Glass-Freeze Analysis Protocol: CPA + Constraint Rate Comparison (DATASET)

Glass-Freeze Analysis Protocol: CPA + Constraint Rate Comparison Debra S. Gavant∗ DPΦInitiative, USA Christian E. Precker† Independent Physicist, Portugal November 2025 Abstract The CPA + Constraint (CPA + C) formulation of the Dynamic Present Theory (DP Φ ) was evaluated across three canonical viscosity datasets: the ortho-terphenyl (OTP) measurements of Laughlin and Uhlmann (1972), the independent OTP dataset of Plazek (1994), and three glycerol–water mixtures reported by Kumar et al. (1994). Across all evaluated datasets, the CPA + C model reproduced the Vogel–Fulcher–Tammann (VFT) model with statistical parity ( 𝑅2>0.99 ) and slightly outperformed it in the Plazek OTP dataset. Unlike the empirical structure of the VFT equation, the CPA + C formulation derives the same curvature from a physically motivated constraint-modulated rate of Continuous Present Actualization (CPA). These findings indicate that the residual noise observed in simpler models represents an actual physical signal: the increase in configurational constraint as it approaches a CPA Lock-In (or coherence stall), which CPA + C effectively isolates. Combined with mechanistic interpretability, this numerical parity establishes CPA + C as a physically grounded alternative to purely empirical viscosity relations, potentially facilitating the rational design of materials with customized flow properties. 1 INTRODUCTION The CPA + Constraint (CPA + C) formulation interprets viscosity as a measurable consequence of constraintinduced resistance to configuration change. As configurational constraint increases, the system’s capacity to reconfigure slows, a process modeled within Dynamic Present Theory (DP Φ ) [ 1 ] as Continuous Present Actualization (CPA), an irreversible, energy-limited rate of state change governed by local energy density and structural load. Within this framework, viscosity reflects resistance to actualization, a reduction in accessible microconfigurations as structural constraint accumulates. The CPA + C model formalizes this by linking viscosity growth to a physically motivated, constraint-modulated actualization rate. This study evaluates whether the CPA + C formulation can quantitatively reproduce the Vogel–Fulcher–Tammann (VFT) equation [ 2 , 3 , 4 ], one of the most successful empirical relations in materials science, across three chemically distinct viscosity datasets: the ortho-terphenyl (OTP) measurements of Laughlin and Uhlmann [ 5 ], the independent OTP dataset of Plazek [6], and glycerol–water mixtures characterized by Kumar et al. [7]. 2 METHODS Viscosity-temperature data for ortho-terphenyl (OTP, 240–385 K) were fitted using four models: the Arrhenius equation, the Vogel-Fulcher-Tammann (VFT) equation, a Simple Exponential, and CPA + Constraint (CPA + C). ∗Corresponding author: [email protected], https://orcid.org/0009-0004-5593-713X. †[email protected], https://orcid.org/0000-0003-0828-6835. 1 The analysis evaluated three chemically distinct systems: the canonical ortho-terphenyl (OTP) measurements of Laughlin and Uhlmann (1972) [ 5 ], the independent OTP dataset of Plazek (1994) [ 6 ], and three glycerol-water mixtures reported by Kumar et al. [ 7 ]. Identical GUI exports were utilized for all parameter extraction, residual analysis, and consistency checks Nonlinear least-squares optimization (Levenberg-Marquardt) was used to minimize the root-mean-square (RMS) error in log10(𝜂) . Model selection was based on AIC and BIC scores, with 95% confidence intervals calculated from the parameter covariance matrix. The value 𝑘 was defined as the number of free-fitted parameters; fixed hyperparameters and duplicate representations (e.g., 𝜂0vs. log10 𝜂0) were not counted. Model fitting and verification were performed on a custom Glass GUI V1.1 (2025) developed by C. E. Precker, which implemented the CPA + C formulation alongside reference models. Post-processing by D. S. Gavant included theoretical synthesis, integration of analytical inputs, collaboration management, and manuscript drafting. Formal definitions of the foundational principles, Continuous Present Actualization (CPA) and Constraint Load ( 𝐶 ), are provided in Dynamic Present Theory I (DP Φ ) [ 1 ]. This study operationalizes these principles as the CPA + C viscosity model. Prior to the acquisition of results, the evaluation criteria and analysis plan in the preregistration protocol [ 8 ] outlined a qualitative expectation that the CPA + C model would reproduce the curvature of the VFT equation. The near-exact quantitative parity across chemically distinct systems was not assumed beforehand. 3 RESULTS The CPA + Constraint (CPA + C) formulation reproduced the fit of the Vogel–Fulcher–Tammann (VFT) equation for ortho-terphenyl viscosity (240–385 K) with statistical parity ( 𝑅2=0.9967 , RMSE ≈ 0.235), successfully capturing the super-Arrhenius curvature across 14 orders of magnitude. The same parity was maintained for all three glycerol–water mixtures reported by Kumar et al. [ 7 ], each yielding 𝑅2≈0.9981 under identical parameter extraction procedures. In the independent OTP dataset of Plazek et al. [ 6 ], the CPA + C model slightly outperformed the VFT reference (AIC = −33.81 vs. −33.42 ; 𝑅2=0.9932 ) with residuals exhibiting no systematic curvature across the temperature domain. Together, these results demonstrate that the CPA + C model reproduces VFT-level accuracy using a comparable number of fitted parameters while also offering a physically interpretable mechanism based on constraint-limited actualization. Table 1: Fit metrics for viscosity models applied to ortho-terphenyl (OTP) data (240–385 K). Model RMSE MAE Bias MAD 𝑅2AIC VFT 0.2346 0.1989 −1.8×10−11 0.1770 0.9967 -95.50 CPA + Constraint 0.2346 0.1989 −1.7×10−70.1770 0.9967 -91.50 Simple Exponential 1.6053 1.2747 0.0357 0.8978 0.8447 39.13 Arrhenius 2.2890 1.9479 -0.2821 0.5397 0.6843 61.97 2 Figure 1: Viscosity of ortho-terphenyl versus temperature. The CPA + Constraint model achieves statistical parity with the empirical VFT equation, successfully capturing the super-Arrhenius curvature over 14 orders of magnitude. 4 DISCUSSION The CPA + Constraint (CPA + C) formulation reproduces VFT-level curvature with negligible statistical deviation while providing a physically motivated mechanism for viscosity growth; as configurational constraint increases, the system’s ability to reconfigure slows, approaching a CPA Lock-In (or coherence stall) threshold. In this view, the VFT 𝑇0 singularity emerges as a non-physical artifact: an extrapolation error from fitting an empirical curve beyond its valid range. The CPA + C model replaces this divergence with a physically grounded alternative: the Constraint Load ( 𝐶 ), which modulates the baseline CPA Rate as the system approaches a real, finite CPA Lock-In temperature (𝑇𝑔). Residual patterns in simpler relations (e.g., the Arrhenius or unmodified exponential forms) are reinterpreted— not as noise—but as structured deviations: signatures of constraint feedback on the actualization rate. The CPA + C formulation isolates and quantifies this structure, providing a direct physical interpretation of the super-Arrhenius regime. Constraint and Actualization. In the CPA + C framework, constraint refers to the effective limitation on accessible microconfigurations as a system becomes more structurally loaded. Physically, constraint reflects the increasing difficulty of rearrangement due to geometric frustration, molecular crowding, or bond-network rigidity. Informationally, it corresponds to a narrowing of viable next-state transitions under local energy and topology 3 conditions. As constraint accumulates, the configuration-change rate slows, culminating in a CPA Lock-In near 𝑇𝑔. Continuous Present Actualization (CPA) models this process as a present-only, constraint-modulated flow. Across all tested systems, CPA + C reproduced the VFT relation while reducing empirical overhead and introducing a physically interpretable mechanism. This cross-dataset agreement suggests that the longstanding success of the VFT form may arise from deeper constraint-driven dynamics that CPA + C explicitly captures. By rooting viscosity scaling in constraint-modulated actualization dynamics, the CPA + C formulation enables principled extrapolation and may support the rational design of materials with tailored flow properties, particularly in regimes where conventional models extrapolate poorly. Acknowledgments The preparation of this manuscript benefited from modern large-language-model tools, which assisted with drafting, editing, and verification. Funding No external funding was received for this work. Data and Code Availability The full datasets, residual exports, and parameter files are included in this repository. The analysis tool (Glass GUI V1.1) was archived by C.E. Precker and is available upon request. References [1] D.S. Gavant, “Dynamic Present Theory I: Unifying Quantum Mechanics and General Relativity,” Zenodo (2025). https://doi.org/10.5281/zenodo.17069890 [2] H. Vogel, “Das Temperaturabhängigkeitsgesetz der Viskosität von Flüssigkeiten,” Physikalische Zeitschrift 22, 645–646 (1921). [3] G.S. Fulcher, “Analysis of recent measurements of the viscosity of glasses,” Journal of the American Ceramic Society 8(6), 339–355 (1925). [4] G. Tammann and W. Hesse, “Die Abhängigkeit der Viskosität von der Temperatur bie unterkühlten Flüssigkeiten,” Zeitschrift für anorganische und allgemeine Chemie 156, 245–257 (1926). [5] W.T. Laughlin and D.R. Uhlmann, “Viscous flow in simple organic liquids,” Journal of Physical Chemistry 76(14), 2317–2325 (1972). https://doi.org/10.1021/j100658a032 [6] D.J. Plazek, C.A. Bero, and I.-C. Chay, “The recoverable compliance of amorphous materials,” Journal of Non-Crystalline Solids 172–174, 181–190 (1994). https://doi.org/10.1016/0022-3093(94) 90431-6 [7] P.N. Shankar and M. Kumar, “Experimental determination of the kinematic viscosity of glycerol-water mixtures,” Proceedings of the Royal Society of London A 444, 573–581 (1994). https://doi.org/10. 1098/rspa.1994.0039 4 [8] D.S. Gavant, “Glass-Freeze Analysis Protocol v0 [Pre-register prior to model fitting],” Zenodo (2025). https://doi.org/10.5281/zenodo.17502949 [9] D.S. Gavant and C.E. Precker, “Glass Freeze Analysis Protocol: CPA + Constraint Rate Comparison [Data set],” Zenodo (2025). https://doi.org/10.5281/zenodo.17546734 5