Phase-Map Topology in CMB Acoustic Phase Deformation — W_CMB v11.0 Package

This deposit constructs the joint mechanism–direction phase map established in v10.0/v10.1 and characterises its topology. The map does not resolve all eight perturbation cells (4 subfamilies × 2 directions). Instead, it reveals a structured topology with physically interpretable regions. Phase-map topology The 2D map (mechanism axis: ℓ50, direction axis: pos_frac) separates the perturbation space into three distinct regions: Isolated P lobe (ns): ℓ50 ≈ 527, direction gap = 0.184, S = 908. Fully resolved. Isolated A lobe (ωb): ℓ50 ≈ 1185, direction gap = 0.166, S = 164. Fully resolved. Crossed E-doublet (Nur + ωcdm): The two E subfamilies are near-degenerate on the mechanism axis (ℓ50 ≈ 1406–1424, S ≈ 3) and sign-inverted on the direction axis. This produces an X-shaped crossing: EN(+δ) overlaps Eω(−δ), and EN(−δ) overlaps Eω(+δ). The crossing is geometry, not noise Free-streaming damping (Nur) and expansion-rate modification (ωcdm) deform the acoustic phase in opposite senses while producing nearly identical unsigned kernel shapes. Their mechanism-axis near-degeneracy reflects geometric similarity in how they affect the expansion history; their direction-axis sign inversion reflects that they push the acoustic phase in opposite directions. The combination creates two degenerate pairs in the 2D plane, giving 6-cell rather than 8-cell resolution. Spine (v3.0 → v11.0) 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 ★ Next step A third coordinate is required if one seeks full 8-cell resolution. The E-doublet crossing defines the precise target for v12.0: an observable that distinguishes free-streaming from expansion-rate modification independently of perturbation direction. Contents Research notes: v11.0 topology, v10.1 direction recovery, v10.0 decomposition (Markdown) Phase-map figure (PNG, new in v11.0) Two computation scripts (Python) and numerical results (JSON)