Second-Order Ordering and the Origin of Quantum Coherence in Entanglement–Algebraic Spacetime

This paper is archived as a speculative research work. This paper establishes the minimal structural conditions required for persistence and causal ordering within the Entanglement–Algebraic Spacetime (EAS) kernel.The kernel is represented by an ordered set of scalar admissibility fields and contains no primitive spacetime, dynamical propagation law, or intrinsic oscillatory variables.We show that any admissibility relation connecting successive scalar fields must preserve relational content in order for persistences to exist. A first-order ordering relation necessarily dissipates relational structure and cannot support persistence.Requiring invariant relational content forces a second-order ordering relation between scalar fields. This relation introduces a two-ledger kernel structure whose invariant quadratic measure preserves coherent relational information across ordering layers.The two-ledger structure naturally produces oscillatory eigenmodes and yields complex amplitudes as the minimal compression of the kernel state.These results establish second-order ordering as the foundational structural principle underlying later interface-level descriptions of interference, quantum mechanics, and field theory within the EAS program.