A Formal Axiomatic Derivation of the Information-Geometric Structural Debt Framework (IGSDF) v20

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).