The Origin of Mass in the Planck Core Framework: A Unified Account of Higgs Mechanism and Binding Energy

This paper presents a unified account of mass generation within the Planck Core Framework, demonstrating that the two seemingly unrelated sources of mass in the Standard Model—the Higgs mechanism and the QCD binding energy—are different manifestations of a single underlying principle. I prove that all mass arises from the energetic cost of sustaining localised, low-entropy entanglement configurations against the network's entropic drive towards its maximally entangled state. The Higgs mass originates from the overlap integral between a topological vortex defect (a fermion) and the scalar breathing mode of the entanglement network (the Higgs condensate), representing the energetic cost of dragging a vortex through the condensate. The QCD binding energy of hadrons arises from the confinement of entanglement threads within a small volume, where colour neutrality forces the network into a high-deficit, high-energy configuration. Both contributions are shown to be proportional to the total number of entanglement threads that must be maintained in a non-equilibrium state. An explicit decomposition of the proton mass is provided, showing that the Higgs contribution (∼9.1∼9.1 MeV, ∼1%∼1%) and the QCD contribution (∼929∼929 MeV, ∼99%∼99%) both follow from the same fundamental formula mc2∝Nthreads⋅⟨ΔEthread⟩mc2∝Nthreads⋅⟨ΔEthread⟩. This unifies mass generation within a single entropic cost principle: mass is the measure of how hard the network must work to prevent a configuration from dissolving back into the sea of maximal entanglement. The result also provides a deeper understanding of the origin of E=mc2E=mc2 as a consequence of entanglement network dynamics.