Topological Deconvolution of the Cosmic Microwave Background: An Analytic Resolution to Cosmological Tensions via the Conformal Transition Operator Ξ

Following a rigorous internal methodological audit, it was determined that applying geometric operators to synthetic, component-separated maps (e.g., SMICA) compromises strict thermodynamic conservation due to artificial galactic masking. Consequently, the deconvolution pipeline has been upgraded to a Discrete Morphological Engine calibrated exclusively for the raw Planck LFI 70 GHz temperature map. This specific channel represents the optimal thermodynamic window for CMB analysis. By contracting diffuse halos into discrete topological vertices via the scale defect $\Xi - 1$, the engine achieves exact thermodynamic conservation ($k=1.000000$) and a structural variance increase of $53.88\%$. The preservation of the unmasked galactic plane ensures total energy continuity, while the high-frequency power spectrum elevation is mathematically identified as the "Dirac Effect" of topological contraction rather than thermal noise amplification.