Black Holes as Failed Convergence: Complete Gradient Flow Framework for Black Hole Physics

Zenodo Update Description (Version Update Summary)• Framework rename and title revision: Replaced the underlying "Constraint-Dispersion Unified Framework (CDUFD)" with the "Emergence-Convergence Framework (ECF)." Updated the title from "A Complete Gradient Flow Framework for Black Hole Physics" to "A Gradient Flow Approach to Black Hole Physics."• Introduction of B/C/D tiered argumentation: Organized all scientific claims into B-tier (rigorous theorems derived within the framework), C-tier (construct choices mapping λ to physical observables), and D-tier (conjectural extensions), following the methodology of ECF V. Added a comprehensive tier table in the methodological stratification section.• Revised singularity theorem: Updated the proof strategy to the B-tier forced gradient-flow framework: λ=1 as a steady state requires a divergent external driving force and is therefore physically unreachable.• Refined Hawking radiation mechanism: Elaborated the "self-cannibalization" survival oscillation picture at the horizon transition zone, with explicit C-tier designation and acknowledgment of external GR input for the ν ∝ 1/M frequency scaling.• Qualified information retrieval status: Explicitly designated the quantitative information retrieval mechanism as a D-tier open problem, clearly distinguishing it from the B-tier singularity resolution.• Expanded interior structure: Added discussion of possible topological defects (vortices, instantons) in the high-λ condensate (C/D-tier).• Added falsification matrix: Provided a complete table of core predictions with explicit falsification conditions and required instruments.• Updated theory comparison: Revised the comparison with LQG, String/Fuzzball, and AdS/CFT to include tier designations for this framework's claims.• Updated references and appendices: Replaced CDUFD references with ECF series DOIs; aligned appendix proofs with the tiered argumentation system.