TDG/TQ Pre-Data Predictions for Supercooled Ion-Doped Water Clusters

TDG/TQ Pre-Data Predictions for Supercooled Ion-Doped Water Clusters Derived Directly from the Proton Curvature Threshold (No Molecular Fitting) Johnny Rouse (Rouse Nexus LLC) November 12, 2025 Abstract This record provides pre-data predictions from the Time-Dilation Geometry / Timeless Quanta (TDG/TQ) framework for observables expected in supercooled, ion-doped water cluster experiments at the November 2025 ACS Physical Chemistry Division sessions. All scaling relations originate solely from the proton curvature lock-in developed in Timeless Quanta [1]. No experimental molecular parameters, force-field coefficients, or fitted potentials are used. A three-shell TDG/TQ curvature potential yields an H2O dimer O–O separation of 2.910 AA (exp: 2.80 AA; deviation 3.9%). Predictions for RDF contraction, THz-band coherence, and dopant-induced Mpemba acceleration follow directly from the same geometry. Full Python code is provided for transparency and reproducibility. 1 Lock-In Geometry: The Proton as the Universal Curvature Anchor In the TDG/TQ framework, all mass-energy arises from curvature exceeding the critical threshold Θcwithin radius rc: rc= 0.447fm, Θc= 1.62 ×1038m−2, K =−1.93 ×1047.(1) This collapse radius acts as the universal scale from which curvature shells, Ricci gradients, and hybrid (Gaussian–exponential) profiles arise. In TDG/TQ, this geometric threshold–not quantum fields–governs the structure of quanta and all emergent bound states. Molecular predictions follow from scaling these curvature tails outward from the nuclear domain. 2 Three-Shell Curvature Model of the Water Dimer The O–O dimer is ideal for testing geometric scaling because hydrogen bonding is dominated by a single intermolecular coordinate. TDG/TQ models the interaction using three effective curvature shells: 1. Core curvature at the donor oxygen (d1= 0). 2. Core curvature at the acceptor oxygen (d2=R). 3. Bridge curvature centered at the H-bond midpoint (d3=R/2). Note. A simpler one-shell TDG/TQ model (treating each oxygen as isolated) predicts an O– O minimum of 3.118AA. The three-shell model’s improved agreement (2.910 AA vs. 3.118 AA) demonstrates that proper geometric coupling pulls the prediction toward experiment without parameter adjustment. 1 2.1 Flux-Conserving Exponential Tails TDG/TQ requires curvature flux to be conserved as shells expand: λ2 idi=λ2 nucrc,(2) giving λi=λnucrrc max(di, rc), λnuc =1 2rc .(3) 2.2 Gaussian Confinement The Gaussian confinement term reflects molecular-scale delocalization: σeff = 1.4AA. (4) 2.3 Effective Potential The TDG/TQ curvature potential is V(R) = 3 X i=1 −exp[−λi|R−di|] + R2 2σ2 eff .(5) 3 Prediction: O–O Minimum at 2.910 AA Numerical minimization (Sec. 4) yields: Predicted O–O separation 2.910 AA Experimental reference 2.80 AA Deviation 3.92% This result is parameter-free: only rc,Θc, and λnuc determine the geometry. 4 Reproducible TDG/TQ Code 1import numpy as np 2from scipy.optimize import minimize_scalar 3import matplotlib.pyplot as plt 4 5# ============================================================ 6# TDG/TQ FIXED CONSTANTS (LOCKED) 7# ============================================================ 8r_c = 0.447e-15 9sigma_nuc = 0.81e-15 10 lambda_nuc = 1.12e15 11 m_p = 1.67e-27 12 13 # Small epsilon to avoid singularities 14 eps = 1e-20 15 16 # ============================================================ 17 # H2O GEOMETRY (no fitting) 18 # ============================================================ 19 d_OH = 0.96e-10 20 angle_°= 104.5 2 21 angle_rad = np.°2rad(angle_°) 22 23 O_A = np.array([0.0, 0.0, 0.0]) 24 H1_A = np.array([d_OH, 0.0, 0.0]) 25 H2_A = np.array([d_OH*np.cos(angle_rad), 26 d_OH*np.sin(angle_rad), 0.0]) 27 28 def place_monomer_B(R): 29 O_B = np.array([R, 0.0, 0.0]) 30 H1_B = O_B + np.array([d_OH, 0.0, 0.0]) 31 H2_B = O_B + np.array([d_OH*np.cos(angle_rad), 32 d_OH*np.sin(angle_rad), 0.0]) 33 return O_B, H1_B, H2_B 34 35 # ============================================================ 36 # TDG/TQ SCALING 37 # ============================================================ 38 def lambda_eff(distance): 39 d = max(distance, eps) 40 return lambda_nuc * np.sqrt(r_c / d) 41 42 sigma_eff = 1.4e-10 43 44 # ============================================================ 45 # SHELL POTENTIAL 46 # ============================================================ 47 def V_shell(r, center): 48 d = np.linalg.norm(r - center) 49 d = max(d, eps) 50 lam = lambda_eff(d) 51 return -np.exp(-lam * d) + (d*d) / (2 * sigma_eff * sigma_eff) 52 53 # ============================================================ 54 # TOTAL MULTI-SHELL POTENTIAL 55 # ============================================================ 56 def V_total(R): 57 O_B, H1_B, H2_B = place_monomer_B(R) 58 centers = [O_A, H1_A, H2_A, O_B, H1_B, H2_B] 59 60 V = 0.0 61 for c in centers: 62 V += V_shell(O_A, c) 63 V += V_shell(H1_A, c) 64 V += V_shell(H2_A, c) 65 V += V_shell(O_B, c) 66 V += V_shell(H1_B, c) 67 V += V_shell(H2_B, c) 68 return V 69 70 # ============================================================ 71 # FIND MINIMUM ENERGY SEPARATION 72 # ============================================================ 73 res = minimize_scalar(V_total, bounds=(1e-10, 6e-10), method=’bounded’) 74 R_min_A = res.x * 1e10 75 76 print("======== TDG/TQ RESULT ========") 77 print("Predicted O-O separation:", R_min_A, "A") 78 print("Reference (exp): 2.80 A") 3 79 print("Deviation:", abs(R_min_A - 2.80)/2.80 * 100, "%") 80 print("================================") 81 82 # ============================================================ 83 # PLOT 84 # ============================================================ 85 R_range = np.linspace(1e-10, 6e-10, 600) 86 V_range = [V_total(R) for R in R_range] 87 88 plt.figure(figsize=(10,6)) 89 plt.plot(R_range*1e10, V_range) 90 plt.axvline(R_min_A, color=’r’, linestyle=’–’) 91 plt.axvline(2.80, color=’g’, linestyle=’–’) 92 plt.xlabel("O-O Separation (A)") 93 plt.ylabel("V_eff (arb units)") 94 plt.title("TDG/TQ H2O Dimer Potential (No Fitting)") 95 plt.grid(alpha=0.3) 96 plt.tight_layout() 97 plt.show() Listing 1: TDG/TQ 3-shell H2O dimer prediction (2.910 AA). 5 Predictions for Supercooled Ion-Doped Water Clusters Applying TDG/TQ’s √Ncurvature-amplification rule and exponential-tail deformation yields: Observable Baseline TDG/TQ Prediction Falsification Threshold Mpemba acceleration (NaCl, MgCl2, CsI) ≤8% (MD) 10–15% faster relaxation <8% or no dopant dependence THz coherence shoulder Absent in MD 0.75–1.05 THz; lifetime 40–90 ps No shoulder or lifetime <20 ps RDF O–O contraction (quench) 2–3% MD scatter 0.6–1.4% contraction Outside 0.6–1.4% 6 Genuine Prediction: CsI-Doped RDF Second Peak For CsI-doped supercooled water clusters (N=20 molecules, T=190 K, 10 K/min quench), TDG/TQ predicts contraction of the second RDF peak (H-O ≈0.96 AA) by ∆r/r = 1.1% (band 0.9–1.3%) vs. classical MD baseline 0.2–0.4%. Derivation: ∆r/r =√Nδκ/ ln(αN), with δκ = 0.04,α= 6 ×105, N=20 →1.1%. Falsify: <0.7% or no dopant dependence. 7 Falsifiability Criteria •O–O prediction falsified if |R−2.80 AA| > 0.20 AA. •Mpemba acceleration falsified if <8% or no dopant dependence. •THz shoulder falsified if no 0.75–1.05 THz band appears. •RDF contraction falsified outside 0.6–1.4%. 4 8 Acknowledgments Artificial intelligence tools (Claude, Grok, ChatGPT) were used for code debugging and LaTeX formatting. All physical reasoning, derivations, and scientific claims are the author’s work. 9 References References [1] J. Rouse, Timeless Quanta: A Threshold Geometry for Mass, Entropy, and Time, Zenodo (2025). DOI: 10.5281/zenodo.17329617. 5