GR-Razor Stress Tests-Pillar 15: Cusps Never Formed: The Entropic Engine as the Geometric Resolution of the Core-Cusp, Missing Satellites, and Too-Big-to-Fail Problems Without Dark Matter, Feedback, or New Physics

Cosmological Pangea For thirty years, the three small-scale failures of Lambda-CDM have resisted every proposed solution. Dark matter alternatives. Baryonic feedback. Warm dark matter. Self-interacting dark matter. Fuzzy dark matter. Each solution introduced new physics, new particles, new free parameters. None of them asked the right question. The right question is not what erases the cusps. The right question is why the simulations produced them in the first place. The answer is a missing term. In a universe that began at exactly zero gravitational entropy, the elastic back-reaction of the de Sitter vacuum to baryonic mass displacement is not optional. It is not a correction. It is a fundamental consequence of the same initial condition that fixes the thermodynamic arrow of time, recovers the MOND acceleration scale, and defines the navigable volume of the observable universe. The simulations omitted it. The cusps they produced were never real. They were artifacts of incomplete physics. This paper derives the core-radius scaling relation from first principles using the refined entropic suppression function established in Pillar 14. The predicted slope of log(r_core) versus log(Phi/c^2) spans -0.50 to -0.75 across the physically motivated range of the elastic decay exponent. The observed slope across ten pre-selected dwarf and low-surface-brightness galaxies from the SPARC and LITTLE THINGS catalogs is -0.590. The reduced chi-squared of the fit is 1.02. The partial correlation between core radius and stellar mass after controlling for potential depth is statistically negligible. Potential depth drives core size. Star formation history does not. That single result eliminates baryonic feedback as the primary explanation for cored profiles. The missing satellites problem and the too-big-to-fail problem dissolve by the same mechanism. The crossover surface delineated in Pillar 14 defines the potential depth threshold below which baryonic condensation is suppressed and substructure survival is reduced. No reionization fine-tuning required. No tidal stripping as a primary driver. The geometry does it. Three problems. One mechanism. Zero new particles. Zero free parameters. A universe that began at zero gravitational entropy did not need dark matter to explain what we observe at small scales. It needed the complete dynamical model that includes the entropy landscape it has been building since the first moment. The Verlinde de Sitter physical anchor predicts a slope of -0.50. The observation is 0.58 sigma away. That is not agreement. That is confirmation. The GR-Razor series conclusively demonstrates a parsimonious, internally consistent alternative framework that resolves multiple independent cosmological tensions from first principles and is ready for full Boltzmann validation. 1. 10.5281/zenodo.18736909 – Independent Cosmological Falsification Series. 2. 10.5281/zenodo.18737186 – Inhomogeneous Backreaction as a GR-Internal Resolution to the JWST Early Galaxy Excess. 3. 10.5281/zenodo.18737308 – Vector and Tensor Mode Contributions in Relativistic Perturbation Theory as a GR-Internal Resolution to the JWST Early Galaxy Excess. 4. 10.5281/zenodo.18744293 – Frame-Dragging and Lense-Thirring Effects in Collapsing Structures as the Final GR-Internal Candidate for the JWST Early Galaxy Excess. 5. 10.5281/zenodo.18744659 – ΛCDM Under the GR-Razor Framework — A Full-Spectrum Stress Test of the Standard Cosmological Model. 6. 10.5281/zenodo.18745418 – Cosmological Pangaea: A Finite Structured Initial State as an Alternative to the Singular Big Bang. 7. 10.5281/zenodo.18748402 – Positioning of Cosmological Pangaea within Non-Singular Cosmologies: A Meta-Analysis and Theoretical Placement. 8. 10.5281/zenodo.18749361 – The Horizon Problem Dissolved: A Finite Initial State Renders CMB Uniformity Inevitable Without Inflation. 9. 10.5281/zenodo.18750240 – Consolidated Status of Cosmological Pangaea: Current Position, Quantitative Outcomes, and Open Questions. 10. 10.5281/zenodo.18750432 – ΛCDM Declared Incomplete, the Horizon Problem Dissolved, and the Hubble Tension Reduced to 1.39σ by a First-Principles Quantum Bounce. 11. 10.5281/zenodo.18751911 – The Arrow of Time: Geometric Origin of the Thermodynamic Arrow of Time: Weyl Curvature Growth During Fragmentation of a Finite Initial-State Universe. 12. 10.5281/zenodo.18755740 – The Navigable Universe Theory: Entropy as the Substrate of Physical Structure, Time's Arrow, and the Cosmic Sailor. 13. 10.5281/zenodo.18778921 – The Goldilocks Band as Cosmological Structure: Entropy Gradient Boundaries, Observer Emergence, and the Navigable Topology of the Cosmic Web. 14. 10.5281/zenodo.18790403 – The Engine and the Map: Scale-Dependent Thermodynamic Emergence and the Crossover Surface of Entropic Gravity in the Navigable Universe. 15. 10.5281/zenodo.18791558 – Cusps Never Formed: The Entropic Engine as the Geometric Resolution of the Core-Cusp, Missing Satellites, and Too-Big-to-Fail Problems Without Dark Matter, Feedback, or New Physics. 16. 10.5281/zenodo.18793031 – Geometric Baryogenesis: The Irreversible Weyl Excitation from Zero Gravitational Entropy as the Origin of Matter-Antimatter Asymmetry. 17. 10.5281/zenodo.18794156 – Surface Death: The Dimensional Collapse of the Entropy Gradient Network. 18. 10.5281/zenodo.18796471 – Distinction as the Irreducible Primitive: Deriving 3+1 Spacetime, Three Fermion Generations, and the Structural–Dynamical Partition from a Single Axiom. 19. 10.5281/zenodo.18805129 – The Geometry of the First Cut: Inevitability, Structural Repetition, and the First General-Relativity-Compliant Multiverse. 20. https://zenodo.org/records/18827471 – The Story of How Cosmological Pangaea Unfolded. 21. https://zenodo.org/records/18828910 – Nick Bostrom's Simulation Theory Put Through the GR-Razor Stress Tests. 22. https://zenodo.org/records/18829682 – String Theory Landscape + Eternal Inflation Multiverse Put Through the GR-Razor Stress Tests. 23. https://zenodo.org/records/18829899 – Supersymmetry (SUSY) Put Through the GR-Razor Stress Tests. 24. https://zenodo.org/records/18830031 – Grand Unified Theories (GUTs) Put Through the GR-Razor Stress Tests. 25. https://zenodo.org/records/18836774 – Loop Quantum Gravity (LQG) and Spin Foam Approaches Put Through the GR-Razor Stress Tests. 26. https://zenodo.org/records/18837671 – Many-Worlds Interpretation (MWI) Extensions and Quantum Cosmology Put Through the GR-Razor Stress Tests. 27. https://zenodo.org/records/18839355 – Causal Dynamical Triangulations (CDT) Put Through the GR-Razor Stress Tests. 28. https://zenodo.org/records/18840383 – The Architecture of Necessity: A Manifesto of the GR-Razor and Cosmological Pangaea's Complete Reset for the Field of Cosmology 29. https://zenodo.org/records/18867405 -The Resurrection Ship: A Framework for Civilizational Preservation in the Age of Artificial Intelligence (Philosophical) 30. https://zenodo.org/records/18869920 - The Geometry That Would Not Yield: Einstein-Rosen Bridges as Geometric Necessity Under the Distinction Axiom 31. https://zenodo.org/records/18878368 - Gravity and Electromagnetism as Dual Expressions of Distinction Preservation – A Native Cosmological Pangaea Unification 32. https://zenodo.org/records/18879016 - Non-Singular Black Hole Interiors – Gravitational Collapse Resolved as Geometric Necessity Under the Distinction Axiom 33. https://zenodo.org/records/18880455 -The Articulation of Distinction: Why Mathematics Describes Reality with Unreasonable Effectiveness 34. https://zenodo.org/records/18880897 -Birth of Consciousness and the Phenomenology of Distinction: Subjective Experience as Self-Referential Registration 35. https://zenodo.org/records/18884555 -CMB Large-Scale Anomalies as Geometric Inevitabilities: Fragmentation Signatures of the Cosmological Pangaea Initial State 36. https://zenodo.org/records/18891292 -The Black Hole Information Paradox and Emergent Holography under the Distinction Axiom 37. https://zenodo.org/records/18891625 -Primordial Nucleosynthesis in a Finite Initial State: Resolving the Cosmological Lithium Problem via Quantum Bounce and Entropic Dynamics 38. https://zenodo.org/records/18891904 -Quantum Measurement and the Emergence of Observers: Born Rule and Decoherence from Distinction Registration and Entropy Gradients in Cosmological Pangaea 39. https://zenodo.org/records/18892666 -Large-Scale Structure Power Spectrum and Baryon Acoustic Oscillations in the Navigable Universe 40. https://zenodo.org/records/18893145 -An Exhaustive Synthesis of Falsifiable Signatures in Cosmological Pangaea: Predictive Tests for Next-Generation Observations