Acknowledgments I would like to express my deepest gratitude to Andrea and his family — Cristina, Alice, and Luca — for their friendship and their unwavering support throughout this project. Andrea played a crucial role in stress-testing the SISSI model and guiding the refinements that ultimately led to the development of version 3. Their encouragement and insight have been invaluable. This release introduces SISSI H₃ v3, a fully revised and stabilized formulation of the SISSI method (Spectral Index for Structural and Systemic Integrity). Compared with version 2, this release represents a complete mathematical and algorithmic refinement, addressing all previously identified limitations and introducing a physically interpretable and reproducible structure. Major improvements over v2: 1. Physically grounded kernel (Gaussian–Gabor) The H₃ operator now uses a normalized Gaussian–Gabor kernel with parameters explicitly tied to the spectral FWHM. This removes arbitrary choices present in v2 and ensures physical consistency across datasets. 2. Correct formulation of the third derivativeThe curvature operator has been fully corrected. v2 contained an ambiguous second–third derivative transition; v3 implements a strict ∇ (∇ (∇f) ) formulation, validated in both theory and practice. 3. Region-wise architecture (5 structural domains) Global correlations from v2 have been abandoned. SISSI H₃ v3 uses five independent spectral regions, each processed and normalized separately. This dramatically improves stability and interpretability, especially in complex molecules. 4. Removal of SGCIglobalThe previous global Z-score index was shown to be numerically unstable and physically ambiguous. It has been completely removed and replaced by the robust H₃ regional framework. 5. Normalization and parameter constraintsAll parameters are now physically constrained: σ = FWHM / 2. 355 ω = 2π / FWHM kernel support = ±3σ dx = max (Δxᵣef, Δxquery) This guarantees reproducibility across independent implementations. 6. Weighted structural coherence indexThe global SISSI H₃ value is now a weighted combination of regional coherence scores, where weights derive from local spectral energy. This solves the imbalance issues observed in v2. 7. Extensive validation and correctness checksv3 has been validated on multiple JCAMP-DX datasets (including positional isomers, isotopologues, alcohols, amines, and aromatic systems). The o-xylene / p-xylene pair used in the demo is consistent with all real-data tests performed. 8. Formal specification document (optional) A complete normative specification (MUST/SHOULD style) accompanies this release, defining the exact mathematical and algorithmic requirements for compliant implementations. Demo availability Due to Zenodo restrictions, the executable demo (Windows binary + JCAMP example files) cannot be included in this upload. Researchers interested in obtaining the official SISSI H₃ demonstration may contact: 📧 Giovanniamato197@gmail. com Author: Giovanni Amato (© 2025, CC BY 4. 0 License)
Giovanni Amato (Fri,) studied this question.