GR-Razor Stress Tests-Pillar 14: The Engine and the Map: Scale-Dependent Thermodynamic Emergence and the Crossover Surface of Entropic Gravity in the Navigable Universe

Cosmological Pangea This paper reports the discovery of a previously unrecognized geometric boundary inherent to the Navigable Universe framework: a crossover surface in gravitational potential and coherence length space that separates two physically distinct regimes of entropic gravity. Below this surface, thermodynamic emergence is dynamically operative, producing the MOND acceleration scale and the Verlinde entropic gravity phenomenology confirmed by observation at galactic scales. Above it, the entropy gradient functions exclusively as a geometric coordinate of the cosmic web, a readable map of irreversible structure formation encoding void topology, filament boundaries, and the full architecture of the observable universe. This boundary was not imposed. It was found. It emerges from the same Planck-scale prefactor in the Clifton-Ellis-Tavakol gravitational entropy density that threatened to break the framework at void scales. That prefactor is not a defect. It is a selector. Combined with higher-order curvature suppression and holographic horizon ratios native to the existing formalism, it defines the precise domain where the entropic engine runs and where only the map remains. The crossover surface is distinct from the Complexity Threshold established in Pillar 13. The framework now contains three complementary geometric boundaries, all derivable from a single initial condition: zero gravitational entropy at the Cosmological Pangaea epoch. No new fields. No new particles. No free parameters. The MOND scale, the Verlinde emergence condition, and the crossover surface converge at the same geometric locus. That is not a coincidence. It is what a universe that began at zero gravitational entropy looks like from the inside. 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