Referee 2 independent checks for OWR-1323-008
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[C1] row i of T^k (primal composition) == A^k g_i (dual iteration)
   F (T=backward shift)                           208 comparisons, 0 mismatches
   F^2 (T=B^2, rank-2 free)                       208 comparisons, 0 mismatches
   I+2F (T=I+2B)                                  208 comparisons, 0 mismatches
   rotation-shift on 2-blocks                     208 comparisons, 0 mismatches
   mult. by t on Q[t,1/(t^2+1)] (not free)        208 comparisons, 0 mismatches
   eigenvector g_1, shift on rest                 208 comparisons, 0 mismatches
   rotation on span{g_1,g_2} (t^2+1 torsion)      208 comparisons, 0 mismatches

[C2] Lemma 4.1: n0 = least n such that every n in [n0,40] is good
   F (T=backward shift)                          all (N,l) eventually good: True
                                                 bound d from proof is sharp (n0 = d+1 for N>=1): True
   F^2 (T=B^2, rank-2 free)                      all (N,l) eventually good: True
                                                 bound d from proof is sharp (n0 = d+1 for N>=1): True
   I+2F (T=I+2B)                                 all (N,l) eventually good: True
   rotation-shift on 2-blocks                    all (N,l) eventually good: True
   mult. by t on Q[t,1/(t^2+1)] (not free)       all (N,l) eventually good: True
                                                 n0 values (N,l,n0): [(0, 1, 0), (0, 4, 0), (1, 1, 1), (1, 4, 1), (2, 1, 1), (2, 4, 3), (3, 1, 1), (3, 4, 3), (4, 1, 2), (4, 4, 4), (5, 1, 2), (5, 4, 4), (6, 1, 2), (6, 4, 4)]
   torsion: eigenvector g_1, shift on rest       V=W=span{g1} fails for all n<=60: True
   torsion: rotation on span{g_1,g_2} (t^2+1 torsion) V=W=span{g1,g2} fails for all n<=60: True

[C3] Menet Thm 4.8 hypothesis (0-based) vs translation in Remark 4.2
   F (T=backward shift)                           720 (N,l,k) cases,  720 agree; holds for all k in [15,30]: True
   F^2 (T=B^2, rank-2 free)                       720 (N,l,k) cases,  720 agree; holds for all k in [15,30]: True
   I+2F (T=I+2B)                                  720 (N,l,k) cases,  720 agree; holds for all k in [15,30]: True
   rotation-shift on 2-blocks                     720 (N,l,k) cases,  720 agree; holds for all k in [15,30]: True
   mult. by t on Q[t,1/(t^2+1)] (not free)        720 (N,l,k) cases,  720 agree; holds for all k in [15,30]: True
   torsion: eigenvector g_1, shift on rest        720 cases,  720 agree; holds for all large k: False
   torsion: rotation on span{g_1,g_2} (t^2+1 torsion)  720 cases,  720 agree; holds for all large k: False

[C4/C5] construction of Theorem 1.1 ((b) => (c))
   F (T=backward shift)
      requirements 66, |F| = 156, rank F = 156, surjectivity reqs ok 8/8, times n_s in [1,154]
      primal T^{n_s} S u vs dual formula: 156/156 coordinates agree; targets hit exactly 18/18  (0.9s)
   F^2 (T=B^2, rank-2 free)
      requirements 66, |F| = 160, rank F = 160, surjectivity reqs ok 8/8, times n_s in [1,98]
      primal T^{n_s} S u vs dual formula: 160/160 coordinates agree; targets hit exactly 18/18  (0.7s)
   I+2F (T=I+2B)
      requirements 66, |F| = 159, rank F = 159, surjectivity reqs ok 8/8, times n_s in [1,156]
      primal T^{n_s} S u vs dual formula: 159/159 coordinates agree; targets hit exactly 18/18  (3.0s)
   rotation-shift on 2-blocks
      requirements 66, |F| = 156, rank F = 156, surjectivity reqs ok 8/8, times n_s in [1,81]
      primal T^{n_s} S u vs dual formula: 156/156 coordinates agree; targets hit exactly 18/18  (1.0s)
   mult. by t on Q[t,1/(t^2+1)] (not free)
      requirements 66, |F| = 155, rank F = 155, surjectivity reqs ok 8/8, times n_s in [1,153]
      primal T^{n_s} S u vs dual formula: 155/155 coordinates agree; targets hit exactly 18/18  (3.3s)

[algebra] Theorem 1.3 identities on random rational instances: 150/150
[algebra] Theorem 1.2 identity S e_j = T^j x0/j! (finite truncations): 50/50
[float]   Lemma 3.1 factorisation f=pg, gh=I for f=e^z-1: max errors 6.66e-16, 2.22e-16
total time 9.7s
