{
  "title": "Dominant weights: motion, order and cancellation",
  "status": "Exact functions, phases and operator identities. Plot windows and twelve row coordinates are explicitly finite samples.",
  "density": {
    "coordinate_window": [-1.0,1.4],
    "curve_samples": 401,
    "density": "exp(q)",
    "conjugated_density": "2 exp(q)",
    "translation": "r=log(2), (L_r f)(q)=f(q-r)",
    "eigenfield": "D^(it) X(r) D^(-it)=exp(irt)X(r)",
    "full_weight": "chi Ad(X(log(c)))=c chi on B_+",
    "rank_one_test": {"vector":"xi(q)=1_[0,1](q) eta, ||eta||=1","chi":"exp(1)-1","twice_chi":"2(exp(1)-1)"},
    "locator": "DWC5.a-DWC5.h"
  },
  "matrix": {
    "h": [[1,0],[0,4]],
    "k": [[5,-3],[-3,5]],
    "cocycle": "c_t=2^(it) R h^(it) R* h^(-it)",
    "t0": "pi/(2 log(2))",
    "r": "t0/2",
    "A_numerator": [["i","-i"],["1","1"]],
    "B_numerator": [["i","-1"],["i","1"]],
    "common_divisor": "sqrt(2)",
    "A_times_B": [["0","-i"],["i","0"]],
    "B_times_A": [["-1","0"],["0","1"]],
    "c_t0_squared": "I",
    "c_2t0": "-I",
    "locator": "DWC5.i-DWC5.o; DWC6.b"
  },
  "row": {
    "bijection": "nu(n,j)=(n+j)(n+j+1)/2+n",
    "sample_n": [0,1,2],
    "sample_j": [0,1,2,3],
    "sample_values": [[0,1,3,6],[2,4,7,11],[5,8,12,17]],
    "isometries": "s_n(e_j tensor eta)=e_nu(n,j) tensor eta",
    "row": "R=sum_(n>=0) r_n tensor E_0n",
    "identities": ["R*R=1","RR*=e=1 tensor E_00","Omega(RaR*)=Omega(a), a>=0"],
    "finite_row": "R_m* R_m=1 tensor sum_(n<m) E_nn; ||R-R_m||=1",
    "locator": "DWC5.p-DWC5.u; DWC6.c-DWC6.d"
  },
  "hypotheses": {
    "rows": [
      {"weight":"Tr_(L2), density exp(Q)","centralizer":"L-infinity(R)","properly_infinite_centralizer":false,"all_real_eigenfield":true},
      {"weight":"Tr_(K tensor L2), density I tensor exp(Q), K infinite","centralizer":"B(K) tensor L-infinity(R)","properly_infinite_centralizer":true,"all_real_eigenfield":true},
      {"weight":"Tr_K, K infinite","centralizer":"B(K)","properly_infinite_centralizer":true,"all_real_eigenfield":false}
    ],
    "rank_one_values": [1,2],
    "rank_one_weights": ["Tr_K","2 Tr_K"],
    "obstruction": "Tr_K Ad(u)(p)=1 for every unitary u and rank-one projection p, whereas 2Tr_K(p)=2",
    "locator": "DWC5.h; DWC5.v-DWC5.w; DWC6.diagnostic A and D"
  }
}