Ahuraic Framework – Initial Numerical Validation Codes

This repository contains the complete numerical validation code for the paper: "Informational Structural Cost (CIS): Derivation, Thermodynamic Correspondence, and Predictive Power of the Ahuraic Framework's Core Organizational Quantity" (Mahdi Jalali, Cogniora Artificial Mind Institute, 2026) The validation is organized into two independent phases, systematically testing the CIS framework across different spin models, system sizes, and structural proxies. Phase 1 (Ising Model – TFIM): - Five spin-1/2 transverse-field Ising chains (Uniform, Fibonacci, Thue–Morse, Sturmian, Random) are studied. - The organisational coupling constant κ is calibrated using the correlation length ξ as a proxy for the structural rank ρ. - Blind predictions on quasiperiodic chains (L=13) yield errors ≤5% for Fibonacci and Thue–Morse, and up to ~7.6% for Sturmian and random chains. - Bootstrap analysis confirms the stability of κ_ξ (CV ≈ 16.5%, 95% CI: [0.0609, 0.0805]). - Finite-size scaling extracts the thermodynamic limit κ∞ ≈ 9.93. - Finite-temperature test verifies the thermodynamic correspondence ⟨ℐ⟩ = βF_org + S_org using the organisational Gibbs distribution. Phase 2 (XXZ & Heisenberg Models): - The framework is extended to Heisenberg and XXZ chains (Δ = 0.5, 1.0, 1.5). - Comparison of structural proxies: correlation length ξ, entanglement entropy S_ent, and spectral gap ΔE. - ξ is reliable only in gapless (critical) regimes; S_ent is confirmed as a more universal proxy across all tested regimes. - Recalibration using S_ent yields blind prediction errors <5% for all models. - Gapless vs. gapped behaviour is illustrated in the Heisenberg model (h=0.1 vs. h=0.5). Repository Contents: - Phase 1 scripts: `kappa_xi_analysis.py`, `extended_validation.py`, `finite_temperature_test.py`, `bootstrap_standalone.py`, `fss_analysis.py` - Phase 2 scripts: `models.py`, `observables.py`, `01_models_validation.py`, `02_model_dependent_kappa_validation.py`, `03_structural_proxy_comparison.py`, `04_calibrate_kappa_Sent.py`, `heisenberg_h01.py` - README files for both phases - `requirements.txt` (Python dependencies: NumPy, SciPy, Matplotlib, scikit-learn) All scripts are self-contained and produce output tables and figures (.txt and .png). The results are fully reproducible on any system with Python 3.7+ and the required libraries installed. License: CC BY 4.0 Citation: Please cite the accompanying paper and this repository as: Jalali, M., Jalali, S., & Jalali, P. (2026). Ahuraic Framework – Initial Numerical Validation Codes (v1.0). Zenodo. [DOI 10.5281/zenodo.21525486]