Low-Dimensional Dust Attractors in Planck HFI 857 GHz: Phase-Space Evidence for a ~1--2 Bias Floor in Primordial Non-Gaussianity

This paper applies non-autonomous operator-theoretic Phase-Mediated Attractor Dynamics (PMAD) to the Planck Public Data Release 2 (PR2) full-mission High Frequency Instrument (HFI) 857~GHz time-ordered information (TOI) streams to evaluate the topological properties of diffuse thermal dust foregrounds and their downstream impacts on primordial non-Gaussianity ($f_{\text{NL}}$) estimation. Rather than evaluating raw telemetry packets, this work characterises the geometric manifold of the post-processed, calibrated \texttt{SIGNAL} column, which has undergone intense upstream linear pre-conditioning. By mapping 1D scanning-order pixel arrays into a variable-anisotropy Sobolev space, we isolate deterministic transfer operator co-cycles masked by traditional power-spectrum metrics. At the local level, 94.1\% of the independent high-latitude sky patches collapse identically onto an exceptionally rigid 9-axis stiff subspace representing a clean data-driven coordinate projection of the stable Covariant Lyapunov Vector (CLV) manifold. Evaluating the continuous spectral trace reveals that the active phase support contracts to an ultra-low fractional floor ($D_A \approx 0.21 - 0.36$), proving that the interstellar medium (ISM) fluctuations track near the infrared fixed point of a universal Wilsonian renormalization group flow. Tracking the local hyper-angles of these non-orthogonal bundles exposes an endogenously generated compliance floor field $\epsilon(x)$ that naturally hardens near localized phase-locking singular points to regularize metric components. A global cross-system Chi-squared test against a contractive millisecond pulsar baseline definitively rejects software processing bias ($\chi^2 = 78,228.49$, $p \to 0$). Crucially, while individual regional profiles conform tightly to the pre-conditioned 4D linear state manifold due to upstream filtering, their collective phase-space geometry demonstrates an asymptotic divergence from stochastic noise models, yielding an overwhelming Integrated Separation Area (ISA) with a Structural Separation Ratio of $1015.64$ against the 1D Noise Null. These geometric features confirm that high-frequency dust residuals are highly non-ergodic, reducing the effective independent mode count to inflate cosmological error bars by $F_\sigma \approx 1.5-2$ and imposing a systematic lower-bound dust bias floor of $\Delta f_{\text{NL}}^{\text{dust}} \sim 1-2$ in standard CMB likelihood pipelines.