Eyüp CEBE

Gravitational Waves and Vector Dark Matter from a Coleman–Weinberg Dark U(1) Sector: Internal-Consistency Audit and Corrected Phase-Transition Analysis

We audit, and independently recompute, the central predictions of a classically scale-invariant dark U(1) model in which a complex scalar obtains its vacuum expectation value through the Coleman–Weinberg mechanism and the massive dark photon A′ is the dark-matter candidate. An ea...

Structural Notes on the Collatz Dynamics: A Forced Gate, a Climbing-Run Characterisation, an Integer-Energy Reformulation, and a Depletion Law for Climbing Runs

ABSTRACT. This is a short expository note on the elementary structure of the Collatz map T. We give self-contained proofs of four facts and state precisely what they do and do not establish. First, a forced-gateobservation: because 16 is the only preimage of 8, every orbit that r...