The CETΩFramework: Informational–Modular Dynamics, Spectral Geometry, and Observable Predictions
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Wepresentthefirstself-containedformulationoftheCETΩframework,aninformational–modularextensionofrelativisticfield theoryincurvedspacetime.CETΩintroducesanadditionalinformationalcoordinate𝜓,amodularHamiltonian𝐾Ω,andastate- dependent spectral curvature MΩ, all embedded in an extended C∗-algebraic and modular-theoretic structure. We develop the complete axiomatic foundation, the extended Haag–Kastler construction, the informational C∗-algebra, and the CETΩspectral triple (AΩ,HΩ,𝐷Ω)governingstate-dependentgeometry. In the macroscopic limit, CETΩ produces effective high-density corrections to the matter stress–energy tensor without modifyingtheEinsteinequations.Thesecorrectionsbecomerelevantindense,metal-poorgas,acceleratingcollapse,suppressing fragmentation,andprovidinganaturaloriginformassiveblack-holeseeds.Wederivetestablepredictionsforhigh-redshiftSMBH formation, gravitational-wave ringdowns, and near-horizon emission measurable by the Event Horizon Telescope (EHT). This work establishes CETΩas a unified and falsifiable framework for high-density gravity, black-hole physics, and early-Universe phenomenology.
