Flat Rotation Curves Without Dark Matter from the Cosmological Entropy Floor

The entropy density field of the Relational–Structural Framework is modified to include a non-linear coupling that activates when the local gravitational acceleration drops below a critical threshold set by the cosmological entropy decay rate. The threshold acceleration a0 = c2√(Λ/3) / (2π) ≈ 1.2 × 10-10 m/s2 emerges naturally from the same parameter λ that gives the cosmological constant Λ = 3λ/D. In the regime where g >> a0, the field is Newtonian (g = GM/r2). In the regime where g << a0, the field becomes g = √(a0GM)/r, producing constant circular velocities v = (GMa0)1/4 — flat rotation curves without dark matter particles. The transition radius rt = √(GM/a0) ≈ 10 kpc for a Milky-Way-mass galaxy matches where observed rotation curves begin to flatten. The Tully-Fisher relation (L ~ v4) follows automatically. The mysterious numerical coincidence a0 ≈ cH0

is explained: both are consequences of the cosmological entropy decay rate. Dark matter phenomenology and dark energy are unified as two manifestations of a single thermodynamic processing floor.

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Generative AI was used to assist with [literature screening / coding support / draft language revision]. All AI-assisted outputs were independently checked by the author, and the author takes full responsibility for the final analysis and text. This is encompassing all the work that has been done and will be done. All code is under MIT licensing. All research papers are under Creative Commons License. All code, outputs and notes are included in the reproducibility bundle zip file.