Listing: Listing

# higher_grade_scaling.py output  (XVI-M work package B; python 3.13.5, sympy 1.14.0)
# CONDITIONAL on Input (S-bv): S = c (Q-i0)^{-1}; c^2 symbolic. Gate V and single-switch collapse unchanged.

# === Section A: complete differentiation of the XVI-L subtraction formula (all N=0..4) ===
# M_{beta alpha}(lam) = binom(beta,alpha) lam^{|beta|-|alpha|} p_{beta-alpha},  p_delta = d^delta varpi(0)
CHECK A N=0 [symbolic]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=0 [symbolic]: M M^{-1} = 1 (exact): True
CHECK A N=0 [symbolic]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=0 [symbolic]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=0 [symbolic]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=0 [symbolic]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=0 [symbolic]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=0 [random_rational_0]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=0 [random_rational_0]: M M^{-1} = 1 (exact): True
CHECK A N=0 [random_rational_0]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=0 [random_rational_0]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=0 [random_rational_0]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=0 [random_rational_0]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=0 [random_rational_0]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=0: literal d^beta(z^alpha varpi_mu/alpha!)(0) equals M_of entries (explicit varpi, first 12x12 block): True
CHECK A N=0: explicit non-radial varpi=exp(q): mu d/dmu w_alpha^{(mu)} = (E-|alpha|) w_alpha^{(mu)} as functions: True
CHECK A N=1 [symbolic]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=1 [symbolic]: M M^{-1} = 1 (exact): True
CHECK A N=1 [symbolic]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=1 [symbolic]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=1 [symbolic]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=1 [symbolic]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=1 [symbolic]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=1 [random_rational_0]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=1 [random_rational_0]: M M^{-1} = 1 (exact): True
CHECK A N=1 [random_rational_0]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=1 [random_rational_0]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=1 [random_rational_0]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=1 [random_rational_0]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=1 [random_rational_0]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=1: literal d^beta(z^alpha varpi_mu/alpha!)(0) equals M_of entries (explicit varpi, first 12x12 block): True
CHECK A N=1: explicit non-radial varpi=exp(q): mu d/dmu w_alpha^{(mu)} = (E-|alpha|) w_alpha^{(mu)} as functions: True
CHECK A N=2 [symbolic]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=2 [symbolic]: M M^{-1} = 1 (exact): True
CHECK A N=2 [symbolic]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=2 [symbolic]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=2 [symbolic]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=2 [symbolic]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=2 [symbolic]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=2 [random_rational_0]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=2 [random_rational_0]: M M^{-1} = 1 (exact): True
CHECK A N=2 [random_rational_0]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=2 [random_rational_0]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=2 [random_rational_0]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=2 [random_rational_0]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=2 [random_rational_0]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=2: literal d^beta(z^alpha varpi_mu/alpha!)(0) equals M_of entries (explicit varpi, first 12x12 block): True
CHECK A N=2: explicit non-radial varpi=exp(q): mu d/dmu w_alpha^{(mu)} = (E-|alpha|) w_alpha^{(mu)} as functions: True
CHECK A N=3 [symbolic]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=3 [symbolic]: M M^{-1} = 1 (exact): True
CHECK A N=3 [symbolic]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=3 [symbolic]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=3 [symbolic]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=3 [symbolic]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=3 [symbolic]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=3 [random_rational_0]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=3 [random_rational_0]: M M^{-1} = 1 (exact): True
CHECK A N=3 [random_rational_0]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=3 [random_rational_0]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=3 [random_rational_0]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=3 [random_rational_0]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=3 [random_rational_0]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=3 [random_rational_1]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=3 [random_rational_1]: M M^{-1} = 1 (exact): True
CHECK A N=3 [random_rational_1]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=3 [random_rational_1]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=3 [random_rational_1]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=3 [random_rational_1]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=3 [random_rational_1]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=3: literal d^beta(z^alpha varpi_mu/alpha!)(0) equals M_of entries (explicit varpi, first 12x12 block): True
CHECK A N=3: explicit non-radial varpi=exp(q): mu d/dmu w_alpha^{(mu)} = (E-|alpha|) w_alpha^{(mu)} as functions: True
CHECK A N=4 [random_rational_0]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=4 [random_rational_0]: M M^{-1} = 1 (exact): True
CHECK A N=4 [random_rational_0]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=4 [random_rational_0]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=4 [random_rational_0]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=4 [random_rational_0]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=4 [random_rational_0]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=4 [random_rational_1]: M^{(rho,mu)} unit lower-triangular (Leibniz, varpi_mu(0)=1): True
CHECK A N=4 [random_rational_1]: M M^{-1} = 1 (exact): True
CHECK A N=4 [random_rational_1]: mu d(M^{-1})/dmu = -M^{-1}(mu dM/dmu)M^{-1} (exact): True
CHECK A N=4 [random_rational_1]: -M^{-1}(mu dM)M^{-1} = D M^{-1} - M^{-1} D, D=diag(|beta|) (dilation grading): True
CHECK A N=4 [random_rational_1]: mu d/dmu P_alpha (complete formula) = (E-|alpha|) P_alpha for all |alpha|<=N: True
CHECK A N=4 [random_rational_1]: w_alpha = (z^alpha/alpha!) T_{N-|alpha|}[1/varpi_mu] varpi_mu (closed form): True
CHECK A N=4 [random_rational_1]: d^beta w_alpha(0) = delta^beta_alpha (|alpha|,|beta|<=N): True
CHECK A N=4: literal d^beta(z^alpha varpi_mu/alpha!)(0) equals M_of entries (explicit varpi, first 12x12 block): True
CHECK A N=4: explicit non-radial varpi=exp(q): mu d/dmu w_alpha^{(mu)} = (E-|alpha|) w_alpha^{(mu)} as functions: True
# Section A consequence (exact, every N, every varpi):  mu d_mu w_alpha = (E-|alpha|) w_alpha ; hence  a_mu(u,alpha) = (-1)^{|alpha|+1} <u,(E-|alpha|) w_alpha>  and  calA coefficient (-1)^{|alpha|}<R u,(N-E) w_alpha> = (-1)^{|alpha|+1}<u,(E-|alpha|)w_alpha> (moments vanish).

# === Section B: finite exact end-to-end test (Euclidean toy homogeneous kernels; NOT the graph kernels) ===
CHECK B toy N=0 u=z^() r^{-4-N-|d|}: A_mu[phi] = mu d/dmu <u,W^mu phi> equals calA[phi]=<u,W^mu((N-E)phi)> exactly: True
CHECK B toy N=0 u=z^(): A_mu[phi] = sum_gamma a_gamma (-1)^|gamma| d^gamma phi(0) with a_gamma from the nu_k formula: True
CHECK B toy N=0: top-order (|gamma|=N) coefficients mu-independent: True
CHECK B toy N=0: a_gamma(mu) = (mu/mu0)^{N-|gamma|} a_gamma(mu0) for every gamma: True
# toy N=0 u=z^(): A_mu[phi] = 2*pi**2 ; coefficients {'()': '2*pi**2'}
CHECK B toy N=1 u=z^0 r^{-4-N-|d|}: A_mu[phi] = mu d/dmu <u,W^mu phi> equals calA[phi]=<u,W^mu((N-E)phi)> exactly: True
CHECK B toy N=1 u=z^0: A_mu[phi] = sum_gamma a_gamma (-1)^|gamma| d^gamma phi(0) with a_gamma from the nu_k formula: True
CHECK B toy N=1: top-order (|gamma|=N) coefficients mu-independent: True
CHECK B toy N=1: a_gamma(mu) = (mu/mu0)^{N-|gamma|} a_gamma(mu0) for every gamma: True
# toy N=1 u=z^0: A_mu[phi] = pi**2*(-23*lam - 3024)/6048 ; coefficients {'()': '-23*pi**2*lam/12096', '0': '-pi**2/2', '1': '0', '2': '0', '3': '0'}
CHECK B toy N=1 u=z^2 r^{-4-N-|d|}: A_mu[phi] = mu d/dmu <u,W^mu phi> equals calA[phi]=<u,W^mu((N-E)phi)> exactly: True
CHECK B toy N=1 u=z^2: A_mu[phi] = sum_gamma a_gamma (-1)^|gamma| d^gamma phi(0) with a_gamma from the nu_k formula: True
CHECK B toy N=1: top-order (|gamma|=N) coefficients mu-independent: True
CHECK B toy N=1: a_gamma(mu) = (mu/mu0)^{N-|gamma|} a_gamma(mu0) for every gamma: True
# toy N=1 u=z^2: A_mu[phi] = pi**2*(140 - lam)/840 ; coefficients {'()': '-pi**2*lam/840', '0': '0', '1': '0', '2': '-pi**2/2', '3': '0'}
CHECK B toy N=2 u=z^01 r^{-4-N-|d|}: A_mu[phi] = mu d/dmu <u,W^mu phi> equals calA[phi]=<u,W^mu((N-E)phi)> exactly: True
CHECK B toy N=2 u=z^01: A_mu[phi] = sum_gamma a_gamma (-1)^|gamma| d^gamma phi(0) with a_gamma from the nu_k formula: True
CHECK B toy N=2: top-order (|gamma|=N) coefficients mu-independent: True
CHECK B toy N=2: a_gamma(mu) = (mu/mu0)^{N-|gamma|} a_gamma(mu0) for every gamma: True
# toy N=2 u=z^01: A_mu[phi] = pi**2*(lam*(5350 - 179969*lam) + 201600)/4838400 ; coefficients {'()': '-179969*pi**2*lam**2/4838400', '0': '-pi**2*lam/2016', '1': '59*pi**2*lam/96768', '2': '-pi**2*lam/13440', '3': '-pi**2*lam/32256', '00': '0', '01': 'pi**2/12', '02': '0', '03': '0', '11': '0', '12': '0', '13': '0', '22': '0', '23': '0', '33': '0'}
CHECK B toy N=2 u=z^00 r^{-4-N-|d|}: A_mu[phi] = mu d/dmu <u,W^mu phi> equals calA[phi]=<u,W^mu((N-E)phi)> exactly: True
CHECK B toy N=2 u=z^00: A_mu[phi] = sum_gamma a_gamma (-1)^|gamma| d^gamma phi(0) with a_gamma from the nu_k formula: True
CHECK B toy N=2: top-order (|gamma|=N) coefficients mu-independent: True
CHECK B toy N=2: a_gamma(mu) = (mu/mu0)^{N-|gamma|} a_gamma(mu0) for every gamma: True
# toy N=2 u=z^00: A_mu[phi] = pi**2*(lam*(17062838*lam + 575) - 3360000)/1612800 ; coefficients {'()': '8531419*pi**2*lam**2/2419200', '0': '23*pi**2*lam/32256', '1': '-pi**2*lam/2016', '2': 'pi**2*lam/6720', '3': '-pi**2*lam/16128', '00': 'pi**2/8', '01': '0', '02': '0', '03': '0', '11': 'pi**2/24', '12': '0', '13': '0', '22': 'pi**2/24', '23': '0', '33': 'pi**2/24'}

# === Section C: exact J(P,m) = int_{S^3} P (Q-i0)^{-m} d sigma (two independent routes) ===
CHECK C: int_{S^3}(Q-i0)^{-2} = -2 i pi^2 (recovers M.6 residue r = -2 i pi^2 c^2): True
CHECK C route B: int_{S^3}(Q-i0)^{-2} = -2 i pi^2: True
CHECK C numeric (Q - i eps)^{-2} check for (a,b)=(0,0): |extrap-exact|<1e-4: True
CHECK C numeric (Q - i eps)^{-4} check for (a,b)=(2,2): |extrap-exact|<1e-4: True
CHECK C numeric (Q - i eps)^{-5} check for (a,b)=(0,4): |extrap-exact|<1e-4: True
CHECK C numeric (Q - i eps)^{-6} check for (a,b)=(4,2): |extrap-exact|<1e-4: True

# === Section D: per-grade coefficients (N=0 audit, then N=1, 2, 3, 4) ===
CHECK d_N = (1,4,10,20,35): True
CHECK p_{e0} = -2 z0 (d^alpha S = c p_alpha (Q-i0)^{-1-|alpha|}): True
CHECK 185 relation vectors parsed from kernel_relation_matrix.txt: True
CHECK D N=0: reconstructed label coefficients sum_b R_{lambda b} a_b equal direct per-label evaluation (all 1 labels, all gamma): True
CHECK D N=0: every relation vector (0) annihilates the top-order, radial-specialization and general-varpi coefficient vectors: True
CHECK D N=0: B_mu = A_mu - calA_mu vanishes on top order |gamma|=N (route A vs route B, exact): True
# N=0: top-order residue slots nonzero = 1 of 1 ; B_mu = 0 (top exact; lower by Section A identity)
CHECK D N=1: reconstructed label coefficients sum_b R_{lambda b} a_b equal direct per-label evaluation (all 4 labels, all gamma): True
CHECK D N=1: every relation vector (0) annihilates the top-order, radial-specialization and general-varpi coefficient vectors: True
CHECK D N=1: B_mu = A_mu - calA_mu vanishes on top order |gamma|=N (route A vs route B, exact): True
# N=1: top-order residue slots nonzero = 4 of 16 ; B_mu = 0 (top exact; lower by Section A identity)
CHECK D N=2: reconstructed label coefficients sum_b R_{lambda b} a_b equal direct per-label evaluation (all 20 labels, all gamma): True
CHECK D N=2: every relation vector (10) annihilates the top-order, radial-specialization and general-varpi coefficient vectors: True
CHECK D N=2: B_mu = A_mu - calA_mu vanishes on top order |gamma|=N (route A vs route B, exact): True
# N=2: top-order residue slots nonzero = 22 of 100 ; B_mu = 0 (top exact; lower by Section A identity)
CHECK D N=3: reconstructed label coefficients sum_b R_{lambda b} a_b equal direct per-label evaluation (all 60 labels, all gamma): True
CHECK D N=3: every relation vector (40) annihilates the top-order, radial-specialization and general-varpi coefficient vectors: True
CHECK D N=3: B_mu = A_mu - calA_mu vanishes on top order |gamma|=N (route A vs route B, exact): True
# N=3: top-order residue slots nonzero = 68 of 400 ; B_mu = 0 (top exact; lower by Section A identity)
CHECK D N=4: reconstructed label coefficients sum_b R_{lambda b} a_b equal direct per-label evaluation (all 170 labels, all gamma): True
CHECK D N=4: every relation vector (135) annihilates the top-order, radial-specialization and general-varpi coefficient vectors: True
CHECK D N=4: B_mu = A_mu - calA_mu vanishes on top order |gamma|=N (route A vs route B, exact): True
# N=4: top-order residue slots nonzero = 194 of 1225 ; B_mu = 0 (top exact; lower by Section A identity)
CHECK D N=0 audit recovered: A_mu(S^2) = calA(S^2) = -2 i pi^2 c^2 delta: True
CHECK D test: Res(d_alpha u) = d_alpha Res(u) for every label of grade N<=3 and every alpha (340 identities): True
CHECK D test: top-order residue map is Lorentz-equivariant on all 6 so(1,3) generators (pull-back action), N=0..4: True
CHECK D test N=0: residue map = exact combination of audited equivariant maps phi_{k,k}: True
CHECK D test N=1: residue map = exact combination of audited equivariant maps phi_{k,k}: True
CHECK D test N=2: residue map = exact combination of audited equivariant maps phi_{k,k}: True
CHECK D test N=3: residue map = exact combination of audited equivariant maps phi_{k,k}: True
CHECK D test N=4: residue map = exact combination of audited equivariant maps phi_{k,k}: True
# residue map in equivariant coordinates (units i pi^2 c^2): {0: {'phi_00': '-2'}, 1: {'phi_00': '1/2'}, 2: {'phi_00': '-1/12', 'phi_11': '-1/48'}, 3: {'phi_00': '1/96', 'phi_11': '1/384'}, 4: {'phi_00': '-1/960', 'phi_11': '-1/3840', 'phi_22': '-1/61440'}}
# wrote scale_derivative_coefficients.json, dilation_defect_coefficients.json, scale_defect_difference.json
# Sections A-D done in 291.1s

# === Section E (B.4): C_scale(mu) collapse / adjoint defect / variationality / matching per reading ===
CHECK E: top-order (prescription-independent) part of C_scale sits in contact degree D=4: True
CHECK E: lower-order slots with k=N-|gamma| sit in D=4-k (k=1..4 -> D=3,2,1,0): True
CHECK E: radial specialization: odd-k lower-order coefficients vanish (parity): True
CHECK E formal: collapse and adjoint defect of the top part are homogeneous of total derivative degree 4 (no cross-degree mixing): True
# formal         top D=4: collapse nnz=14112 (per N {'0': 744, '1': 4440, '2': 10278, '3': 10040, '4': 4604}), adjoint-defect nnz=16608, self-adjoint=False (1.1s)
CHECK E chi_plateau: collapse and adjoint defect of the top part are homogeneous of total derivative degree 4 (no cross-degree mixing): True
# chi_plateau    top D=4: collapse nnz=2522 (per N {'0': 744, '1': 1728, '2': 2386, '3': 1550, '4': 514}), adjoint-defect nnz=4090, self-adjoint=False (0.3s)
CHECK E prep_plateau: collapse and adjoint defect of the top part are homogeneous of total derivative degree 4 (no cross-degree mixing): True
# prep_plateau   top D=4: collapse nnz=4580 (per N {'0': 0, '1': 0, '2': 2274, '3': 4072, '4': 4604}), adjoint-defect nnz=4090, self-adjoint=False (0.5s)
CHECK E double_plateau: collapse and adjoint defect of the top part are homogeneous of total derivative degree 4 (no cross-degree mixing): True
# double_plateau top D=4: collapse nnz=490 (per N {'0': 0, '1': 0, '2': 474, '3': 514, '4': 514}), adjoint-defect nnz=0, self-adjoint=True (0.1s)
CHECK E double plateau: the collapsed prescription-independent scale tensor is NONZERO and self-adjoint (variational): True
CHECK E formal: collapsed top scale tensor is NOT self-adjoint (non-variational); full defect retained: True
CHECK E chi_plateau: collapsed top scale tensor is NOT self-adjoint (non-variational); full defect retained: True
CHECK E prep_plateau: collapsed top scale tensor is NOT self-adjoint (non-variational); full defect retained: True
CHECK E formal: N=0 component collapse has 744 nonzero keys (reproduces M.6 Theorem thm:M6-collapse(1)): True
CHECK E double plateau: N=0 and N=1 residue components collapse to 0 (N=0 consistent with M.6); N=2,3,4 carry the tensor: True
CHECK E double plateau: top scale tensor is NOT in span(E_R2, E_RC2) (exact rank test 2 -> 3): True
CHECK E double plateau: top scale tensor is NOT a multiple of E_{R2-(188813/88456)RC2}: True
CHECK E double plateau: top scale tensor is not a multiple of E_EH (degree mismatch D=4 vs 2): True
CHECK E: exact span solution verified: True
CHECK E double plateau: top scale tensor lies in the 5-dim span of Lorentz-covariant D=4 quadratic Euler tensors: True
CHECK E: exact span solution verified: True
CHECK E: exact span solution verified: True
CHECK E double plateau: d_mu E^{mu nu} != 0 for the top scale tensor (not linearized-gauge invariant): True
CHECK E double plateau: d_mu E^{mu nu} = 0 for E_R2, E_RC2 (control): True
# double plateau top tensor = Euler tensor of -71*L1/120 - 27*L2/80 - 11*L3/10 + 19*L4/30 - 13*L5/15  (covariant basis); R2 -> {'L1=h_{mn} Box^2 h^{mn}': '0', 'L2=h Box^2 h': '1', 'L3=(d^m h_{mn}) Box (d_r h^{rn})': '0', 'L4=h Box d^m d^n h_{mn}': '-2', 'L5=(d^m d^n h_{mn})^2': '1'} ; RC2 -> {'L1=h_{mn} Box^2 h^{mn}': '1/4', 'L2=h Box^2 h': '1/4', 'L3=(d^m h_{mn}) Box (d_r h^{rn})': '1/2', 'L4=h Box d^m d^n h_{mn}': '-1/2', 'L5=(d^m d^n h_{mn})^2': '1/2'}
CHECK E formal radial k=2: collapse homogeneous of degree D=2: True
CHECK E formal radial k=4: collapse homogeneous of degree D=0: True
CHECK E formal envelope k=1: ker Coll inside SA-parameter space (dimension check): True
# formal         envelope k=1 (D=3): params=120 rank Coll=120 dim SA=0 var image=0 
CHECK E formal envelope k=2: ker Coll inside SA-parameter space (dimension check): True
# formal         envelope k=2 (D=2): params=84 rank Coll=84 dim SA=0 var image=0 
CHECK E formal envelope k=3: ker Coll inside SA-parameter space (dimension check): True
# formal         envelope k=3 (D=1): params=56 rank Coll=56 dim SA=0 var image=0 
CHECK E formal envelope k=4: ker Coll inside SA-parameter space (dimension check): True
# formal         envelope k=4 (D=0): params=35 rank Coll=35 dim SA=26 var image=26 
CHECK E chi_plateau radial k=2: collapse homogeneous of degree D=2: True
CHECK E chi_plateau radial k=4: collapse homogeneous of degree D=0: True
CHECK E chi_plateau envelope k=1: ker Coll inside SA-parameter space (dimension check): True
# chi_plateau    envelope k=1 (D=3): params=120 rank Coll=120 dim SA=0 var image=0 
CHECK E chi_plateau envelope k=2: ker Coll inside SA-parameter space (dimension check): True
# chi_plateau    envelope k=2 (D=2): params=84 rank Coll=84 dim SA=0 var image=0 
CHECK E chi_plateau envelope k=3: ker Coll inside SA-parameter space (dimension check): True
# chi_plateau    envelope k=3 (D=1): params=56 rank Coll=56 dim SA=0 var image=0 
CHECK E chi_plateau envelope k=4: ker Coll inside SA-parameter space (dimension check): True
# chi_plateau    envelope k=4 (D=0): params=35 rank Coll=35 dim SA=26 var image=26 
CHECK E prep_plateau radial k=2: collapse homogeneous of degree D=2: True
CHECK E prep_plateau radial k=4: collapse homogeneous of degree D=0: True
CHECK E prep_plateau envelope k=1: ker Coll inside SA-parameter space (dimension check): True
# prep_plateau   envelope k=1 (D=3): params=120 rank Coll=120 dim SA=0 var image=0 
CHECK E prep_plateau envelope k=2: ker Coll inside SA-parameter space (dimension check): True
# prep_plateau   envelope k=2 (D=2): params=84 rank Coll=84 dim SA=0 var image=0 
CHECK E prep_plateau envelope k=3: ker Coll inside SA-parameter space (dimension check): True
# prep_plateau   envelope k=3 (D=1): params=56 rank Coll=56 dim SA=0 var image=0 
CHECK E prep_plateau envelope k=4: ker Coll inside SA-parameter space (dimension check): True
# prep_plateau   envelope k=4 (D=0): params=35 rank Coll=35 dim SA=26 var image=26 
CHECK E double_plateau radial k=2: collapse homogeneous of degree D=2: True
CHECK E double_plateau radial k=4: collapse homogeneous of degree D=0: True
CHECK E double_plateau envelope k=1: ker Coll inside SA-parameter space (dimension check): True
# double_plateau envelope k=1 (D=3): params=120 rank Coll=120 dim SA=0 var image=0 
CHECK E double_plateau envelope k=2: ker Coll inside SA-parameter space (dimension check): True
# double_plateau envelope k=2 (D=2): params=84 rank Coll=84 dim SA=49 var image=49 targets cap image=0
CHECK E double_plateau envelope k=3: ker Coll inside SA-parameter space (dimension check): True
# double_plateau envelope k=3 (D=1): params=56 rank Coll=56 dim SA=0 var image=0 
CHECK E double_plateau envelope k=4: ker Coll inside SA-parameter space (dimension check): True
# double_plateau envelope k=4 (D=0): params=35 rank Coll=35 dim SA=26 var image=26 targets cap image=1
# wrote full_scale_collapse_certificates.json (33.2s)
# wrote matched_scale_ledger.txt
# total runtime 324.3s ; 185 checks
ALL CHECKS PASSED
exit 0