{An $R^8$ Bank Scaffold with Triadic Rigidity and Bank-Time Phase Self-Induction:} {A Reproducible CMB Topology Probe Using Real Planck 2018 PR3 SMICA Data}}

We report a reproducible end-to-end protocol that connects a discrete internal ``bank'' scaffold(based on an $R^8$ phase fiber with discrete holonomy) to real-data diagnostics in the cosmicmicrowave background (CMB). The aim is not to claim a completed ultraviolet (UV) derivation, but to(i) specify a minimal infrared effective field theory (IR--EFT) consistent with strict causalconstraints and (ii) execute stress-tested, index-locked analyses on real Planck 2018 PR3 full-missionmaps, with Monte Carlo simulation used only for null-hypothesis calibration. The working hypothesis is that the observed 4D Universe is a single ``leaf'' coupled to an internal$R^8$ bank fiber. The bank supports a refined discrete holonomy $\mathbb{Z}_{48}$, while the leaf seesan effective visible $\mathbb{Z}_{24}$ phase symmetry. The $\mathbb{Z}_{24}$ sectors naturally formeight triads corresponding to the cosets of a $\mathbb{Z}_3\subset\mathbb{Z}_{24}$ subgroup generatedby a $+8$ shift in the phase index. Triadic rigidity (stiff intra-triad coupling) projects the lowenergy dynamics onto a coherent triad-average subspace (eight light modes). A weak inter-triadcoupling then unifies these eight into a single collective breathing mode on the leaf. Separately,the smallness of the observed vacuum energy is attributed to a projective overlap factor$\varepsilon_{\rm leaf}\ll 1$ such that $\rho_\Lambda^{(4)}=\varepsilon_{\rm leaf}\,\rho_{\rm bank}$,with $\varepsilon_{\rm leaf}\sim 10^{-120\text{--}123}$. Bank-time phase self-induction provides aconcrete mechanism for ultra-slow relative phase drift: the leaf is not a static crystal, yet itsrelative phase motion remains hierarchically slow. The real-data component of this work is a CMB ``topology probe'' restricted to low multipoles$\ell=2$ (quadrupole) and $\ell=3$ (octupole). The observational input is the Planck 2018 PR3 SMICAHEALPix FITS map COM\_CMB\_IQU-smica\_2048\_R3.00\_full.fits acquired directly from ESA Planck LegacyArchive distribution endpoints. The analysis is index-locked to the inpainted temperature fieldI\_STOKES\_INP by explicit FITS column inspection (index 5 in this product). This step eliminated acritical failure mode (accidental use of Q/U polarization columns as temperature), ensuring that allreported ``real-data'' results derive from the intended CMB temperature field. To prevent provenanceambiguity, we record the exact local FITS filename, HDU/index, and a SHA256 fingerprint of the fileused, and we export a minimal low-$\ell$ harmonic bundle ($a_{2m}$ and $a_{3m}$) enabling NumPy-onlythird-party verification of the $\ell=2,3$ tensor-axis observables. We evaluated two axis estimators. The primary estimator is a harmonic-space power-tensor eigenvector(principal axis) defined for each multipole $\ell$ by the principal eigenvector of$Q_{ij}^{(\ell)}=\frac{1}{2}\,a_\ell^\dagger(J_iJ_j+J_jJ_i)a_\ell$ in the $(2\ell+1)$ representation.Treating axes as headless vectors (identifying $\hat{n}\sim -\hat{n}$), we define the quadrupole--octupoleseparation angle $\theta_{23}=\arccos(|\hat{n}_2\cdot\hat{n}_3|)$. As a complementary, non-canonicalmorphological diagnostic, we also computed a hotspot axis by selecting the direction of the maximumpixel in $\ell$-only maps. For the real Planck SMICA I\_STOKES\_INP map we find $\theta_{23}^{\rm tensor}=8.0615^\circ$ for thepower-tensor estimator, while the hotspot estimator yields $\theta_{23}^{\rm hotspot}=22.9644^\circ$.For the raw temperature field I\_STOKES (index 0), the hotspot angle is $24.1629^\circ$. Thus thehistorical $\sim 23^\circ\text{--}24^\circ$ ``signature'' is recovered as a hotspot-based morphologicalfeature, whereas the principal-axis tensor alignment is tighter. To probe triadic rigidity directly on the sphere, we constructed an octupole-only map $m_3$ anddefined a triadic symmetry score using rotations by 120 degrees and 240 degrees around the octupoletensor axis:$S=\frac{1}{2}[\mathrm{corr}(m_3,R_{120}m_3)+\mathrm{corr}(m_3,R_{240}m_3)]$.In the real-data run we measure $S_{\rm obs}=0.9992$ and detect no measurable offset from 120 degrees(tilt consistent with zero at the scan resolution for this internal octupole symmetry test). Thishigh score indicates near-perfect threefold invariance of the octupole around its tensor axis in theimplemented pipeline. We calibrated significance using an isotropic Gaussian null: random realizations were generated withhealpy.synalm using a low-$\ell$ power spectrum $\hat{C}_\ell$ extracted from the real map. Under thisnull, the mean headless angle between random axes is approximately $57.3^\circ$ as expected. For$\theta_{23}^{\rm tensor}$ we find $p_\theta=P(\theta_{23}\le 8.0615^\circ)=0.00890$ in 10,000simulations. For the triadic score, 10,000 simulations produced zero exceedances of $S\ge 0.9992$ inthe current map-rotation implementation, implying $p_S