**R⁸ Triadic Bank: A Topological Self-Trapping Explanation of Wave–Particle Duality (Z₄₈→Z₂₄ Projection)**

We present a reproducible R^8 “triadic bank” framework that connects a discrete internal phase scaffold (refined holonomy Z48 with visible even-subgroup projection Z24) to both (i) a toy origin mechanism for Z144→Z48→Z24 capture/projection signatures and (ii) a real-data, index-locked low-ℓ CMB topology probe using Planck 2018 PR3 SMICA. The scaffold partitions the visible Z24 sectors into eight triads (cosets of Z3 generated by a +8 shift), yielding a stiff triadic rigidity spectrum with sixteen heavy intra-triad modes near 3κ and eight light modes in the triad-average subspace. A weak inter-triad ring coupling unifies triad averages into a collective breathing mode. We introduce bank-time phase self-induction by coupling a normalized collective leaf coordinate φ≡φL to a bank clock b(t) via an inductive kinetic term. In a reduced two-coordinate model with explicit inertias, T=(Iφ/2)φ̇^2+(Ib/2)ḃ^2+(L/2)(φ̇−ḃ)^2 and V=(μ^2/2)(φ−b)^2, the non-zero relative-mode frequency obeys the master formula ω_rel^2=μ^2(Iφ+Ib)/(IφIb+L(Iφ+Ib)). With Iφ=1 inherited from the underlying rotor kinetic term and Ib=1 by normalization, this yields the ultralight scaling ω_rel^2=2μ^2/(2L+1). A toy origin mechanism demonstrates how a recurrence-like hit near a Z144 grid in T^8 can be followed by gradient capture into Z48 wells, while naive Z24 visibility produces an exact half-step mismatch Δθ=π/24≈0.13089969 rad for odd-parity Z48 indices. A deterministic even-subgroup projection (k48→k48_even:=2⌊k48/2⌋, then k24=k48_even/2) resolves the midpoint tie and restores Z24 compatibility to machine precision, cleanly separating dynamical capture from algebraic visibility. For the real-data CMB probe, we analyze Planck PR3 SMICA COM_CMB_IQU-smica_2048_R3.00_full.fits using the inpainted temperature field I_STOKES_INP (HDU 1, field index 5), locked by explicit column-name inspection and a SHA-256 file fingerprint 60952c645eb33d151905ddf5837477e15ca02a3261feca4ceca3c3feece4f9ac. The extraction environment is locked (Python 3.12.12, NumPy 2.0.2, healpy 1.19.0) and we export a low-ℓ NPZ payload containing the complex a2m (5) and a3m (7) coefficients for NumPy-only verification. Using a headless power-tensor axis estimator we report θ23^tensor=8.0615°, while a hotspot morphological estimator yields θ23^hotspot=22.9644°. A triadic symmetry score for the octupole yields S_obs=0.9992 in the implemented pipeline. Monte Carlo null calibration is performed under an isotropic Gaussian hypothesis, with a strict “axis-within-loop” clause: all axes and the octupole axis used in the triadic score are recomputed per realization, and any tilt-maximization procedure is applied identically to data and nulls. With 10,000 null simulations we obtain pθ=P(θ23≤8.0615°)=0.00890 and 0 exceedances for S≥0.9992 at this resolution. We emphasize that all significance claims are pipeline-conditional and motivate cross-map replication (NILC/SEVEM/Commander) and harmonic-space computation of the triadic score to eliminate rotation/interpolation artifacts. We also distinguish Hopf bifurcation (dynamical emergence of a limit cycle) from Hopf-type topological language (defect invariants), treating them as distinct mechanisms.