Version 3.0 finalizes the strong-curvature structure of Informational Field Theory in Strong Curvature (IFT-SC) and completes the operational description of where informational recursion fails inside compact objects. This update removes all remaining ambiguities in the freeze mechanism and brings the paper into full consistency with the URT dependency map and the proportionality law defined in URT. Key updates in v3.0: • Final definition of curvature-induced stiffnessThe gravitational stiffness term is fixed as:sigma_grav = k_B * T_P * (K / K_crit),with K_crit = l_P^(-4).This provides a parameter-free mapping from curvature to informational stiffness. • Final recursion-freeze conditionIrreversible recursion becomes impossible whereversigma >> k_B * T_loc.In this regime the efficiency collapses (lambda -> 0), eliminating the compressive branch of the recursion operator.This defines a freeze radius r_f inside the horizon. • Finite informational depthBelow r_f, no further entropy production occurs and no new informational states can be generated.The internal recursion sequence terminates at a finite index, preventing any approach to a classical singularity in informational terms. • Correction to introductory scopeSection 1 now refers only to Schwarzschild geometry, matching the content of the paper and removing the prior Kerr reference. • Strengthened GR consistencyThe version clarifies that IFT-SC does not modify Einstein’s equations.Curvature is taken directly from GR; URT constrains only which informational updates are physically admissible. • Foundation for downstream papersThe stiffness field sigma(r) and the freeze boundary r_f established here serve as fixed inputs for Paper 3 (sigma-wave dynamics) and Paper 4 (black-hole information).No new operators or assumptions have been added. Version 3.0 provides a complete, self-consistent description of informational irreversibility in strong curvature. It formalizes the finite depth of physical evolution inside black holes and establishes the operational boundary where informational recursion halts. All existing predictions and falsification criteria remain unchanged. URT PAPER FAMILY This work forms part of the Unified Recursion Theory (URT) research program, which develops a cross-domain framework for physical evolution based on constrained informational recursion and an energy–entropy proportionality law. Each paper in the series is self-contained, while collectively establishing the theoretical structure across quantum, geometric, biological, cosmological, and particle-level domains. Related URT works available on Zenodo: FOUNDATIONAL PAPERS 1. Unified Recursion Theory — Core Framework (URT Core) DOI: 10.5281/zenodo.17642761Record: https://zenodo.org/records/17642761 2. Discrete Admissible Regimes in Unified Recursion Theory: Operator Closure, Constraint Topology, and the Necessity of Five Operators DOI: 10.5281/zenodo.18148192Record: https://zenodo.org/records/18148193 3. Informational Field Theory in Strong Curvature (IFT-SC) DOI: 10.5281/zenodo.17850379Record: https://zenodo.org/records/17850379 4. Dynamical Evolution of the Informational Stiffness Field (ISW Theory) DOI: 10.5281/zenodo.17860533Record: https://zenodo.org/records/17860533 RESOLUTION PAPERS (PHYSICAL PARADOXES) 5. Informational Recursion and the Dissolution of the Black Hole Information Paradox DOI: 10.5281/zenodo.17868662Record: https://zenodo.org/records/17868662 6. ORM and the Quantum Measurement Problem (ORM) DOI: 10.5281/zenodo.17881944Record: https://zenodo.org/records/17881944 BRIDGING / CONSTRAINT PAPER 7. Distinguishability Geometry in Informational State Space DOI: 10.5281/zenodo.17957062Record: https://zenodo.org/records/17957062 Provides the geometric foundation for informational state space.Underpins the emergence of spacetime, efficiency universality, and landscape geometry. THEORETICAL EXPANSION PAPERS 8. Emergent Spacetime from Informational Recursion DOI: 10.5281/zenodo.17885555Record: https://zenodo.org/records/17885555 9. λ-Universality Across Scales (λ-UAS) DOI: 10.5281/zenodo.17934065Record: https://zenodo.org/records/17934065 10. Free-Energy Landscape Geometry in Unified Recursion Theory DOI: 10.5281/zenodo.17940995Record: https://zenodo.org/records/17940995 BIOLOGY / COMPLEXITY PAPER 11. URT in Biology: Efficiency, Folding Funnels, Replication Fidelity, and Molecular Motor Dynamics DOI: 10.5281/zenodo.17945209Record: https://zenodo.org/records/17945209 COSMOLOGICAL EXTENSIONS 12. Cyclic Cosmology from Informational Recursion DOI: 10.5281/zenodo.17955043Record: https://zenodo.org/records/17955043 13. Antimatter as Inverse Recursion: Temporal Operator Asymmetry and Matter–Antimatter Imbalance in Unified Recursion Theory DOI: 10.5281/zenodo.17955043Record: https://zenodo.org/records/17955625