A Unified Framework for 10 TeV to EeV Diffuse Neutrino Sky and KM3-230213A

Establishing a unified origin that simultaneously accounts for the wide-band diffuse flux and recent ultra-high-energy (UHE) detections is a pressing challenge in multi-messenger astrophysics. Successive shock regimes in shock-breakout candidates, most notably low-luminosity gamma-ray bursts (LL GRBs), naturally introduce distinct physical environments producing a multi-component neutrino flux extending from 10 TeV to the UHE regime. Integrating prompt and afterglow phases within a unified dynamical framework yields a self-consistent explanation for this broadband emission. In this work, we discuss this framework, building on MWL observations. We show that the prompt emission from GRB~060218-like events accounts for $\gtrsim 10\%$ of the diffuse flux at 100~TeV, while GRB~100316D-like configurations predict a distinct flux peak near $10^{-9}\rm~GeV~cm^{-2}~s^{-1}~sr^{-1}$ at 100~PeV, providing a physical interpretation for the 220 PeV KM3-230213A event. This decoupling explains the lack of low-energy counterparts for individual UHE detections while maintaining consistency with the total diffuse neutrino flux. Ultimately, this framework identifies SBO-like LL~GRBs as a unifying origin for these phenomena, providing a physical link across a wide band from 10 TeV to EeV energies testable by next-generation observatories, including GRAND, IceCube-Gen2, and RNO-G.