '1', '0'] ['-2/5', '0', '1', '0', '0', '0', '1', '-23/5', '0', '0', '0', '0', '-2/5', '0', '1'] q = [['-1053/10', '621/10'], ['621/10', '0']] discriminant b^2 - ac = 385641/100 N = 6: dim U(6) = 4 eigenvalues of rho on U(6): -2.000/6, +0.000/6, +0.000/6, +2.000/6 (as k in e^{2 pi i k/6}) eigenvalues of rho^2 on U(6): -1.000/3, +0.000/3, +0.000/3, +1.000/3 rho-invariant block: dim 2; rho^2-invariant block: dim 2 quadric q on the invariant block (basis vectors in coordinates on Br(6)): ['-1/3', '1', '0', '1', '-4', '1', '0', '10/3', '-4', '1', '-4', '1', '-1/3', '1', '0'] ['-1/3', '0', '1', '0', '0', '0', '1', '-17/3', '0', '0', '0', '0', '-1/3', '0', '1'] q = [['-520/3', '340/3'], ['340/3', '0']] discriminant b^2 - ac = 115600/9 N = 7: dim U(6) = 4 eigenvalues of rho on U(6): -2.000/6, +0.000/6, +0.000/6, +2.000/6 (as k in e^{2 pi i k/6}) eigenvalues of rho^2 on U(6): -1.000/3, -0.000/3, +0.000/3, +1.000/3 rho-invariant block: dim 2; rho^2-invariant block: dim 2 quadric q on the invariant block (basis vectors in coordinates on Br(6)): ['-2/7', '1', '0', '1', '-9/2', '1', '0', '53/14', '-9/2', '1', '-9/2', '1', '-2/7', '1', '0'] ['-2/7', '0', '1', '0', '0', '0', '1', '-47/7', '0', '0', '0', '0', '-2/7', '0', '1'] q = [['-3685/14', '2585/14'], ['2585/14', '0']] discriminant b^2 - ac = 6682225/196 --- projlevels.py gennc 8 31 Oct 18:24 --- === rho^2-category generated by TL, levels <= 8 === round 1: dims 2:1, 4:2, 6:5, 8:14 N = 5: level 2: 1 (HL 1, TL 1, Br 1), level 4: 2 (HL 2, TL 2, Br 3), level 6: 5 (HL 6, TL 5, Br 15), level 8: 14 (HL 24, TL 14, Br 105) (0s) --- projlevels.py gen 10 5 7 31 Oct 18:24 --- === rho^2-category generated by TL and xi_kappa, levels <= 10 === round 1: dims 2:1, 4:2, 6:6, 8:22, 10:88 round 2: dims 2:1, 4:2, 6:6, 8:24, 10:115 round 3: dims 2:1, 4:2, 6:6, 8:24, 10:120 round 4: dims 2:1, 4:2, 6:6, 8:24, 10:120 N = 5: level 2: 1 (HL 1, TL 1, Br 1), level 4: 2 (HL 2, TL 2, Br 3), level 6: 6 (HL 6, TL 5, Br 15), level 8: 24 (HL 24, TL 14, Br 105), level 10: 120 (HL 120, TL 42, Br 945) (37s) round 1: dims 2:1, 4:2, 6:6, 8:22, 10:88 round 2: dims 2:1, 4:2, 6:6, 8:24, 10:115 round 3: dims 2:1, 4:2, 6:6, 8:24, 10:120 round 4: dims 2:1, 4:2, 6:6, 8:24, 10:120 N = 7: level 2: 1 (HL 1, TL 1, Br 1), level 4: 2 (HL 2, TL 2, Br 3), level 6: 6 (HL 6, TL 5, Br 15), level 8: 24 (HL 24, TL 14, Br 105), level 10: 120 (HL 120, TL 42, Br 945) (34s) --- projlevels.py gen 10 5 31 Oct 18:27 --- === rho^2-category generated by TL and xi_kappa, levels <= 10 === round 1: dims 2:1, 4:2, 6:6, 8:22, 10:88 round 2: dims 2:1, 4:2, 6:6, 8:24, 10:115 round 3: dims 2:1, 4:2, 6:6, 8:24, 10:120 round 4: dims 2:1, 4:2, 6:6, 8:24, 10:120 N = 5: level 2: 1 (HL 1, TL 1, Br 1), level 4: 2 (HL 2, TL 2, Br 3), level 6: 6 (HL 6, TL 5, Br 15), level 8: 24 (HL 24, TL 14, Br 105), level 10: 120 (HL 120, TL 42, Br 945) (80s) --- projlevels.py gen 12 5 31 Oct 18:29 --- === rho^2-category generated by TL and xi_kappa, levels <= 12 === --- projlevels.py cert PH 4 8 31 Oct 18:29 --- PH level 8 N=8: {'dimU': 2, 'status': 'EXCLUDED', 'blocks': {'0': {'dim': 2, 'ok': True, 'margin': 0.6537710189819336, 'rotations': 1, 'forms': 60}}} --- projlevels.py cert PR 4 8 31 Oct 18:29 --- PR level 8 N=8: {'dimU': 31, 'status': 'EXCLUDED', 'blocks': {'0': {'dim': 13, 'ok': True, 'margin': 0.00037827213594515273, 'rotations': 1, 'forms': 60}, '1': {'dim': 8, 'ok': True, 'margin': 0.02060501634524234, 'rotations': 2, 'forms': 60}, '2': {'dim': 10, 'ok': True, 'margin': 0.0007184078382199845, 'rotations': 1, 'forms': 60}}} --- projlevels.py table 31 Oct 18:29 --- PR level 8 N=4: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.6e-03, k=1: dim 8 margin 3.0e-02, k=2: dim 10 margin 3.2e-03 PR level 8 N=5: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.8e-03, k=1: dim 8 margin 3.1e-02, k=2: dim 10 margin 4.4e-03 PR level 8 N=6: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.1e-03, k=1: dim 8 margin 2.8e-02, k=2: dim 10 margin 2.2e-03 PR level 8 N=7: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 4.6e-04, k=1: dim 8 margin 2.4e-02, k=2: dim 10 margin 1.3e-03 PR level 8 N=8: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 3.8e-04, k=1: dim 8 margin 2.1e-02, k=2: dim 10 margin 7.2e-04 PR level 8 N=9: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.0e-04, k=1: dim 8 margin 1.8e-02, k=2: dim 10 margin 4.2e-04 PR level 8 N=10: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 4.6e-05, k=1: dim 8 margin 1.6e-02, k=2: dim 10 margin 2.0e-04 PR level 8 N=12: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 6.8e-05, k=1: dim 8 margin 1.2e-02, k=2: dim 10 margin 1.3e-04 PR level 8 N=16: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.4e-05, k=1: dim 8 margin 8.5e-03, k=2: dim 10 margin 7.3e-05 PH level 8 N=4: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 4.8e-01 PH level 8 N=5: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.7e-01 PH level 8 N=6: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.8e-01 PH level 8 N=7: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.6e-01 PH level 8 N=8: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.5e-01 PH level 8 N=9: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.5e-01 PH level 8 N=10: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.5e-01 PH level 8 N=12: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.6e-01 PH level 8 N=16: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.7e-01 PR level 10 N=5: dim U 293, OPEN, blocks k=0: dim 61 margin -3.1e-05, k=1: dim 116 margin 1.0e-05, k=2: dim 116 margin -1.9e-05 PR level 10 N=6: dim U 293, OPEN, blocks k=0: dim 61 margin -2.5e-05, k=1: dim 116 margin -1.4e-05, k=2: dim 116 margin -3.3e-05 PR level 10 N=7: dim U 293, OPEN, blocks k=0: dim 61 margin -2.7e-05, k=1: dim 116 margin -8.4e-06, k=2: dim 116 margin -2.5e-05 PR level 10 N=8: dim U 293, OPEN, blocks k=0: dim 61 margin -2.7e-05, k=1: dim 116 margin -5.9e-06, k=2: dim 116 margin -1.7e-05 PR level 10 N=9: dim U 293, OPEN, blocks k=0: dim 61 margin -2.8e-05, k=1: dim 116 margin -4.3e-06, k=2: dim 116 margin -1.1e-05 PR level 10 N=10: dim U 293, OPEN, blocks k=0: dim 61 margin -3.1e-05, k=1: dim 116 margin -3.6e-06, k=2: dim 116 margin -6.2e-06 PR level 10 N=12: dim U 293, OPEN, blocks k=0: dim 61 margin -3.8e-05, k=1: dim 116 margin -2.9e-06, k=2: dim 116 margin -3.0e-06 PR level 10 N=16: dim U 293, OPEN, blocks k=0: dim 61 margin -4.8e-05, k=1: dim 116 margin -2.5e-06, k=2: dim 116 margin -2.9e-06 PH level 10 N=5: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 4.8e-03, k=1: dim 4 margin 1.5e-01, k=2: dim 4 margin 2.0e-01 PH level 10 N=6: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 2.2e-03, k=1: dim 4 margin 1.8e-01, k=2: dim 4 margin 2.3e-01 PH level 10 N=7: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 1.1e-03, k=1: dim 4 margin 2.0e-01, k=2: dim 4 margin 2.4e-01 PH level 10 N=8: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 6.2e-04, k=1: dim 4 margin 2.1e-01, k=2: dim 4 margin 2.5e-01 PH level 10 N=9: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 3.9e-04, k=1: dim 4 margin 2.2e-01, k=2: dim 4 margin 2.6e-01 PH level 10 N=10: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 2.5e-04, k=1: dim 4 margin 2.2e-01, k=2: dim 4 margin 2.7e-01 PH level 10 N=12: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 1.2e-04, k=1: dim 4 margin 2.2e-01, k=2: dim 4 margin 2.7e-01 PH level 10 N=16: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 3.8e-05, k=1: dim 4 margin 2.3e-01, k=2: dim 4 margin 2.8e-01 --- projlevels.py gen 12 5 31 Oct 18:48 --- === rho^2-category generated by TL and xi_kappa, levels <= 12 === --- projlevels.py cert PH 4 6 31 Oct 18:49 --- PH level 8 N=6: {'dimU': 2, 'status': 'EXCLUDED', 'blocks': {'0': {'dim': 2, 'ok': True, 'margin': 0.6831413904825846, 'rotations': 1, 'forms': 60}}} --- projlevels.py cert PR 4 6 31 Oct 18:49 --- PR level 8 N=6: {'dimU': 31, 'status': 'EXCLUDED', 'blocks': {'0': {'dim': 13, 'ok': True, 'margin': 0.0010914321333560539, 'rotations': 1, 'forms': 60}, '1': {'dim': 8, 'ok': True, 'margin': 0.027502982345301526, 'rotations': 2, 'forms': 60}, '2': {'dim': 10, 'ok': True, 'margin': 0.002233040917700816, 'rotations': 1, 'forms': 60}}} --- projlevels.py gen 12 31 Oct 22:54 --- === rho^2-category generated by TL and xi_kappa, levels <= 12 === round 1: dims 2:1, 4:2, 6:6, 8:22, 10:88, 12:366 round 2: dims 2:1, 4:2, 6:6, 8:24, 10:115, 12:654 --- projlevels.py gen 12 31 Oct 23:16 --- === rho^2-category generated by TL and xi_kappa, levels <= 12 === round 1: dims 2:1, 4:2, 6:6, 8:22, 10:88, 12:366 round 2: dims 2:1, 4:2, 6:6, 8:24, 10:115, 12:654 round 3: dims 2:1, 4:2, 6:6, 8:24, 10:120, 12:712 round 4: dims 2:1, 4:2, 6:6, 8:24, 10:120, 12:718 round 5: dims 2:1, 4:2, 6:6, 8:24, 10:120, 12:720 round 6: dims 2:1, 4:2, 6:6, 8:24, 10:120, 12:720 N = 5: level 2: 1 (HL 1, TL 1, Br 1), level 4: 2 (HL 2, TL 2, Br 3), level 6: 6 (HL 6, TL 5, Br 15), level 8: 24 (HL 24, TL 14, Br 105), level 10: 120 (HL 120, TL 42, Br 945), level 12: 720 (HL 720, TL 132, Br 10395) (1054s) round 1: dims 2:1, 4:2, 6:6, 8:22, 10:88, 12:366 round 2: dims 2:1, 4:2, 6:6, 8:24, 10:115, 12:654 round 3: dims 2:1, 4:2, 6:6, 8:24, 10:120, 12:712 round 4: dims 2:1, 4:2, 6:6, 8:24, 10:120, 12:718 round 5: dims 2:1, 4:2, 6:6, 8:24, 10:120, 12:720 round 6: dims 2:1, 4:2, 6:6, 8:24, 10:120, 12:720 N = 7: level 2: 1 (HL 1, TL 1, Br 1), level 4: 2 (HL 2, TL 2, Br 3), level 6: 6 (HL 6, TL 5, Br 15), level 8: 24 (HL 24, TL 14, Br 105), level 10: 120 (HL 120, TL 42, Br 945), level 12: 720 (HL 720, TL 132, Br 10395) (995s) ==================================================================================================== ===== projlevelstable.txt ==================================================================================================== --- projlevels.py table 31 Oct 18:29 --- 18:29:52 PR level 8 N=4: dim U = 31, real rotation blocks {0: 13, 1: 8, 2: 10} (0.0 min) 18:29:52 block k=0 (dim 13, 60 forms x 1 rotations): positive definite, margin 1.65e-03 (0.0 min) 18:29:52 block k=1 (dim 8, 60 forms x 2 rotations): positive definite, margin 3.05e-02 (0.0 min) 18:29:52 block k=2 (dim 10, 60 forms x 1 rotations): positive definite, margin 3.20e-03 (0.0 min) 18:29:52 PR level 8 N=4: EXCLUDED, smallest margin 1.65e-03 (0.0 min) PR level 8 N=4: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.6e-03, k=1: dim 8 margin 3.0e-02, k=2: dim 10 margin 3.2e-03 18:29:52 PR level 8 N=5: dim U = 31, real rotation blocks {0: 13, 1: 8, 2: 10} (0.0 min) 18:29:52 block k=0 (dim 13, 60 forms x 1 rotations): positive definite, margin 1.77e-03 (0.0 min) 18:29:52 block k=1 (dim 8, 60 forms x 2 rotations): positive definite, margin 3.11e-02 (0.0 min) 18:29:52 block k=2 (dim 10, 60 forms x 1 rotations): positive definite, margin 4.45e-03 (0.0 min) 18:29:52 PR level 8 N=5: EXCLUDED, smallest margin 1.77e-03 (0.0 min) PR level 8 N=5: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.8e-03, k=1: dim 8 margin 3.1e-02, k=2: dim 10 margin 4.4e-03 18:29:52 PR level 8 N=6: dim U = 31, real rotation blocks {0: 13, 1: 8, 2: 10} (0.0 min) 18:29:52 block k=0 (dim 13, 60 forms x 1 rotations): positive definite, margin 1.09e-03 (0.0 min) 18:29:53 block k=1 (dim 8, 60 forms x 2 rotations): positive definite, margin 2.75e-02 (0.0 min) 18:29:53 block k=2 (dim 10, 60 forms x 1 rotations): positive definite, margin 2.23e-03 (0.0 min) 18:29:53 PR level 8 N=6: EXCLUDED, smallest margin 1.09e-03 (0.0 min) PR level 8 N=6: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.1e-03, k=1: dim 8 margin 2.8e-02, k=2: dim 10 margin 2.2e-03 18:29:53 PR level 8 N=7: dim U = 31, real rotation blocks {0: 13, 1: 8, 2: 10} (0.0 min) 18:29:53 block k=0 (dim 13, 60 forms x 1 rotations): positive definite, margin 4.59e-04 (0.0 min) 18:29:53 block k=1 (dim 8, 60 forms x 2 rotations): positive definite, margin 2.43e-02 (0.0 min) 18:29:53 block k=2 (dim 10, 60 forms x 1 rotations): positive definite, margin 1.26e-03 (0.0 min) 18:29:53 PR level 8 N=7: EXCLUDED, smallest margin 4.59e-04 (0.0 min) PR level 8 N=7: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 4.6e-04, k=1: dim 8 margin 2.4e-02, k=2: dim 10 margin 1.3e-03 18:29:53 PR level 8 N=8: dim U = 31, real rotation blocks {0: 13, 1: 8, 2: 10} (0.0 min) 18:29:53 block k=0 (dim 13, 60 forms x 1 rotations): positive definite, margin 3.78e-04 (0.0 min) 18:29:53 block k=1 (dim 8, 60 forms x 2 rotations): positive definite, margin 2.06e-02 (0.0 min) 18:29:53 block k=2 (dim 10, 60 forms x 1 rotations): positive definite, margin 7.18e-04 (0.0 min) 18:29:53 PR level 8 N=8: EXCLUDED, smallest margin 3.78e-04 (0.0 min) PR level 8 N=8: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 3.8e-04, k=1: dim 8 margin 2.1e-02, k=2: dim 10 margin 7.2e-04 18:29:53 PR level 8 N=9: dim U = 31, real rotation blocks {0: 13, 1: 8, 2: 10} (0.0 min) 18:29:53 block k=0 (dim 13, 60 forms x 1 rotations): positive definite, margin 1.04e-04 (0.0 min) 18:29:53 block k=1 (dim 8, 60 forms x 2 rotations): positive definite, margin 1.78e-02 (0.0 min) 18:29:53 block k=2 (dim 10, 60 forms x 1 rotations): positive definite, margin 4.16e-04 (0.0 min) 18:29:53 PR level 8 N=9: EXCLUDED, smallest margin 1.04e-04 (0.0 min) PR level 8 N=9: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.0e-04, k=1: dim 8 margin 1.8e-02, k=2: dim 10 margin 4.2e-04 18:29:53 PR level 8 N=10: dim U = 31, real rotation blocks {0: 13, 1: 8, 2: 10} (0.0 min) 18:29:53 block k=0 (dim 13, 60 forms x 1 rotations): positive definite, margin 4.56e-05 (0.0 min) 18:29:53 block k=1 (dim 8, 60 forms x 2 rotations): positive definite, margin 1.59e-02 (0.0 min) 18:29:53 block k=2 (dim 10, 60 forms x 1 rotations): positive definite, margin 1.97e-04 (0.0 min) 18:29:53 PR level 8 N=10: EXCLUDED, smallest margin 4.56e-05 (0.0 min) PR level 8 N=10: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 4.6e-05, k=1: dim 8 margin 1.6e-02, k=2: dim 10 margin 2.0e-04 18:29:53 PR level 8 N=12: dim U = 31, real rotation blocks {0: 13, 1: 8, 2: 10} (0.0 min) 18:29:53 block k=0 (dim 13, 60 forms x 1 rotations): no certificate yet (best 2.87e-06) (0.0 min) 18:29:53 block k=0 (dim 13, 150 forms x 1 rotations): positive definite, margin 6.85e-05 (0.0 min) 18:29:53 block k=1 (dim 8, 60 forms x 2 rotations): positive definite, margin 1.24e-02 (0.0 min) 18:29:53 block k=2 (dim 10, 60 forms x 1 rotations): positive definite, margin 1.34e-04 (0.0 min) 18:29:53 PR level 8 N=12: EXCLUDED, smallest margin 6.85e-05 (0.0 min) PR level 8 N=12: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 6.8e-05, k=1: dim 8 margin 1.2e-02, k=2: dim 10 margin 1.3e-04 18:29:53 PR level 8 N=16: dim U = 31, real rotation blocks {0: 13, 1: 8, 2: 10} (0.0 min) 18:29:53 block k=0 (dim 13, 60 forms x 1 rotations): positive definite, margin 1.42e-05 (0.0 min) 18:29:53 block k=1 (dim 8, 60 forms x 2 rotations): positive definite, margin 8.48e-03 (0.0 min) 18:29:53 block k=2 (dim 10, 60 forms x 1 rotations): positive definite, margin 7.32e-05 (0.0 min) 18:29:53 PR level 8 N=16: EXCLUDED, smallest margin 1.42e-05 (0.0 min) PR level 8 N=16: dim U 31, EXCLUDED, blocks k=0: dim 13 margin 1.4e-05, k=1: dim 8 margin 8.5e-03, k=2: dim 10 margin 7.3e-05 18:29:53 PH level 8 N=4: dim U = 2, real rotation blocks {0: 2, 1: 0, 2: 0} (0.0 min) 18:29:53 block k=0 (dim 2, 60 forms x 1 rotations): positive definite, margin 4.83e-01 (0.0 min) 18:29:53 PH level 8 N=4: EXCLUDED, smallest margin 4.83e-01 (0.0 min) PH level 8 N=4: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 4.8e-01 18:29:53 PH level 8 N=5: dim U = 2, real rotation blocks {0: 2, 1: 0, 2: 0} (0.0 min) 18:29:53 block k=0 (dim 2, 60 forms x 1 rotations): positive definite, margin 6.73e-01 (0.0 min) 18:29:53 PH level 8 N=5: EXCLUDED, smallest margin 6.73e-01 (0.0 min) PH level 8 N=5: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.7e-01 18:29:53 PH level 8 N=6: dim U = 2, real rotation blocks {0: 2, 1: 0, 2: 0} (0.0 min) 18:29:53 block k=0 (dim 2, 60 forms x 1 rotations): positive definite, margin 6.83e-01 (0.0 min) 18:29:53 PH level 8 N=6: EXCLUDED, smallest margin 6.83e-01 (0.0 min) PH level 8 N=6: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.8e-01 18:29:53 PH level 8 N=7: dim U = 2, real rotation blocks {0: 2, 1: 0, 2: 0} (0.0 min) 18:29:53 block k=0 (dim 2, 60 forms x 1 rotations): positive definite, margin 6.61e-01 (0.0 min) 18:29:53 PH level 8 N=7: EXCLUDED, smallest margin 6.61e-01 (0.0 min) PH level 8 N=7: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.6e-01 18:29:53 PH level 8 N=8: dim U = 2, real rotation blocks {0: 2, 1: 0, 2: 0} (0.0 min) 18:29:53 block k=0 (dim 2, 60 forms x 1 rotations): positive definite, margin 6.54e-01 (0.0 min) 18:29:53 PH level 8 N=8: EXCLUDED, smallest margin 6.54e-01 (0.0 min) PH level 8 N=8: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.5e-01 18:29:53 PH level 8 N=9: dim U = 2, real rotation blocks {0: 2, 1: 0, 2: 0} (0.0 min) 18:29:53 block k=0 (dim 2, 60 forms x 1 rotations): positive definite, margin 6.52e-01 (0.0 min) 18:29:53 PH level 8 N=9: EXCLUDED, smallest margin 6.52e-01 (0.0 min) PH level 8 N=9: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.5e-01 18:29:53 PH level 8 N=10: dim U = 2, real rotation blocks {0: 2, 1: 0, 2: 0} (0.0 min) 18:29:53 block k=0 (dim 2, 60 forms x 1 rotations): positive definite, margin 6.53e-01 (0.0 min) 18:29:53 PH level 8 N=10: EXCLUDED, smallest margin 6.53e-01 (0.0 min) PH level 8 N=10: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.5e-01 18:29:53 PH level 8 N=12: dim U = 2, real rotation blocks {0: 2, 1: 0, 2: 0} (0.0 min) 18:29:53 block k=0 (dim 2, 60 forms x 1 rotations): positive definite, margin 6.57e-01 (0.0 min) 18:29:53 PH level 8 N=12: EXCLUDED, smallest margin 6.57e-01 (0.0 min) PH level 8 N=12: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.6e-01 18:29:53 PH level 8 N=16: dim U = 2, real rotation blocks {0: 2, 1: 0, 2: 0} (0.0 min) 18:29:53 block k=0 (dim 2, 60 forms x 1 rotations): positive definite, margin 6.66e-01 (0.0 min) 18:29:53 PH level 8 N=16: EXCLUDED, smallest margin 6.66e-01 (0.0 min) PH level 8 N=16: dim U 2, EXCLUDED, blocks k=0: dim 2 margin 6.7e-01 18:29:53 PR level 10 N=5: dim U = 293, real rotation blocks {0: 61, 1: 116, 2: 116} (0.0 min) 18:29:56 gluing table BR level 10: 945 x 945, done in 0.1 min (saved) 18:29:57 block k=0 (dim 61, 60 forms x 1 rotations): no certificate yet (best -2.90e-05) (0.0 min) 18:29:58 block k=0 (dim 61, 150 forms x 1 rotations): no certificate yet (best -3.04e-05) (0.0 min) 18:29:59 block k=0 (dim 61, 300 forms x 1 rotations): no certificate yet (best -3.01e-05) (0.0 min) 18:30:01 block k=0 (dim 61, 500 forms x 1 rotations): no certificate yet (best -3.05e-05) (0.1 min) 18:30:03 block k=0 (dim 61, 700 forms x 1 rotations): no certificate yet (best -3.15e-05) (0.1 min) 18:30:07 block k=1 (dim 116, 60 forms x 5 rotations): no certificate yet (best 9.42e-06) (0.1 min) 18:30:15 block k=1 (dim 116, 150 forms x 5 rotations): positive definite, margin 1.03e-05 (0.2 min) 18:30:18 block k=2 (dim 116, 60 forms x 5 rotations): no certificate yet (best -1.50e-05) (0.1 min) 18:30:21 block k=2 (dim 116, 150 forms x 5 rotations): no certificate yet (best -1.65e-05) (0.1 min) 18:30:29 block k=2 (dim 116, 300 forms x 5 rotations): no certificate yet (best -1.69e-05) (0.2 min) 18:30:38 block k=2 (dim 116, 500 forms x 5 rotations): no certificate yet (best -1.60e-05) (0.4 min) 18:30:46 block k=2 (dim 116, 700 forms x 5 rotations): no certificate yet (best -1.90e-05) (0.5 min) 18:30:46 PR level 10 N=5: NOT excluded with these forms, smallest margin -3.15e-05 (0.9 min) PR level 10 N=5: dim U 293, OPEN, blocks k=0: dim 61 margin -3.1e-05, k=1: dim 116 margin 1.0e-05, k=2: dim 116 margin -1.9e-05 18:30:46 PR level 10 N=6: dim U = 293, real rotation blocks {0: 61, 1: 116, 2: 116} (0.0 min) 18:30:46 block k=0 (dim 61, 60 forms x 1 rotations): no certificate yet (best -2.92e-05) (0.0 min) 18:30:47 block k=0 (dim 61, 150 forms x 1 rotations): no certificate yet (best -3.04e-05) (0.0 min) 18:30:48 block k=0 (dim 61, 300 forms x 1 rotations): no certificate yet (best -2.97e-05) (0.0 min) 18:30:50 block k=0 (dim 61, 500 forms x 1 rotations): no certificate yet (best -2.93e-05) (0.1 min) 18:30:52 block k=0 (dim 61, 700 forms x 1 rotations): no certificate yet (best -2.50e-05) (0.1 min) 18:30:54 block k=1 (dim 116, 60 forms x 5 rotations): no certificate yet (best -1.31e-05) (0.0 min) 18:30:59 block k=1 (dim 116, 150 forms x 5 rotations): no certificate yet (best -1.27e-05) (0.1 min) 18:31:08 block k=1 (dim 116, 300 forms x 5 rotations): no certificate yet (best -1.50e-05) (0.3 min) 18:31:16 block k=1 (dim 116, 500 forms x 5 rotations): no certificate yet (best -1.51e-05) (0.4 min) 18:31:31 block k=1 (dim 116, 700 forms x 5 rotations): no certificate yet (best -1.43e-05) (0.6 min) 18:31:33 block k=2 (dim 116, 60 forms x 5 rotations): no certificate yet (best -9.92e-06) (0.0 min) 18:31:36 block k=2 (dim 116, 150 forms x 5 rotations): no certificate yet (best -1.08e-05) (0.1 min) 18:31:41 block k=2 (dim 116, 300 forms x 5 rotations): no certificate yet (best -9.54e-06) (0.2 min) 18:31:47 block k=2 (dim 116, 500 forms x 5 rotations): no certificate yet (best -9.61e-06) (0.3 min) 18:31:53 block k=2 (dim 116, 700 forms x 5 rotations): no certificate yet (best -3.27e-05) (0.4 min) 18:31:53 PR level 10 N=6: NOT excluded with these forms, smallest margin -3.27e-05 (1.1 min) PR level 10 N=6: dim U 293, OPEN, blocks k=0: dim 61 margin -2.5e-05, k=1: dim 116 margin -1.4e-05, k=2: dim 116 margin -3.3e-05 18:31:53 PR level 10 N=7: dim U = 293, real rotation blocks {0: 61, 1: 116, 2: 116} (0.0 min) 18:31:53 block k=0 (dim 61, 60 forms x 1 rotations): no certificate yet (best -3.21e-05) (0.0 min) 18:31:54 block k=0 (dim 61, 150 forms x 1 rotations): no certificate yet (best -2.90e-05) (0.0 min) 18:31:56 block k=0 (dim 61, 300 forms x 1 rotations): no certificate yet (best -2.70e-05) (0.0 min) 18:31:57 block k=0 (dim 61, 500 forms x 1 rotations): no certificate yet (best -2.45e-05) (0.1 min) 18:31:59 block k=0 (dim 61, 700 forms x 1 rotations): no certificate yet (best -2.71e-05) (0.1 min) 18:32:01 block k=1 (dim 116, 60 forms x 5 rotations): no certificate yet (best -7.58e-06) (0.0 min) 18:32:06 block k=1 (dim 116, 150 forms x 5 rotations): no certificate yet (best -7.21e-06) (0.1 min) 18:32:12 block k=1 (dim 116, 300 forms x 5 rotations): no certificate yet (best -9.13e-06) (0.2 min) 18:32:22 block k=1 (dim 116, 500 forms x 5 rotations): no certificate yet (best -8.70e-06) (0.4 min) 18:32:34 block k=1 (dim 116, 700 forms x 5 rotations): no certificate yet (best -8.36e-06) (0.6 min) 18:32:36 block k=2 (dim 116, 60 forms x 5 rotations): no certificate yet (best -8.12e-06) (0.0 min) 18:32:39 block k=2 (dim 116, 150 forms x 5 rotations): no certificate yet (best -7.18e-06) (0.1 min) 18:32:43 block k=2 (dim 116, 300 forms x 5 rotations): no certificate yet (best -6.67e-06) (0.2 min) 18:32:48 block k=2 (dim 116, 500 forms x 5 rotations): no certificate yet (best -9.80e-06) (0.2 min) 18:32:54 block k=2 (dim 116, 700 forms x 5 rotations): no certificate yet (best -2.52e-05) (0.3 min) 18:32:54 PR level 10 N=7: NOT excluded with these forms, smallest margin -2.71e-05 (1.0 min) PR level 10 N=7: dim U 293, OPEN, blocks k=0: dim 61 margin -2.7e-05, k=1: dim 116 margin -8.4e-06, k=2: dim 116 margin -2.5e-05 18:32:54 PR level 10 N=8: dim U = 293, real rotation blocks {0: 61, 1: 116, 2: 116} (0.0 min) 18:32:55 block k=0 (dim 61, 60 forms x 1 rotations): no certificate yet (best -3.43e-05) (0.0 min) 18:32:56 block k=0 (dim 61, 150 forms x 1 rotations): no certificate yet (best -2.84e-05) (0.0 min) 18:32:57 block k=0 (dim 61, 300 forms x 1 rotations): no certificate yet (best -2.76e-05) (0.0 min) 18:32:59 block k=0 (dim 61, 500 forms x 1 rotations): no certificate yet (best -2.65e-05) (0.1 min) 18:33:01 block k=0 (dim 61, 700 forms x 1 rotations): no certificate yet (best -2.71e-05) (0.1 min) 18:33:03 block k=1 (dim 116, 60 forms x 5 rotations): no certificate yet (best -6.14e-06) (0.0 min) 18:33:07 block k=1 (dim 116, 150 forms x 5 rotations): no certificate yet (best -5.48e-06) (0.1 min) 18:33:13 block k=1 (dim 116, 300 forms x 5 rotations): no certificate yet (best -6.50e-06) (0.2 min) 18:33:21 block k=1 (dim 116, 500 forms x 5 rotations): no certificate yet (best -6.42e-06) (0.3 min) 18:33:31 block k=1 (dim 116, 700 forms x 5 rotations): no certificate yet (best -5.92e-06) (0.5 min) 18:33:34 block k=2 (dim 116, 60 forms x 5 rotations): no certificate yet (best -8.01e-06) (0.0 min) 18:33:37 block k=2 (dim 116, 150 forms x 5 rotations): no certificate yet (best -5.62e-06) (0.1 min) 18:33:41 block k=2 (dim 116, 300 forms x 5 rotations): no certificate yet (best -6.25e-06) (0.2 min) 18:33:46 block k=2 (dim 116, 500 forms x 5 rotations): no certificate yet (best -6.48e-06) (0.3 min) 18:33:52 block k=2 (dim 116, 700 forms x 5 rotations): no certificate yet (best -1.69e-05) (0.3 min) 18:33:52 PR level 10 N=8: NOT excluded with these forms, smallest margin -2.71e-05 (1.0 min) PR level 10 N=8: dim U 293, OPEN, blocks k=0: dim 61 margin -2.7e-05, k=1: dim 116 margin -5.9e-06, k=2: dim 116 margin -1.7e-05 18:33:52 PR level 10 N=9: dim U = 293, real rotation blocks {0: 61, 1: 116, 2: 116} (0.0 min) 18:33:53 block k=0 (dim 61, 60 forms x 1 rotations): no certificate yet (best -3.65e-05) (0.0 min) 18:33:54 block k=0 (dim 61, 150 forms x 1 rotations): no certificate yet (best -3.00e-05) (0.0 min) 18:33:55 block k=0 (dim 61, 300 forms x 1 rotations): no certificate yet (best -2.85e-05) (0.1 min) 18:33:57 block k=0 (dim 61, 500 forms x 1 rotations): no certificate yet (best -2.81e-05) (0.1 min) 18:33:59 block k=0 (dim 61, 700 forms x 1 rotations): no certificate yet (best -2.77e-05) (0.1 min) 18:34:01 block k=1 (dim 116, 60 forms x 5 rotations): no certificate yet (best -5.17e-06) (0.0 min) 18:34:05 block k=1 (dim 116, 150 forms x 5 rotations): no certificate yet (best -4.51e-06) (0.1 min) 18:34:10 block k=1 (dim 116, 300 forms x 5 rotations): no certificate yet (best -5.40e-06) (0.2 min) 18:34:17 block k=1 (dim 116, 500 forms x 5 rotations): no certificate yet (best -4.73e-06) (0.3 min) 18:34:26 block k=1 (dim 116, 700 forms x 5 rotations): no certificate yet (best -4.34e-06) (0.5 min) 18:34:28 block k=2 (dim 116, 60 forms x 5 rotations): no certificate yet (best -8.88e-06) (0.0 min) 18:34:31 block k=2 (dim 116, 150 forms x 5 rotations): no certificate yet (best -4.89e-06) (0.1 min) 18:34:35 block k=2 (dim 116, 300 forms x 5 rotations): no certificate yet (best -5.44e-06) (0.2 min) 18:34:42 block k=2 (dim 116, 500 forms x 5 rotations): no certificate yet (best -3.88e-06) (0.3 min) 18:34:48 block k=2 (dim 116, 700 forms x 5 rotations): no certificate yet (best -1.06e-05) (0.4 min) 18:34:48 PR level 10 N=9: NOT excluded with these forms, smallest margin -2.77e-05 (0.9 min) PR level 10 N=9: dim U 293, OPEN, blocks k=0: dim 61 margin -2.8e-05, k=1: dim 116 margin -4.3e-06, k=2: dim 116 margin -1.1e-05 18:34:48 PR level 10 N=10: dim U = 293, real rotation blocks {0: 61, 1: 116, 2: 116} (0.0 min) 18:34:48 block k=0 (dim 61, 60 forms x 1 rotations): no certificate yet (best -3.73e-05) (0.0 min) 18:34:49 block k=0 (dim 61, 150 forms x 1 rotations): no certificate yet (best -3.21e-05) (0.0 min) 18:34:51 block k=0 (dim 61, 300 forms x 1 rotations): no certificate yet (best -3.05e-05) (0.0 min) 18:34:53 block k=0 (dim 61, 500 forms x 1 rotations): no certificate yet (best -3.21e-05) (0.1 min) 18:34:54 block k=0 (dim 61, 700 forms x 1 rotations): no certificate yet (best -3.14e-05) (0.1 min) 18:34:57 block k=1 (dim 116, 60 forms x 5 rotations): no certificate yet (best -4.30e-06) (0.0 min) 18:35:01 block k=1 (dim 116, 150 forms x 5 rotations): no certificate yet (best -3.91e-06) (0.1 min) 18:35:07 block k=1 (dim 116, 300 forms x 5 rotations): no certificate yet (best -4.82e-06) (0.2 min) 18:35:13 block k=1 (dim 116, 500 forms x 5 rotations): no certificate yet (best -3.85e-06) (0.3 min) 18:35:21 block k=1 (dim 116, 700 forms x 5 rotations): no certificate yet (best -3.62e-06) (0.4 min) 18:35:23 block k=2 (dim 116, 60 forms x 5 rotations): no certificate yet (best -1.28e-05) (0.0 min) 18:35:26 block k=2 (dim 116, 150 forms x 5 rotations): no certificate yet (best -4.76e-06) (0.1 min) 18:35:31 block k=2 (dim 116, 300 forms x 5 rotations): no certificate yet (best -4.13e-06) (0.2 min) 18:35:37 block k=2 (dim 116, 500 forms x 5 rotations): no certificate yet (best -3.47e-06) (0.3 min) 18:35:44 block k=2 (dim 116, 700 forms x 5 rotations): no certificate yet (best -6.24e-06) (0.4 min) 18:35:44 PR level 10 N=10: NOT excluded with these forms, smallest margin -3.14e-05 (0.9 min) PR level 10 N=10: dim U 293, OPEN, blocks k=0: dim 61 margin -3.1e-05, k=1: dim 116 margin -3.6e-06, k=2: dim 116 margin -6.2e-06 18:35:44 PR level 10 N=12: dim U = 293, real rotation blocks {0: 61, 1: 116, 2: 116} (0.0 min) 18:35:44 block k=0 (dim 61, 60 forms x 1 rotations): no certificate yet (best -4.67e-05) (0.0 min) 18:35:45 block k=0 (dim 61, 150 forms x 1 rotations): no certificate yet (best -3.99e-05) (0.0 min) 18:35:47 block k=0 (dim 61, 300 forms x 1 rotations): no certificate yet (best -4.00e-05) (0.0 min) 18:35:49 block k=0 (dim 61, 500 forms x 1 rotations): no certificate yet (best -3.87e-05) (0.1 min) 18:35:50 block k=0 (dim 61, 700 forms x 1 rotations): no certificate yet (best -3.76e-05) (0.1 min) 18:35:53 block k=1 (dim 116, 60 forms x 5 rotations): no certificate yet (best -3.47e-06) (0.0 min) 18:35:57 block k=1 (dim 116, 150 forms x 5 rotations): no certificate yet (best -3.30e-06) (0.1 min) 18:36:02 block k=1 (dim 116, 300 forms x 5 rotations): no certificate yet (best -3.86e-06) (0.2 min) 18:36:08 block k=1 (dim 116, 500 forms x 5 rotations): no certificate yet (best -3.22e-06) (0.3 min) 18:36:15 block k=1 (dim 116, 700 forms x 5 rotations): no certificate yet (best -2.95e-06) (0.4 min) 18:36:18 block k=2 (dim 116, 60 forms x 5 rotations): no certificate yet (best -1.51e-05) (0.0 min) 18:36:21 block k=2 (dim 116, 150 forms x 5 rotations): no certificate yet (best -3.77e-06) (0.1 min) 18:36:26 block k=2 (dim 116, 300 forms x 5 rotations): no certificate yet (best -3.29e-06) (0.2 min) 18:36:32 block k=2 (dim 116, 500 forms x 5 rotations): no certificate yet (best -3.11e-06) (0.3 min) 18:36:41 block k=2 (dim 116, 700 forms x 5 rotations): no certificate yet (best -3.01e-06) (0.4 min) 18:36:41 PR level 10 N=12: NOT excluded with these forms, smallest margin -3.76e-05 (0.9 min) PR level 10 N=12: dim U 293, OPEN, blocks k=0: dim 61 margin -3.8e-05, k=1: dim 116 margin -2.9e-06, k=2: dim 116 margin -3.0e-06 18:36:41 PR level 10 N=16: dim U = 293, real rotation blocks {0: 61, 1: 116, 2: 116} (0.0 min) 18:36:41 block k=0 (dim 61, 60 forms x 1 rotations): no certificate yet (best -5.52e-05) (0.0 min) 18:36:42 block k=0 (dim 61, 150 forms x 1 rotations): no certificate yet (best -5.04e-05) (0.0 min) 18:36:43 block k=0 (dim 61, 300 forms x 1 rotations): no certificate yet (best -5.07e-05) (0.0 min) 18:36:45 block k=0 (dim 61, 500 forms x 1 rotations): no certificate yet (best -4.84e-05) (0.1 min) 18:36:47 block k=0 (dim 61, 700 forms x 1 rotations): no certificate yet (best -4.77e-05) (0.1 min) 18:36:50 block k=1 (dim 116, 60 forms x 5 rotations): no certificate yet (best -2.81e-06) (0.0 min) 18:36:53 block k=1 (dim 116, 150 forms x 5 rotations): no certificate yet (best -2.69e-06) (0.1 min) 18:36:57 block k=1 (dim 116, 300 forms x 5 rotations): no certificate yet (best -2.94e-06) (0.2 min) 18:37:02 block k=1 (dim 116, 500 forms x 5 rotations): no certificate yet (best -2.78e-06) (0.3 min) 18:37:10 block k=1 (dim 116, 700 forms x 5 rotations): no certificate yet (best -2.52e-06) (0.4 min) 18:37:12 block k=2 (dim 116, 60 forms x 5 rotations): no certificate yet (best -1.38e-05) (0.0 min) 18:37:15 block k=2 (dim 116, 150 forms x 5 rotations): no certificate yet (best -2.97e-06) (0.1 min) 18:37:19 block k=2 (dim 116, 300 forms x 5 rotations): no certificate yet (best -3.05e-06) (0.2 min) 18:37:24 block k=2 (dim 116, 500 forms x 5 rotations): no certificate yet (best -3.12e-06) (0.2 min) 18:37:32 block k=2 (dim 116, 700 forms x 5 rotations): no certificate yet (best -2.90e-06) (0.4 min) 18:37:32 PR level 10 N=16: NOT excluded with these forms, smallest margin -4.77e-05 (0.9 min) PR level 10 N=16: dim U 293, OPEN, blocks k=0: dim 61 margin -4.8e-05, k=1: dim 116 margin -2.5e-06, k=2: dim 116 margin -2.9e-06 18:37:32 PH level 10 N=5: dim U = 13, real rotation blocks {0: 5, 1: 4, 2: 4} (0.0 min) 18:37:32 gluing table HL level 10: 120 x 120, done in 0.0 min (saved) 18:37:32 block k=0 (dim 5, 60 forms x 1 rotations): positive definite, margin 4.76e-03 (0.0 min) 18:37:32 block k=1 (dim 4, 60 forms x 5 rotations): positive definite, margin 1.48e-01 (0.0 min) 18:37:32 block k=2 (dim 4, 60 forms x 5 rotations): positive definite, margin 1.98e-01 (0.0 min) 18:37:32 PH level 10 N=5: EXCLUDED, smallest margin 4.76e-03 (0.0 min) PH level 10 N=5: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 4.8e-03, k=1: dim 4 margin 1.5e-01, k=2: dim 4 margin 2.0e-01 18:37:32 PH level 10 N=6: dim U = 13, real rotation blocks {0: 5, 1: 4, 2: 4} (0.0 min) 18:37:32 block k=0 (dim 5, 60 forms x 1 rotations): positive definite, margin 2.15e-03 (0.0 min) 18:37:32 block k=1 (dim 4, 60 forms x 5 rotations): positive definite, margin 1.82e-01 (0.0 min) 18:37:32 block k=2 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.27e-01 (0.0 min) 18:37:32 PH level 10 N=6: EXCLUDED, smallest margin 2.15e-03 (0.0 min) PH level 10 N=6: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 2.2e-03, k=1: dim 4 margin 1.8e-01, k=2: dim 4 margin 2.3e-01 18:37:32 PH level 10 N=7: dim U = 13, real rotation blocks {0: 5, 1: 4, 2: 4} (0.0 min) 18:37:32 block k=0 (dim 5, 60 forms x 1 rotations): positive definite, margin 1.10e-03 (0.0 min) 18:37:32 block k=1 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.02e-01 (0.0 min) 18:37:32 block k=2 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.44e-01 (0.0 min) 18:37:32 PH level 10 N=7: EXCLUDED, smallest margin 1.10e-03 (0.0 min) PH level 10 N=7: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 1.1e-03, k=1: dim 4 margin 2.0e-01, k=2: dim 4 margin 2.4e-01 18:37:32 PH level 10 N=8: dim U = 13, real rotation blocks {0: 5, 1: 4, 2: 4} (0.0 min) 18:37:32 block k=0 (dim 5, 60 forms x 1 rotations): positive definite, margin 6.18e-04 (0.0 min) 18:37:32 block k=1 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.14e-01 (0.0 min) 18:37:32 block k=2 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.54e-01 (0.0 min) 18:37:32 PH level 10 N=8: EXCLUDED, smallest margin 6.18e-04 (0.0 min) PH level 10 N=8: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 6.2e-04, k=1: dim 4 margin 2.1e-01, k=2: dim 4 margin 2.5e-01 18:37:32 PH level 10 N=9: dim U = 13, real rotation blocks {0: 5, 1: 4, 2: 4} (0.0 min) 18:37:32 block k=0 (dim 5, 60 forms x 1 rotations): positive definite, margin 3.91e-04 (0.0 min) 18:37:32 block k=1 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.18e-01 (0.0 min) 18:37:32 block k=2 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.61e-01 (0.0 min) 18:37:32 PH level 10 N=9: EXCLUDED, smallest margin 3.91e-04 (0.0 min) PH level 10 N=9: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 3.9e-04, k=1: dim 4 margin 2.2e-01, k=2: dim 4 margin 2.6e-01 18:37:32 PH level 10 N=10: dim U = 13, real rotation blocks {0: 5, 1: 4, 2: 4} (0.0 min) 18:37:32 block k=0 (dim 5, 60 forms x 1 rotations): positive definite, margin 2.50e-04 (0.0 min) 18:37:32 block k=1 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.20e-01 (0.0 min) 18:37:32 block k=2 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.66e-01 (0.0 min) 18:37:32 PH level 10 N=10: EXCLUDED, smallest margin 2.50e-04 (0.0 min) PH level 10 N=10: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 2.5e-04, k=1: dim 4 margin 2.2e-01, k=2: dim 4 margin 2.7e-01 18:37:32 PH level 10 N=12: dim U = 13, real rotation blocks {0: 5, 1: 4, 2: 4} (0.0 min) 18:37:32 block k=0 (dim 5, 60 forms x 1 rotations): positive definite, margin 1.19e-04 (0.0 min) 18:37:32 block k=1 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.24e-01 (0.0 min) 18:37:32 block k=2 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.71e-01 (0.0 min) 18:37:32 PH level 10 N=12: EXCLUDED, smallest margin 1.19e-04 (0.0 min) PH level 10 N=12: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 1.2e-04, k=1: dim 4 margin 2.2e-01, k=2: dim 4 margin 2.7e-01 18:37:32 PH level 10 N=16: dim U = 13, real rotation blocks {0: 5, 1: 4, 2: 4} (0.0 min) 18:37:32 block k=0 (dim 5, 60 forms x 1 rotations): positive definite, margin 3.78e-05 (0.0 min) 18:37:32 block k=1 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.31e-01 (0.0 min) 18:37:32 block k=2 (dim 4, 60 forms x 5 rotations): positive definite, margin 2.75e-01 (0.0 min) 18:37:32 PH level 10 N=16: EXCLUDED, smallest margin 3.78e-05 (0.0 min) PH level 10 N=16: dim U 13, EXCLUDED, blocks k=0: dim 5 margin 3.8e-05, k=1: dim 4 margin 2.3e-01, k=2: dim 4 margin 2.8e-01 ==================================================================================================== ===== projtencertout.txt ==================================================================================================== 31 Oct 22:17 projtencert.py: projective level 10, half-liberated, merged block rho = +-1, exact for all N >= 5 |P_2^*(10)| = 120; crossing pairings of P_2^*(8), code order: ((0, 1), (2, 5), (3, 6), (4, 7)); ((0, 3), (1, 4), (2, 5), (6, 7)); ((0, 3), (1, 4), (2, 7), (5, 6)); ((0, 3), (1, 6), (2, 5), (4, 7)); ((0, 3), (1, 6), (2, 7), (4, 5)); ((0, 5), (1, 2), (3, 6), (4, 7)); ((0, 5), (1, 4), (2, 7), (3, 6)); ((0, 5), (1, 6), (2, 3), (4, 7)); ((0, 5), (1, 6), (2, 7), (3, 4)); ((0, 7), (1, 4), (2, 5), (3, 6)) rotation orbits: 17, sizes [1, 2, 2, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 10, 10, 10]; rho = 1 sums: 17, rho = -1 signed sums: 11 rho = 1: rank of cap_0 on the sums = 13 (pivot minor D(N) = -192N^2 + 256N^4 - 124N^6 + 26N^8 - 2N^10; D(N + 5) has coefficients of one sign: True, so D(N) != 0 for N >= 5), kernel dimension 4, basis degrees [9, 6, 9, 7], independent wherever D(N) != 0 rho = -1: rank of cap_0 on the sums = 10 (pivot minor D(N) = -16N^2 + 4N^4; D(N + 5) has coefficients of one sign: True, so D(N) != 0 for N >= 5), kernel dimension 1, basis degrees [3], independent wherever D(N) != 0 merged block: dimension 5; the ten caps vanish and rho acts by +1 (first 4) and -1 (last 1), identically in N 11 forms (10 crossings at level 8, then kappa): integer polynomial matrices of degree <= 20 c(N) of Proposition 11.x(3), paper order: (-3N^2, -3N^2, 30N, 20N, -3N^2, 20N, -3N^2, 30, -18N, -18N, -18); code order: (-3N^2, -3N^2, 20N, 30N, -3N^2, 20N, 30, -3N^2, -18N, -18N, -18) leading minor 1: degree 21, leading coefficient 168, all coefficients of m(N + 7) positive: True leading minor 2: degree 36, leading coefficient 14112, all coefficients of m(N + 7) positive: True leading minor 3: degree 57, leading coefficient 1185408, all coefficients of m(N + 7) positive: True leading minor 4: degree 70, leading coefficient 298609920, all coefficients of m(N + 7) positive: True leading minor 5: degree 77, leading coefficient 100332933120, all coefficients of m(N + 7) positive: True => sum_k c_k(N) Q_k(N) is positive definite on the merged block for all real N >= 7: True N = 5: c = (-5, -5, 10, 1, -5, 10, 6, -5, -3, -3, -2) (code order), exact LDL^t pivots all positive: True N = 6: c = (-4, -4, 10, 1, -4, 10, 4, -4, -2, -2, -1) (code order), exact LDL^t pivots all positive: True conclusion: the merged rho = +-1 block of U(10) is excluded for every N >= 5, exactly: True (2s) (paper: Subsection 12.4, the table row "10 | 13 | 5,4,4 | all N >= 5 | excluded, exact"; the Phi_5 blocks keep the certificate of Proposition 11.x(4), even rotations sufficing there) ==================================================================================================== ===== wordsleft.txt ==================================================================================================== 01 Nov 01:12 length 20: words not killed by a single relation, two-step outcome aaabcaabcbbacaabcccb killed in two steps: p = 1, y = b, through bbabcaabcbbacaabcccb aaabcaabcbbacccbaacb killed in two steps: p = 1, y = b, through bbabcaabcbbacccbaacb aaabcaabcccabbcbaacb killed in two steps: p = 1, y = b, through bbabcaabcccabbcbaacb aaabccabcccbaccbabbc killed in two steps: p = 1, y = b, through bbabccabcccbaccbabbc aaabccacbbabccabcccb killed in two steps: p = 1, y = b, through bbabccacbbabccabcccb aaabccacbbacbbbcabbc killed in two steps: p = 1, y = b, through bbabccacbbacbbbcabbc aaabcccbaacabbcbaacb killed in two steps: p = 1, y = b, through bbabcccbaacabbcbaacb aaabcccbaccbabbcaccb killed in two steps: p = 1, y = b, through bbabcccbaccbabbcaccb aaacbaacbbbaccbcaabc killed in two steps: p = 1, y = b, through bbacbaacbbbaccbcaabc aaacbaacbccabaacbbbc killed in two steps: p = 1, y = b, through bbacbaacbccabaacbbbc aaacbaacbccabbbcaabc killed in two steps: p = 1, y = b, through bbacbaacbccabbbcaabc aaacbbabccabcccbaccb killed in two steps: p = 1, y = b, through bbacbbabccabcccbaccb aaacbbabccacbbacbbbc killed in two steps: p = 1, y = b, through bbacbbabccacbbacbbbc aaacbbacbbbcabbcaccb killed in two steps: p = 1, y = b, through bbacbbacbbbcabbcaccb aaacbbbcaabaccbcaabc killed in two steps: p = 1, y = b, through bbacbbbcaabaccbcaabc aaacbbbcabbcaccbabbc killed in two steps: p = 1, y = b, through bbacbbbcabbcaccbabbc aabaccbacbbaccbaccbc killed in two steps: p = 1, y = b, through bbbaccbacbbaccbaccbc baaaccbacbbaccbaccbc babbccbacbbaccbaccbc babaccaacbbaccbaccbc babaccbbcbbaccbaccbc aabaccbacccabbbaccbc killed in two steps: p = 1, y = b, through bbbaccbacccabbbaccbc baaaccbacccabbbaccbc babbccbacccabbbaccbc babaccaacccabbbaccbc babaccbbcccabbbaccbc aabaccbacccabccabbbc killed in two steps: p = 1, y = b, through bbbaccbacccabccabbbc baaaccbacccabccabbbc babbccbacccabccabbbc babaccaacccabccabbbc babaccbbcccabccabbbc aabaccbcaabcaaacbbbc killed in two steps: p = 1, y = b, through bbbaccbcaabcaaacbbbc baaaccbcaabcaaacbbbc babbccbcaabcaaacbbbc babaccacaabcaaacbbbc aabaccbcaabcabbcaabc killed in two steps: p = 1, y = b, through bbbaccbcaabcabbcaabc baaaccbcaabcabbcaabc babbccbcaabcabbcaabc babaccacaabcabbcaabc aabcaaacbaacbbbaccbc killed in two steps: p = 1, y = b, through bbbcaaacbaacbbbaccbc baacaaacbaacbbbaccbc aabcaaacbaacbccabbbc killed in two steps: p = 1, y = b, through bbbcaaacbaacbccabbbc baacaaacbaacbccabbbc aabcaaacbbbcaabaccbc killed in two steps: p = 1, y = b, through bbbcaaacbbbcaabaccbc baacaaacbbbcaabaccbc aabcaabaccbcaabcabbc killed in two steps: p = 1, y = b, through bbbcaabaccbcaabcabbc baacaabaccbcaabcabbc aabcaabcbbacaabcccba killed in two steps: p = 1, y = b, through bbbcaabcbbacaabcccba baacaabcbbacaabcccba babcaabcbbacaabcccaa babcaabcbbacaabcccbb aabcaabcbbacccbaacba killed in two steps: p = 1, y = b, through bbbcaabcbbacccbaacba baacaabcbbacccbaacba babcaabcbbacccbaacaa babcaabcbbacccbaacbb aabcaabccabcaabcbbac killed in two steps: p = 1, y = b, through bbbcaabccabcaabcbbac baacaabccabcaabcbbac aabcaabcccabbcbaacba killed in two steps: p = 1, y = b, through bbbcaabcccabbcbaacba baacaabcccabbcbaacba babcaabcccabbcbaacaa babcaabcccabbcbaacbb aabcabbcaabcaabaccbc killed in two steps: p = 1, y = b, through bbbcabbcaabcaabaccbc baacabbcaabcaabaccbc aabcabbcaccbabbcabbc killed in two steps: p = 1, y = b, through bbbcabbcaccbabbcabbc baacabbcaccbabbcabbc aabcbbacaabcaabccabc killed in two steps: p = 1, y = b, through bbbcbbacaabcaabccabc baacbbacaabcaabccabc aabcbbacaabcccbaaabc killed in two steps: p = 1, y = b, through bbbcbbacaabcccbaaabc baacbbacaabcccbaaabc aabcbbacbbaccbacbbac killed in two steps: p = 1, y = b, through bbbcbbacbbaccbacbbac baacbbacbbaccbacbbac aabcbbacccabbbacbbac killed in two steps: p = 1, y = b, through bbbcbbacccabbbacbbac baacbbacccabbbacbbac aabcbbacccbaacbaaabc killed in two steps: p = 1, y = b, through bbbcbbacccbaacbaaabc baacbbacccbaacbaaabc aabccabcaabcbbacaabc killed in two steps: p = 1, y = b, through bbbccabcaabcbbacaabc baaccabcaabcbbacaabc babccbbcaabcbbacaabc babccaacaabcbbacaabc aabccabccacbbabccabc killed in two steps: p = 1, y = b, through bbbccabccacbbabccabc baaccabccacbbabccabc babccbbccacbbabccabc babccaaccacbbabccabc babccabccbcbbabccabc aabccabcccbaccbabbca killed in two steps: p = 1, y = b, through bbbccabcccbaccbabbca baaccabcccbaccbabbca babccbbcccbaccbabbca babccaacccbaccbabbca babccabcccbaccbabbcb aabccacbbabccabcccba killed in two steps: p = 1, y = b, through bbbccacbbabccabcccba baaccacbbabccabcccba babccbcbbabccabcccba babccacbbabccabcccaa babccacbbabccabcccbb aabccacbbacbbbcabbca killed in two steps: p = 1, y = b, through bbbccacbbacbbbcabbca baaccacbbacbbbcabbca babccbcbbacbbbcabbca babccacbbacbbbcabbcb aabcccabbcabbbacbbac killed in two steps: p = 1, y = b, through bbbcccabbcabbbacbbac baacccabbcabbbacbbac aabcccabbcbaacbaaabc killed in two steps: p = 1, y = b, through bbbcccabbcbaacbaaabc baacccabbcbaacbaaabc aabcccbaaabcaabcbbac killed in two steps: p = 1, y = b, through bbbcccbaaabcaabcbbac baacccbaaabcaabcbbac aabcccbaacabbcbaacba killed in two steps: p = 1, y = b, through bbbcccbaacabbcbaacba baacccbaacabbcbaacba babcccbaacabbcbaacaa babcccbaacabbcbaacbb aabcccbaccbabbcaccba killed in two steps: p = 1, y = b, through bbbcccbaccbabbcaccba baacccbaccbabbcaccba babcccbaccbabbcbccba babcccbaccbabbcaccaa babcccbaccbabbcaccbb aacabbcabbbacbbacccb killed in two steps: p = 1, y = b, through bbcabbcabbbacbbacccb aacabbcabbbacccabbcb killed in two steps: p = 1, y = b, through bbcabbcabbbacccabbcb aacabbcabccabbcabbcb killed in two steps: p = 1, y = b, through bbcabbcabccabbcabbcb aacabbcbaacbaaabcccb killed in two steps: p = 1, y = b, through bbcabbcbaacbaaabcccb aacabbcbaacbaccbaacb killed in two steps: p = 1, y = b, through bbcabbcbaacbaccbaacb aacbaaabcaabcbbacccb killed in two steps: p = 1, y = b, through bbcbaaabcaabcbbacccb aacbaaabcaabcccabbcb killed in two steps: p = 1, y = b, through bbcbaaabcaabcccabbcb aacbaaabcccbaacabbcb killed in two steps: p = 1, y = b, through bbcbaaabcccbaacabbcb aacbaacabbcbaacbaccb killed in two steps: p = 1, y = b, through bbcbaacabbcbaacbaccb aacbaacbbacbaacbccab killed in two steps: p = 1, y = b, through bbcbaacbbacbaacbccab aacbaacbbbaccbcaabca killed in two steps: p = 1, y = b, through bbcbaacbbbaccbcaabca bacbaacbbbaccbcaabcb aacbaacbccabaacbbbca killed in two steps: p = 1, y = b, through bbcbaacbccabaacbbbca bacbaacbccabaacbbbcb aacbaacbccabbbcaabca killed in two steps: p = 1, y = b, through bbcbaacbccabbbcaabca bacbaacbccabbbcaabcb aacbaccbaacbaacabbcb killed in two steps: p = 1, y = b, through bbcbaccbaacbaacabbcb aacbaccbabbcaccbaccb killed in two steps: p = 1, y = b, through bbcbaccbabbcaccbaccb aacbbabccabcccbaccba killed in two steps: p = 1, y = b, through bbcbbabccabcccbaccba bacbbabccabcccaaccba bacbbabccabcccbbccba bacbbabccabcccbaccaa bacbbabccabcccbaccbb aacbbabccacbbacbbbca killed in two steps: p = 1, y = b, through bbcbbabccacbbacbbbca bacbbabccacbbacbbbcb aacbbacbaacbccabaacb killed in two steps: p = 1, y = b, through bbcbbacbaacbccabaacb aacbbacbbabccacbbacb killed in two steps: p = 1, y = b, through bbcbbacbbabccacbbacb aacbbacbbbcabbcaccba killed in two steps: p = 1, y = b, through bbcbbacbbbcabbcaccba bacbbacbbbcabbcbccba bacbbacbbbcabbcaccaa bacbbacbbbcabbcaccbb aacbbbaccbacccabccab killed in two steps: p = 1, y = b, through bbcbbbaccbacccabccab aacbbbaccbcaabcaaacb killed in two steps: p = 1, y = b, through bbcbbbaccbcaabcaaacb aacbbbcaaacbaacbccab killed in two steps: p = 1, y = b, through bbcbbbcaaacbaacbccab aacbbbcaabaccbcaabca killed in two steps: p = 1, y = b, through bbcbbbcaabaccbcaabca bacbbbcaabaccbcaabcb aacbbbcabbcaccbabbca killed in two steps: p = 1, y = b, through bbcbbbcabbcaccbabbca bacbbbcabbcaccbabbcb aacbccabaacbaacbbacb killed in two steps: p = 1, y = b, through bbcbccabaacbaacbbacb aacbccabaacbbbcaaacb killed in two steps: p = 1, y = b, through bbcbccabaacbbbcaaacb aacbccabbbacccabccab killed in two steps: p = 1, y = b, through bbcbccabbbacccabccab aacbccabbbcaabcaaacb killed in two steps: p = 1, y = b, through bbcbccabbbcaabcaaacb aacbccabccabbcabccab killed in two steps: p = 1, y = b, through bbcbccabccabbcabccab abaacbaacbbacbaacbcc killed in two steps: p = 1, y = b, through bbabcbaacbbacbaacbcc abaacbbbaccbacccabcc killed in two steps: p = 1, y = b, through bbabcbbbaccbacccabcc abaacbbbcaaacbaacbcc killed in two steps: p = 1, y = b, through bbabcbbbcaaacbaacbcc abaacbccabbbacccabcc killed in two steps: p = 1, y = b, through bbabcbccabbbacccabcc abaacbccabccabbcabcc killed in two steps: p = 1, y = b, through bbabcbccabccabbcabcc abaccbacbbaccbaccbca killed in two steps: p = 1, y = b, through bbaccbacbbaccbaccbcb abaccbacccabbbaccbca killed in two steps: p = 1, y = b, through bbaccbacccabbbaccbcb abaccbacccabccabbbca killed in two steps: p = 1, y = b, through bbaccbacccabccabbbcb abaccbcaabcaaacbbbca killed in two steps: p = 1, y = b, through bbaccbcaabcaaacbbbcb abaccbcaabcabbcaabca killed in two steps: p = 1, y = b, through bbaccbcaabcabbcaabcb abbbacbbacaabcbbaccc killed in two steps: p = 1, y = b, through bbabacbbacaabcbbaccc abbbacbbacaabcccabbc killed in two steps: p = 1, y = b, through bbabacbbacaabcccabbc abbbacbbacccbaacabbc killed in two steps: p = 1, y = b, through bbabacbbacccbaacabbc abbbaccbcaabaccbaccc killed in two steps: p = 1, y = b, through bbabaccbcaabaccbaccc abbbacccabbcbaacabbc killed in two steps: p = 1, y = b, through bbabacccabbcbaacabbc abbbacccabccabaacbcc killed in two steps: p = 1, y = b, through bbabacccabccabaacbcc abbbcaabaccbacccabcc killed in two steps: p = 1, y = b, through bbabcaabaccbacccabcc abbbcaabcaaacbaacbcc killed in two steps: p = 1, y = b, through bbabcaabcaaacbaacbcc abbcaaabccabcccbaccb killed in two steps: p = 1, y = b, through bbacaaabccabcccbaccb abbcaaabccacbbacbbbc killed in two steps: p = 1, y = b, through bbacaaabccacbbacbbbc abbcaaacbbbcabbcaccb killed in two steps: p = 1, y = b, through bbacaaacbbbcabbcaccb abbcaabcaabaccbcaabc killed in two steps: p = 1, y = b, through bbacaabcaabaccbcaabc abbcaabcabbcaccbabbc killed in two steps: p = 1, y = b, through bbacaabcabbcaccbabbc abbcabbbacbbacaabccc killed in two steps: p = 1, y = b, through bbacabbbacbbacaabccc abbcabbbacbbacccbaac killed in two steps: p = 1, y = b, through bbacabbbacbbacccbaac abbcabbbacccabbcbaac killed in two steps: p = 1, y = b, through bbacabbbacccabbcbaac abbcabbcaabcabbcaccb killed in two steps: p = 1, y = b, through bbacabbcaabcabbcaccb abbcabbcbaacabbcabcc killed in two steps: p = 1, y = b, through bbacabbcbaacabbcabcc abbcabccabaacbccabcc killed in two steps: p = 1, y = b, through bbacabccabaacbccabcc abbcabccabbcabbcbaac killed in two steps: p = 1, y = b, through bbacabccabbcabbcbaac abbcaccbaaabcccbaccb killed in two steps: p = 1, y = b, through bbacaccbaaabcccbaccb abbcaccbaaacbbacbbbc killed in two steps: p = 1, y = b, through bbacaccbaaacbbacbbbc abbcaccbabbcaaacbbbc killed in two steps: p = 1, y = b, through bbacaccbabbcaaacbbbc abbcaccbabbcabbcaabc killed in two steps: p = 1, y = b, through bbacaccbabbcabbcaabc abbcaccbaccbaacbaccb killed in two steps: p = 1, y = b, through bbacaccbaccbaacbaccb abbcbaacabbcabbbaccc killed in two steps: p = 1, y = b, through bbacbaacabbcabbbaccc abbcbaacabbcabccabbc killed in two steps: p = 1, y = b, through bbacbaacabbcabccabbc abbcbaacbaaabcaabccc killed in two steps: p = 1, y = b, through bbacbaacbaaabcaabccc abbcbaacbaaabcccbaac killed in two steps: p = 1, y = b, through bbacbaacbaaabcccbaac abbcbaacbaccbaacbaac killed in two steps: p = 1, y = b, through bbacbaacbaccbaacbaac abcaaacbaacbbbaccbca killed in two steps: p = 1, y = b, through bbcaaacbaacbbbaccbcb abcaaacbaacbccabbbca killed in two steps: p = 1, y = b, through bbcaaacbaacbccabbbcb abcaaacbbbcaabaccbca killed in two steps: p = 1, y = b, through bbcaaacbbbcaabaccbcb abcaabaccbcaabcabbca killed in two steps: p = 1, y = b, through bbcaabaccbcaabcabbcb abcaabcbbacaabcaabcc killed in two steps: p = 1, y = b, through bbcaabcbbacaabcbabcc abcaabcbbacaabcccbaa killed in two steps: p = 1, y = b, through bbcaabcbbacaabcccbab abcaabcbbacccbaacbaa killed in two steps: p = 1, y = b, through bbcaabcbbacccbaacbab abcaabccabcaabcbbaca killed in two steps: p = 1, y = b, through bbcaabccabcaabcbbacb abcaabccabccacbbabcc killed in two steps: p = 1, y = b, through bbcaabccabccacababcc abcaabcccabbcbaacbaa killed in two steps: p = 1, y = b, through bbcaabcccabbcbaacbab abcabbcaabcaabaccbca killed in two steps: p = 1, y = b, through bbcabbcaabcaabaccbcb abcabbcaccbabbcabbca killed in two steps: p = 1, y = b, through bbcabbcaccbabbcabbcb abcbbacaabcaabccabca killed in two steps: p = 1, y = b, through bbcbbacaabcaabccabcb abcbbacaabcccbaaabca killed in two steps: p = 1, y = b, through bbcbbacaabcccbaaabcb abcbbacbbaccbacbbaca killed in two steps: p = 1, y = b, through bbcbbacbbaccbacbbacb abcbbacccabbbacbbaca killed in two steps: p = 1, y = b, through bbcbbacccabbbacbbacb abcbbacccbaacbaaabca killed in two steps: p = 1, y = b, through bbcbbacccbaacbaaabcb abccabaacbbbaccbaccc killed in two steps: p = 1, y = b, through bbccababcbbbaccbaccc abccabaacbccabbbaccc killed in two steps: p = 1, y = b, through bbccababcbccabbbaccc abccabaacbccabccabbc killed in two steps: p = 1, y = b, through bbccababcbccabccabbc abccabbbcaabaccbaccc killed in two steps: p = 1, y = b, through bbccababcaabaccbaccc abccabbcabbcbaacabbc killed in two steps: p = 1, y = b, through bbccabacabbcbaacabbc abccabbcabccabaacbcc killed in two steps: p = 1, y = b, through bbccabacabccabaacbcc abccabcaabcbbacaabca killed in two steps: p = 1, y = b, through bbccabcaabcbbacaabcb abccabcaabccabccacbb killed in two steps: p = 1, y = b, through bbccabcaabccabccacab abccabccacbbabccabca killed in two steps: p = 1, y = b, through bbccabccacbbabccabcb abccabcccbaaabccacbb killed in two steps: p = 1, y = b, through bbccabcccbaaabccacab abccabcccbaccbaaacbb killed in two steps: p = 1, y = b, through bbccabcccbaccbaaacab abccabcccbaccbabbcaa killed in two steps: p = 1, y = b, through bbccabcccbaccbabbcab abccacbbabccabcaabcc killed in two steps: p = 1, y = b, through bbccacbbabccabcbabcc abccacbbabccabcccbaa killed in two steps: p = 1, y = b, through bbccacbbabccabcccbab abccacbbacbaacbbacbb killed in two steps: p = 1, y = b, through bbccacbbacbaacbbacab abccacbbacbbbcaaacbb killed in two steps: p = 1, y = b, through bbccacbbacbbbcaaacab abccacbbacbbbcabbcaa killed in two steps: p = 1, y = b, through bbccacbbacbbbcabbcab abcccabbcabbbacbbaca killed in two steps: p = 1, y = b, through bbcccabbcabbbacbbacb abcccabbcbaacbaaabca killed in two steps: p = 1, y = b, through bbcccabbcbaacbaaabcb abcccbaaabcaabcbbaca killed in two steps: p = 1, y = b, through bbcccbaaabcaabcbbacb abcccbaaabccacbbabcc killed in two steps: p = 1, y = b, through bbcccbaaabccacababcc abcccbaacabbcbaacbaa killed in two steps: p = 1, y = b, through bbcccbaacabbcbaacbab abcccbaccbaaacbbabcc killed in two steps: p = 1, y = b, through bbcccbaccbaaacababcc abcccbaccbabbcaaabcc killed in two steps: p = 1, y = b, through bbcccbaccbabbcababcc abcccbaccbabbcaccbaa killed in two steps: p = 1, y = b, through bbcccbaccbabbcaccbab acaabcaabccabcaabcbb killed in two steps: p = 1, y = b, through bcaabcaabccabcaabcab acaabcbbacbbaccbacbb killed in two steps: p = 1, y = b, through bcaabcbbacbbaccbacab acaabcbbacccabbbacbb killed in two steps: p = 1, y = b, through bcaabcbbacccabbbacab acaabcccabbcabbbacbb killed in two steps: p = 1, y = b, through bcaabcccabbcabbbacab acaabcccbaaabcaabcbb killed in two steps: p = 1, y = b, through bcaabcccbaaabcaabcab acabbcabbbacbbacccba killed in two steps: p = 1, y = b, through bcabbcabbbacbbacccaa bcabbcabbbacbbacccbb acabbcabbbacccabbcba killed in two steps: p = 1, y = b, through bcabbcabbbacccabbcaa bcabbcabbbacccabbcbb acabbcabccabbcabbcba killed in two steps: p = 1, y = b, through bcabbcabccabbcabbcaa bcabbcabccabbcabbcbb acabbcbaacbaaabcccba killed in two steps: p = 1, y = b, through bcabbcbaacbaaabcccaa bcabbcbaacbaaabcccbb acabbcbaacbaccbaacba killed in two steps: p = 1, y = b, through bcabbcbaacbaccbaacaa bcabbcbaacbaccbaacbb acbaaabcaabcbbacccba killed in two steps: p = 1, y = b, through bcbaaabcaabcbbacccaa bcbaaabcaabcbbacccbb acbaaabcaabcccabbcba killed in two steps: p = 1, y = b, through bcbaaabcaabcccabbcaa bcbaaabcaabcccabbcbb acbaaabcccbaacabbcba killed in two steps: p = 1, y = b, through bcbaaabcccbaacabbcaa bcbaaabcccbaacabbcbb acbaacabbcbaacbaccba killed in two steps: p = 1, y = b, through bcbaacabbcbaacaaccba bcbaacabbcbaacbbccba bcbaacabbcbaacbaccaa bcbaacabbcbaacbaccbb acbaacbbacbaacbccaba killed in two steps: p = 1, y = b, through bcbaacbbacbaacaccaba bcbaacbbacbaacbccbba bcbaacbbacbaacbccaaa bcbaacbbacbaacbccabb acbaacbbacbbabccacbb killed in two steps: p = 1, y = b, through bcbaacbbacbbabccacab acbaacbbbaccbcaabcaa killed in two steps: p = 1, y = b, through bcbaacbbbaccbcaabcab acbaacbccabaacbaacbb killed in two steps: p = 1, y = b, through bcbaacbccabaacbaacab acbaacbccabaacbbbcaa killed in two steps: p = 1, y = b, through bcbaacbccabaacbbbcab acbaacbccabbbcaabcaa killed in two steps: p = 1, y = b, through bcbaacbccabbbcaabcab acbaccbaacbaacabbcba killed in two steps: p = 1, y = b, through bcbaccbaacbaacabbcaa bcbaccbaacbaacabbcbb acbaccbabbcaccbaccba killed in two steps: p = 1, y = b, through bcbaccbabbcbccbaccba bcbaccbabbcaccaaccba bcbaccbabbcaccbbccba bcbaccbabbcaccbaccaa bcbaccbabbcaccbaccbb acbbabccabcaabccabcc killed in two steps: p = 1, y = b, through bcbbabccabcbabccabcc acbbabccabcccbaaabcc killed in two steps: p = 1, y = b, through bcbbabccabcccbababcc acbbabccabcccbaccbaa killed in two steps: p = 1, y = b, through bcbbabccabcccbaccbab acbbabccacbbacbaacbb killed in two steps: p = 1, y = b, through bcbbabccacbbacbaacab acbbabccacbbacbbbcaa killed in two steps: p = 1, y = b, through bcbbabccacbbacbbbcab acbbacaabcbbacbbaccb killed in two steps: p = 1, y = b, through bcbbacaabcbbacabaccb acbbacaabcbbacccabbb killed in two steps: p = 1, y = b, through bcbbacaabcbbacccabab acbbacaabcccabbcabbb killed in two steps: p = 1, y = b, through bcbbacaabcccabbcabab acbbacbaacbbacbbabcc killed in two steps: p = 1, y = b, through bcbbacbaacbbacababcc acbbacbaacbccabaacba killed in two steps: p = 1, y = b, through bcbbacbaacbccabaacaa bcbbacbaacbccabaacbb acbbacbbabccacbbacba killed in two steps: p = 1, y = b, through bcbbacbbabccacbbacaa bcbbacbbabccacbbacbb acbbacbbbcaaacbbabcc killed in two steps: p = 1, y = b, through bcbbacbbbcaaacababcc acbbacbbbcabbcaaabcc killed in two steps: p = 1, y = b, through bcbbacbbbcabbcababcc acbbacbbbcabbcaccbaa killed in two steps: p = 1, y = b, through bcbbacbbbcabbcaccbab acbbaccbacbbacaabcbb killed in two steps: p = 1, y = b, through bcbbaccbacbbacaabcab acbbaccbaccbcaabaccb killed in two steps: p = 1, y = b, through bcbbaccbaccbcbabaccb acbbacccbaacabbcabbb killed in two steps: p = 1, y = b, through bcbbacccbaacabbcabab acbbbaccbacccabccaba killed in two steps: p = 1, y = b, through bcbbbaccbacccbbccaba bcbbbaccbacccaaccaba bcbbbaccbacccabccbba bcbbbaccbacccabccaaa bcbbbaccbacccabccabb acbbbaccbcaabcaaacba killed in two steps: p = 1, y = b, through bcbbbaccbcaabcaaacaa bcbbbaccbcaabcaaacbb acbbbcaaacbaacbccaba killed in two steps: p = 1, y = b, through bcbbbcaaacbaacaccaba bcbbbcaaacbaacbccbba bcbbbcaaacbaacbccaaa bcbbbcaaacbaacbccabb acbbbcaaacbbabccacbb killed in two steps: p = 1, y = b, through bcbbbcaaacbbabccacab acbbbcaabaccbcaabcaa killed in two steps: p = 1, y = b, through bcbbbcaabaccbcaabcab acbbbcabbcaaabccacbb killed in two steps: p = 1, y = b, through bcbbbcabbcaaabccacab acbbbcabbcaccbaaacbb killed in two steps: p = 1, y = b, through bcbbbcabbcaccbaaacab acbbbcabbcaccbabbcaa killed in two steps: p = 1, y = b, through bcbbbcabbcaccbabbcab acbccabaacbaacbbacba killed in two steps: p = 1, y = b, through bcbccabaacbaacbbacaa bcbccabaacbaacbbacbb acbccabaacbbbcaaacba killed in two steps: p = 1, y = b, through bcbccabaacbbbcaaacaa bcbccabaacbbbcaaacbb acbccabbbacccabccaba killed in two steps: p = 1, y = b, through bcbccabbbacccbbccaba bcbccabbbacccaaccaba bcbccabbbacccabccbba bcbccabbbacccabccaaa bcbccabbbacccabccabb acbccabbbcaabcaaacba killed in two steps: p = 1, y = b, through bcbccabbbcaabcaaacaa bcbccabbbcaabcaaacbb acbccabccabbcabccaba killed in two steps: p = 1, y = b, through bcbccabccabbcbbccaba bcbccabccabbcaaccaba bcbccabccabbcabccbba bcbccabccabbcabccaaa bcbccabccabbcabccabb accbaaabcccbaccbabbc killed in two steps: p = 1, y = b, through bccbababcccbaccbabbc accbaaacbbabccabcccb killed in two steps: p = 1, y = b, through bccbabacbbabccabcccb accbaaacbbacbbbcabbc killed in two steps: p = 1, y = b, through bccbabacbbacbbbcabbc accbaacbaacabbcbaacb killed in two steps: p = 1, y = b, through bccbabcbaacabbcbaacb accbaacbaccbabbcaccb killed in two steps: p = 1, y = b, through bccbabcbaccbabbcaccb accbabbcaaabccabcccb killed in two steps: p = 1, y = b, through bccbabacaaabccabcccb accbabbcaaacbbbcabbc killed in two steps: p = 1, y = b, through bccbabacaaacbbbcabbc accbabbcabbcaabcabbc killed in two steps: p = 1, y = b, through bccbabacabbcaabcabbc accbabbcaccbaaabcccb killed in two steps: p = 1, y = b, through bccbabacaccbaaabcccb accbabbcaccbaccbaacb killed in two steps: p = 1, y = b, through bccbabacaccbaccbaacb accbacbbacaabcbbacbb killed in two steps: p = 1, y = b, through bccbacbbacaabcbbacab accbacbbaccbaccbcaab killed in two steps: p = 1, y = b, through bccbacbbaccbaccbcbab accbaccbaacbaccbabbc killed in two steps: p = 1, y = b, through bccbaccbabcbaccbabbc accbaccbcaabaccbacbb killed in two steps: p = 1, y = b, through bccbaccbcaabaccbacab accbacccabbbaccbcaab killed in two steps: p = 1, y = b, through bccbacccabbbaccbcbab accbacccabccabaacbbb killed in two steps: p = 1, y = b, through bccbacccabccabaacbab accbacccabccabbbcaab killed in two steps: p = 1, y = b, through bccbacccabccabbbcbab accbcaabaccbacbbaccb killed in two steps: p = 1, y = b, through bccbcaabaccbacabaccb accbcaabaccbacccabbb killed in two steps: p = 1, y = b, through bccbcaabaccbacccabab accbcaabcaaacbaacbbb killed in two steps: p = 1, y = b, through bccbcaabcaaacbaacbab accbcaabcaaacbbbcaab killed in two steps: p = 1, y = b, through bccbcaabcaaacbbbcbab accbcaabcabbcaabcaab killed in two steps: p = 1, y = b, through bccbcaabcabbcaabcbab acccabbbacbbacaabcbb killed in two steps: p = 1, y = b, through bcccabbbacbbacaabcab acccabbbaccbcaabaccb killed in two steps: p = 1, y = b, through bcccabbbaccbcbabaccb acccabbcbaacabbcabbb killed in two steps: p = 1, y = b, through bcccabbcbaacabbcabab acccabccabaacbbbaccb killed in two steps: p = 1, y = b, through bcccabccabaacbabaccb acccabccabaacbccabbb killed in two steps: p = 1, y = b, through bcccabccabaacbccabab acccabccabbbcaabaccb killed in two steps: p = 1, y = b, through bcccabccabbbcbabaccb acccbaacabbcabbbacbb killed in two steps: p = 1, y = b, through bcccbaacabbcabbbacab acccbaacbaaabcaabcbb killed in two steps: p = 1, y = b, through bcccbaacbaaabcaabcab ==================================================================================================== ===== wordsout.txt ==================================================================================================== 31 Oct 12:42 words.py, lengths up to 18 length 2: 0 exotic words beginning with a (e.g. -); not killed by a single rotation relation: 0 (0s) length 4: 0 exotic words beginning with a (e.g. -); not killed by a single rotation relation: 0 (0s) length 6: 0 exotic words beginning with a (e.g. -); not killed by a single rotation relation: 0 (0s) length 8: 0 exotic words beginning with a (e.g. -); not killed by a single rotation relation: 0 (0s) length 10: 10 exotic words beginning with a (e.g. ababcbabac); not killed by a single rotation relation: 0 (0s) length 12: 240 exotic words beginning with a (e.g. aaababcbabac); not killed by a single rotation relation: 0 (0s) length 14: 3654 exotic words beginning with a (e.g. aaaaababcbabac); not killed by a single rotation relation: 0 (4s) length 16: 45360 exotic words beginning with a (e.g. aaaaaaababcbabac); not killed by a single rotation relation: 0 (75s) length 18: 502482 exotic words beginning with a (e.g. aaaaaaaaababcbabac); not killed by a single rotation relation: 0 (1608s) (paper: 10, 240, 3654, 45360 exotic words at lengths 10, 12, 14, 16, all killed; lengths 18 and 20 are new) 31 Oct 17:54 words.py, lengths up to 20 length 2: 0 exotic words beginning with a (e.g. -); not killed by a single rotation relation: 0 (0s) length 4: 0 exotic words beginning with a (e.g. -); not killed by a single rotation relation: 0 (0s) length 6: 0 exotic words beginning with a (e.g. -); not killed by a single rotation relation: 0 (0s) length 8: 0 exotic words beginning with a (e.g. -); not killed by a single rotation relation: 0 (0s) length 10: 10 exotic words beginning with a (e.g. ababcbabac); not killed by a single rotation relation: 0 (0s) length 12: 240 exotic words beginning with a (e.g. aaababcbabac); not killed by a single rotation relation: 0 (0s) length 14: 3654 exotic words beginning with a (e.g. aaaaababcbabac); not killed by a single rotation relation: 0 (2s) length 16: 45360 exotic words beginning with a (e.g. aaaaaaababcbabac); not killed by a single rotation relation: 0 (46s) length 18: 502482 exotic words beginning with a (e.g. aaaaaaaaababcbabac); not killed by a single rotation relation: 0 (735s) length 20: 5186470 exotic words beginning with a (e.g. aaaaaaaaaaababcbabac); not killed by a single rotation relation: 240 e.g. acccbaacbaaabcaabcbb (13682s) (paper: 10, 240, 3654, 45360 exotic words at lengths 10, 12, 14, 16, all killed; lengths 18 and 20 are new)