Structural Cosmology v2.0: An Effective Field Theory Framework for the Structural Field Subtitle From Phenomenological Cosmology to Systematic EFT Description

Structural Cosmology v2.0 proposes a systematic Effective Field Theory (EFT) formulation of the structural field Δ, a real scalar field representing the degree of structural difference from an unmanifested background (Isness). Building on the phenomenological framework established in Structural Cosmology v1.x, where a single structural potential was proposed to provide a unified interpretation of dark energy, dark matter, and observable matter through regime-dependent dynamics, this release develops a symmetry-based EFT description organized by effective operators and power counting. The framework introduces an effective action S_eff[gμν, Δ] decomposed into five interconnected sectors governing geometry, structural field dynamics, geometry–field interactions, matter, and projection to observables. The EFT construction is guided by: Diffeomorphism invariance Approximate shift symmetry Discrete Z₂ symmetry Operator hierarchy and power counting Explicit validity-domain analysis Projection operators connecting structural dynamics to cosmological observables A central component is the projection operator Π_g[Δ], which provides an illustrative mapping between structural field dynamics and observable quantities such as: Expansion history H(z) Growth-rate observable fσ₈(z) Matter power spectrum P(k) Galaxy rotation curves Weak lensing observables The release further extends the falsifiability framework of Structural Cosmology by introducing EFT-specific evaluation criteria C21–C25: EFT Consistency Operator Stability Cutoff Independence Regime Consistency Predictive Distinguishability from ΛCDM The ontological foundation is provided by The Is Framework: I → D → S → A → F (Isness → Difference → Structure → Appearance → Feedback) which serves as the conceptual backbone linking structural dynamics, observables, and theory revision. This repository contains the complete v2.0 manuscript, all 19 figures, and a reproducible Python demonstration illustrating the structural potential, effective mass, regime classification, EFT operator hierarchy, power counting, projection operators, validity checks, and falsifiability criteria. All theoretical constructions, observational mappings, and future predictions are presented as illustrative proposals intended for further theoretical development, empirical testing, and revision.