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The research seeks to refine the theoretical framework for understanding black holes by introducing a gradient flow approach and tiered argumentation.

June 30, 2026Open Access

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

Key Points

The research seeks to refine the theoretical framework for understanding black holes by introducing a gradient flow approach and tiered argumentation.
Renamed the underlying framework from Constraint-Dispersion Unified Framework to Emergence-Convergence Framework.
Organized scientific claims into B/C/D tiers based on rigor, construct choices, and conjectural extensions.
Updated the singularity theorem and refined the Hawking radiation mechanism with explicit designations for each tier.
Established that the λ=1 steady state requires a divergent driving force, thus is unattainable.
Outlined a refined mechanism for Hawking radiation with explicit frequency scaling based on black hole mass.
Identified a quantitative information retrieval mechanism as an open problem, critical for future theoretical development.

Abstract

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.

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