rejection tests for check_certificates.py (data file sha256 ba5b98ee9b0bc2bcf33fe642341008676f06ab81911b83927e4972be5323e3cc)
baseline  N1000                            unmodified data, parts ABCD: accepted
baseline  control-N4-three-steady-states   unmodified data, parts ABCD: accepted
test  1   N1000                            parts ABC  beta multiplied by 1 + 10^-4 (the window of rho has relative half-width 3*10^-5) -> REJECTED   [A  original equations (2),(3),(4) hold exactly, all C_j > 0, Sigma = Sigma* at the 6 values of S: True;  signs of the right-hand side of (1): + - - - ]
test  2   N1000                            parts ABC  beta multiplied by 1 - 10^-4 -> REJECTED   [A  original equations (2),(3),(4) hold exactly, all C_j > 0, Sigma = Sigma* at the 6 values of S: True;  signs of the right-hand side of (1): + + + + ]
test  3   N1000                            parts ABC  S_T = 9906787/10^7 instead of 9906777/10^7 (sixth decimal; last test point moved to the new X) -> REJECTED   [A  original equations (2),(3),(4) hold exactly, all C_j > 0, Sigma = Sigma* at the 6 values of S: True;  signs of the right-hand side of (1): + + + + ]
test  4   N1000                            parts ABC  S_T = 9906767/10^7 instead of 9906777/10^7 (last test point moved to the new X) -> REJECTED   [A  original equations (2),(3),(4) hold exactly, all C_j > 0, Sigma = Sigma* at the 6 values of S: True;  signs of the right-hand side of (1): + - - - ]
test  5   N1000                            parts ABC  nu_1 and kappa multiplied by 1.01 (Sigma* stays 1/2) -> REJECTED   [A  original equations (2),(3),(4) hold exactly, all C_j > 0, Sigma = Sigma* at the 6 values of S: True;  signs of the right-hand side of (1): + + + + ]
test  6   N1000                            parts ABC  chain length N = 990 instead of 1000 -> REJECTED   [A  original equations (2),(3),(4) hold exactly, all C_j > 0, Sigma = Sigma* at the 6 values of S: True;  signs of the right-hand side of (1): + - + + ]
test  7   N1000                            parts ABC  chain length N = 1005 instead of 1000 -> REJECTED   [A  original equations (2),(3),(4) hold exactly, all C_j > 0, Sigma = Sigma* at the 6 values of S: True;  signs of the right-hand side of (1): + - + - ]
test  8   N1000                            parts A    kappa changed so that Sigma* is no longer 1/2 -> REJECTED   [refused: Sigma_star is not the root of q in (0, min(L1, R))]
test  9   N1000                            parts A    b = 0 (not a positive parameter) -> REJECTED   [refused: parameter b = 0 is not positive]
test 10   N1000                            parts A    beta negative -> REJECTED   [refused: parameter beta = -343447/200000000000 is not positive]
test 11   N1000                            parts AB   test point 1977/2000 replaced by 1971/2000 (same side of the second root as 197/200) -> REJECTED   [A  original equations (2),(3),(4) hold exactly, all C_j > 0, Sigma = Sigma* at the 6 values of S: True;  signs of the right-hand side of (1): + - - - ]
test 12   N1000                            parts AB   two test points interchanged -> REJECTED   [FAILED: the test points must increase from x0 to X]
test 13   N1000                            parts AB   first test point 1/50 instead of x0 = 1/100 -> REJECTED   [FAILED: the test points must increase from x0 to X]
test 14   N1000                            parts B    expected sign pattern +-+-++  -> REJECTED   [B  signs of P at the test points: + - + - + -   [FAILED]]
test 15   N1000                            parts C    expected count 3 instead of 5 -> REJECTED   [number of roots of P in [x0, X]: 5, all simple; signs of P' at the roots: - + - + -   [FAILED]]
test 16   N1000                            parts C    expected count 7 instead of 5 -> REJECTED   [number of roots of P in [x0, X]: 5, all simple; signs of P' at the roots: - + - + -   [FAILED]]
test 17   N1000                            parts C    expected signs of P' given as +-+-+ -> REJECTED   [number of roots of P in [x0, X]: 5, all simple; signs of P' at the roots: - + - + -   [FAILED]]
test 18   N1000                            parts D    Descartes: cut point 1977/2000 removed (an interval then contains two roots) -> REJECTED   [every interval has 0 or 1 sign changes: False; number of roots of P in (x0, X): 5   [FAILED]]
test 19   N1000                            parts D    Descartes: last cut point 999/1000 instead of X -> REJECTED   [refused: cut points must increase from x0 to X]
test 20   control-N4-three-steady-states   parts D    Descartes, control N = 4: cut point 1/25 removed (two roots in one interval) -> REJECTED   [every interval has 0 or 1 sign changes: False; number of roots of P in (x0, X): 3   [FAILED]]
test 21   control-N4-three-steady-states   parts D    Descartes, control N = 4: cut points not increasing -> REJECTED   [refused: cut points must increase from x0 to X]
test 22   control-N4-three-steady-states   parts ABC  control N = 4: beta = 50 instead of 1/200 -> REJECTED   [A  original equations (2),(3),(4) hold exactly, all C_j > 0, Sigma = Sigma* at the 4 values of S: True;  signs of the right-hand side of (1): + - - - ]
22 corruptions, all rejected: True;  unmodified data accepted: see the baseline lines
