Listing: Listing

# scaling_anomaly.py output
# Stage 4 / M.6: dilation identity, S^2 residue, anomaly assignment, collapse probe
# CONDITIONAL: residue evaluation uses Input (S-bv); Gate S-bv not discharged
CHECK dilation identity: mu d/dmu varpi_mu = E varpi_mu (rho=0): True
# identity (N=0): A_mu(u) = (E+4) R_{L,mu}(u) = - <u, E varpi_mu> delta
CHECK N=0 structural identity A_mu = (E+4) R_{L,mu} recorded (analytic; see M.6): True
CHECK contour residue at z_m tends to -1: True
CHECK angular u-integral Iu0 = -2 i pi: True
CHECK sphere integral of (Q-i0)^{-2} = -2 i pi^2: True
# CONDITIONAL ON (S-bv): int_{S^3} (Q-i0)^{-2} d sigma = -2 i pi^2
CHECK S^2 residue coefficient r = -2 i pi^2 c^2: True
CHECK S^2 residue nonzero for every c != 0 (S-bv): True
# CONDITIONAL ON (S-bv): A_mu(S^2) = r delta with r = -2 i pi^2 c^2 != 0
# Residue independent of mu and of radial profile of varpi (varpi(0)=1)
# Higher-N residues (N>=1): Unresolved in this dispatch (formula recorded in M.6)
CHECK N=0 coherent basis is the single S^2 label {(),()}: True
CHECK anomaly assignment sits at contact variable index 0 (N=0,gamma=()): True
# N=0 anomaly component C_anom: C[0] = r; higher-grade (N>=1) coordinates explicitly set to ZERO for this probe
# (higher-N residues Unresolved: C_anom is NOT the full graph scale variation)
# collapse[formal]: nnz=744 sa_defect_nnz=4602 variational_nonzero=False
# collapse[chi_plateau]: nnz=744 sa_defect_nnz=1938 variational_nonzero=False
# collapse[prep_plateau]: nnz=0 sa_defect_nnz=0 variational_nonzero=False
# collapse[double_plateau]: nnz=0 sa_defect_nnz=0 variational_nonzero=False
CHECK formal: S^2 anomaly collapse nonzero: True
CHECK formal: S^2 anomaly collapse NOT self-adjoint: True
CHECK formal: S^2 anomaly is NOT a nonzero variational tensor: True
CHECK chi-plateau: S^2 anomaly collapse nonzero: True
CHECK chi-plateau: S^2 anomaly NOT self-adjoint: True
CHECK prep-plateau: S^2 anomaly collapses to 0 (sigma-derivatives): True
CHECK double-plateau: S^2 anomaly collapses to 0 (matching domain): True
CHECK S^2 coefficient ahatbar supported only on |partial sigma|=2 (C_2 sector): True
CHECK double-plateau R2 and RC2 Euler tensors are linearly independent: True
CHECK double-plateau Collapse(C_anom)=0, so matched projection = 0: True
# Matched projection onto span(E_R2, E_RC2) in double plateau: (0,0)
# Unmatched remainder in double plateau: 0 (collapse itself vanishes)
# Unmatched remainder in formal reading: full Collapse(C_anom) retained (non-variational)
CHECK M-C not claimable: the full controlled matched scaling calculation is unfinished: True
# M-C remains incomplete because the full controlled matched scaling calculation is unfinished.
# The N=0 component alone contributes no nonzero plateau matching.
# wrote scaling_anomaly_cert.json
# wrote scaling_anomaly_cert.txt
ALL CHECKS PASSED