Ceiling and Cliff: Tsirelson-Limited Correlations as a Structural Constraint on Molecular Bonding

Zenodo v1.1 Description Overview We propose a quantum information-theoretic framework for characterizing covalent bond formation based on the Tsirelson bound β = 2√2. The CHSH maximum acts as a geometric ceiling (universally saturated in singlet states), while the cliff—the signature of bond formation—emerges from a composite index κ_phys that combines bond character, quantum excess, and binding energy gain. Key Finding The Tsirelson bound β = 2√2 acts as a formal ceiling on admissible quantum correlations, while molecular bonding emerges only when this ceiling is weighted by both chemical connectivity and energetic benefit. Falsifiable Tests System Bond Type κ_max Result H₂ Covalent 0.064 Peak ✓ He₂ Non-covalent ≈ 0 Null ✓ HF Covalent 0.270 Peak ✓ Contents Manuscript ceiling_cliff_pra_v2.pdf - Main manuscript (3 pages) ceiling_cliff_pra_v2.tex - LaTeX source Figures figure1.png - Figure 1: H₂ CHSH analysis (4-panel) figure2.png - Figure 2: Null test (He₂) and replication (HF) si_figure_s1_basis.png - Figure S1: Basis set dependence Data h2_tstt_publication_data.csv - H₂ numerical data si_table_s1_basis.csv - Basis set comparison Code h2_publication_final.py - H₂ analysis pra_evidence.py - He₂ and HF analysis si_basis_comparison.py - Basis set verification Reproducibility pip install pyscf numpy matplotlib python code/h2_publication_final.py python code/pra_evidence.py v1.1 Update (January 3, 2026) Added null test: He₂ (κ_phys ≈ 0) Added replication: HF (κ_phys peak) Updated manuscript with Figure 2 and Table 1