Observation-Induced Frame Dependence and the Hubble Tension: A Phase-Modulated Information Rivalry Analysis

The Hubble tension — a ~5σ discrepancy between CMB and distance-ladder measurements of H₀ — has resisted resolution through both systematic-error analysis and new-physics proposals. This work proposes a structural alternative grounded in the Phase-Modulated Information Rivalry (PMIR) framework: the tension is not a measurement error but a mathematically predicted consequence of applying two qualitatively different observation maps to the same underlying latent cosmological process. Systematic phase diagram analysis across five observation map families and 11,250 parameter points identifies the softplus family as the CMB analog (smooth large-scale integrating frame) and the sigmoid-scaled family as the distance-ladder analog (locally amplifying hierarchical frame). When the same latent process is observed through each frame, the distance-ladder frame consistently yields a higher effective expansion rate — matching both the direction and magnitude of the observed tension. The best-match AR(1) simulation predicts 8.33% tension against the observed 8.31%. Replacing the AR(1) process with a ΛCDM matter power spectrum (Eisenstein-Hu transfer function) yields 10.21%, with spectral decomposition identifying small-scale modes (k > 0.3 h/Mpc) as the dominant tension-generating band, yielding 8.47% — within 0.16% of the observed value. The Box-Cox phase transition at λ* ≈ 0.033 marks the algebraic boundary between non-hierarchy-inducing and hierarchy-inducing observation frames. v2.2 revision: Prediction P6 has been reformulated following direct testing against the published SH0ES FITS data products (Riess et al. 2022). The full SH0ES global fit was reproduced from the raw covariance matrix C, equation matrix L, and data vector y, recovering H₀ = 73.04 km/s/Mpc in exact agreement with the published result. The 37×37 μhost covariance block was extracted and analyzed. The original uniform pass-through prediction (ρ* = 0.65 per rung) was ruled out at 18σ (observed ρ̄ = 0.11). The revised P6 predicts a mode-decomposed pass-through structure: anchor-class systematics propagate with ρ ≈ 1 (full pass-through) while calibration-class systematics show ρ ≈ 0.10 (strong re-calibration at the Cepheid→SN interface). All 666 off-diagonal covariance elements are positive — confirming a universal shared systematic floor — with shared amplitude σ_sys = 0.021 mag consistent with the published 0.019 mag. This bimodal structure is confirmed by the data and provides a sharper, more falsifiable formulation of the composed-observer mechanism. Six falsifiable predictions are derived and confronted with existing data.