We present Structural Differentiation Gravity (SDG) v1.9 as a minimal and observationally testable framework for interpreting cosmic acceleration. In this work, we demonstrate that an SDG background expansion history can remain nearly degenerate with a reference ΛCDM-like model at the level of H(z), while the structure growth sector exhibits systematic and scale-consistent suppression in fσ8(z). This leads to a clear observational consequence: geometry and growth are not necessarily linked. We introduce a diagnostic representation in the geometry–growth plane defined by (ΔH/H, Δ(fσ8)/fσ8), which provides a direct and falsifiable test of this decoupling. While background observables may agree with ΛCDM, growth observables reveal systematic deviations, forming a distinct trajectory in this plane. This establishes a single observational discriminator between projection-based interpretations of cosmic acceleration and conventional physical acceleration models. All figures are fully reproducible using the provided Python implementation, ensuring transparency and verifiability. This work is intended for peaceful exploration of the structure of the universe. Its purpose is understanding, not control, and any future application should respect the continuity of life and existence, and be guided by responsibility toward humanity.
Koji Okino (Wed,) studied this question.
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