Diagram–Hilbert Space with Entropy-Originated Topological Projection (DHS/EOTF) An operational phenomenology interface for neutrino mixing and emergent gravity

This manuscript frames the Diagram–Hilbert Space (DHS) and Entropy-Originated Topological Projection (EOTF) approach as a test-facing research program by specifying two explicit interfaces: (i) a pipeline from DHS/EOTF projected quantities to effective neutrino mass operators and then to PMNS observables with controlled parameter and scale robustness; and (ii) a gravity pipeline that states the conditions for an Einstein-like limit and organizes deviations in standard experimental languages (PPN, equivalence-principle tests, and cosmology). The goal is operational clarity—i.e., defining what must be computed, what assumptions are required, and which observables are predicted—rather than claiming experimental confirmation.