Completion of the Eight-Cell Phase Map in CMB Acoustic Phase Deformation — W_CMB v12.0 Package

This deposit completes the WCMB phase-map programme initiated in v10.0. The v11.0 2D map (ℓ50 × pos_frac) identified a structured topology: isolated A and P lobes, and an E-doublet whose internal sign inversion produces an X-shaped crossing, giving 6-cell resolution. This v12.0 note introduces IQR (interquartile range of the unsigned accumulation kernel) as a third coordinate that resolves the E-doublet, completing the eight-cell phase map in 3D observable space. The E-doublet resolution At both crossing points in the 2D map, IQR separates EN from Eω with zero overlap: Crossing EN IQR Eω IQR Gap 1: EN(+δ) vs Eω(−δ) 950, 976 991, 993 29 2: EN(−δ) vs Eω(+δ) 946, 962 990, 989 35.5 IQR is not a globally independent axis — it correlates with ℓ50 at r ≈ −0.94. However, at the E-doublet crossing where ℓ50 is degenerate (≈ 1406–1424), IQR provides distinct local resolution. This makes it a local degeneracy breaker, not a universal third coordinate. Physical interpretation The three coordinates form a coherent measurement system: ℓ50 (location): Where in ℓ-space the deformation concentrates. Identifies the perturbation family (E/A/P). IQR (breadth): How spread out the deformation is. Free-streaming perturbations (Nur) produce concentrated deformation (IQR ≈ 958); expansion-rate perturbations (ωcdm) produce broader deformation (IQR ≈ 991). Resolves E-internal degeneracy. pos_frac (direction): Whether the parameter increased or decreased. Orthogonal to both mechanism coordinates (r ≈ −0.008). Spine (v3.0 → v12.0) v3.0: W_CMB is established v4.0: Internal geometry is family-structured v5.0: That geometry is discriminative (ARI = 1.000, 3 families) v5.0 v6.0/v6.1: Σmν is E-adjacent in normalized kernel v5.0 v8.0-lite: E-adjacency is compression, not information absence v9.0: Signed cumulative ≡ magnitude after normalization v9.1: Sign encodes direction, not mechanism v10.0: Mechanism–direction decomposition (S ≈ 99, r ≈ −0.008) ★ v10.1: E-family sign inversion resolved — direction recovery (S > 100) ★ v11.0: Phase-map topology — isolated A/P lobes + crossed E-doublet ★ v12.0: IQR breaks E-doublet — eight-cell resolution in 3D (ℓ50, pos_frac, IQR) ★ Contents Research notes: v12.0 eight-cell completion, v11.0 topology, v10.1 direction recovery, v10.0 decomposition (Markdown) Eight-cell 3D figure (PNG, new in v12.0) + earlier diagnostic figures Two computation scripts (Python) and numerical results (JSON)