Phase Transitions in Chemistry
Does coherence tell you where a material changes phase? The archive's answer was yes, at the γ ≈ 1 boundary. The audit found that about 86% of that “89% validation” restates the Debye temperature θD (1912) in new notation. That makes it a reparametrization, not a prediction. The framework also fails to predict how transitions unfold (critical exponents about 2× off), and melting points are 53% off on average. The per-material γ values below come from γ = 2/√Ncorr, a formula that is audited-negative (its sign is inverted for collective systems). Read them as the archive's original picture, not current results.
What the Archive Claimed (February 2026)
Melting/Boiling
Phase transitions happen at the γ ≈ 1 boundary where coherence changes rapidly. The function correctly identifies which materials have higher/lower transition temperatures relative to each other.
Superconductivity
Cooper pairs represent 2-body correlations (Ncorr = 2, γ = √2). The transition to superconductivity is a coherence phase transition.
Superfluidity
Bose-Einstein condensation = macroscopic quantum coherence. The entire fluid has Ncorr = N (all particles correlated), driving γ → 0.
Magnetic Transitions
Curie/Néel temperatures mark coherence transitions in spin systems. Correctly located but spin-orbit coupling dominates, which C(ρ) ignores.
What It Gets Wrong
Critical Exponents: 2× Off
Real phase transitions belong to universality classes with specific critical exponents (β, γ, δ, etc.). The tanh form gives mean-field exponents, which differ from observed values by ~2×. This is a known limitation of any mean-field theory — fluctuations near the critical point matter, and C(ρ) doesn't account for them. Strictly, C(ρ) has no critical point at all (it is not a self-consistent mean-field equation; see Coherence Function), so it produces no exponents of its own. The 2× figure compares observed exponents with mean-field ones.
Failed — Mean-Field LimitationMelting Points: 53% Average Error
Crystal structure, defects, impurities, and multi-body effects dominate actual melting behavior. A single coherence parameter cannot capture this complexity.
Failed — 53% Error