
This submission provides the complete theoretical derivation and computational implementation of the Information-Geometric Structural Debt Framework (IGSDF), a minimal-parameter Grand Unified Theory (GUT). By replacing substance-based ontology with a relation-based information geometry, the framework derives physical reality from an irreducible six-level Hilbert space register known as the C3L3M pixel. Key Theoretical Contributions: Derivation of Gravity: Spacetime and the Einstein field equations (EFE) are derived as emergent properties of an informational-entropic substrate through a variational principle on the Spectral Obidi Action ($I_{SOA} = -Tr(\ln \Delta)$). Spacetime distance is reinterpreted as the information-theoretic cost of distinguishing pixel configurations via the Fisher-Rao metric. Singularity Resolution: The framework resolves the Big Bang singularity via a fourth-order renormalization group (RG) flow using quantized beta coefficients ($\beta_1=1/12, \beta_2=1/24, \beta_3=1/48$) and a T-Dual inversion mechanism ($R \to 1/R$) that prevents infinite curvature by inverting the complexity radius $Z$. Mass Hierarchy: The Standard Model particle spectrum is derived from prime rotational closures of the pixel register, with mass-energy results for the electron ($0.511$ MeV) and proton ($938.27$ MeV) derived from holographic complexity ($m = Z^2 \pi / 2$). Persistence Law: The framework unifies stability across scales via the Universal Law of Structural Persistence (ULSP), which requires systems to extract a 0.730 Stability Margin from the universal $(\pi-3)\pi$ geometric remainder. Computational Implementation (Brain_Block): The associated Python package, Brain_Block, provides a Numba-accelerated modular architecture for simulating these dynamics. Validation: The implementation achieves $R^2 > 0.90$ correlation against NIST experimental boiling points by mapping intermolecular structural debt to local coherence limits. Modules: Includes the GeometricEngine (Foundation), SimulationCore (Parallel Kernel), and DebtStability (Quantum Error Correction).
Function Renormalization Group (FRG), Information Geometry, Galactic Rotation Curves, CDM Anomalies, Dark Matter Alternative, Quantum Information Theory, Emergent Gravity, Thermodynamics of Spacetime, Theoretical Cosmology, Hubble Tension
Function Renormalization Group (FRG), Information Geometry, Galactic Rotation Curves, CDM Anomalies, Dark Matter Alternative, Quantum Information Theory, Emergent Gravity, Thermodynamics of Spacetime, Theoretical Cosmology, Hubble Tension
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