PUH Theorem 318 (The Convergence Window Has No Mechanism) — A Planck Core's Area Goes as m², Not m^(2/3), So Surface-to-Mass RISES with Mass and T198's Theorem 4 Inverts; No Candidate Mechanism Supplies the Required Scaling
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Key Points
The aim is to analyze the convergence mechanism in planetary formation and its dependence on mass scaling, specifically examining the surface-to-mass ratio dynamics.
Detailed theoretical derivation of mass scaling for Planck cores versus ordinary bodies.
Analysis of surface drag, gravitational friction, and cosmological decay mechanisms.
Evaluation of existing literature for mass dependence and the implications on the convergence window.
Surface-to-mass ratio dynamics reveal that for Planck cores, the area per unit mass rises with mass contrary to lighter cores, reversing expected outcomes.
None of the examined mechanisms (surface drag, gravitational friction, cosmological decay) support the expected mass-dependent deceleration of lighter cores over heavier ones.
Theoretical implications suggest that no existing mechanism can drive the convergence of planetary seed shells with stellar mass cores as proposed.
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Implication
Theoretical note challenges the convergence mechanism in solar system formation, indicating mass scaling issues affect outcomes.