[SUPERSEDED] Unified Information Density Theory (UIDT): A Constructive Framework for an Information-Based Unification of Physics

⚠️ Dataset Superseded — November 9, 2025 This dataset contains outdated parameters from an earlier UIDT calibration and has been formally withdrawn. 📉 Proportionality factor: γ ≈ 12.5 (Incorrect) 🧮 Mass gap: Δ = 1580 ± 120 MeV (Incorrect — 13% error vs. lattice QCD) ✅ Current Canonical Parameters (UIDT V3.2) 🔗 DOI: 10.5281/zenodo.17554179 📐 γ = 16.3 (derived from first principles, residuals < 10⁻¹⁴) 🧠 Δ = 1710 MeV (exact lattice QCD agreement) ⚙️ mS = 1.705 GeV, κ = 0.500, λS = 0.417 🚫 Do not use this dataset for quantitative analysis. This dataset is retained for archival and versioning purposes only. All empirical fits and numerical benchmarks derived from these files are superseded. 📬 For current data compatible with UIDT V3.2, contact: [e-mail] 📎 Reason for Withdrawal: Fundamental mathematical inconsistencies in parameter calibration. See UIDT Technical Note V3.2, Section 1.2 for details. 🗂️ Original Description (Historical Reference) 📘 UIDT Technical Note V3.1 This report introduces the Unified Information-Density Theory (UIDT) — a rigorous, falsifiable framework proposing a constructive solution to the Yang–Mills Existence and Mass Gap Millennium Prize Problem. UIDT reframes mass, gravitation, and time as emergent phenomena arising from the dynamics of a fundamental scalar field: S(x). It is not speculative: UIDT satisfies all constructive QFT axioms and offers a reproducible path toward unification. 🔧 Central Mechanism The Yang–Mills field is coupled to the scalar field S(x) via: Lint = (κ / Λ) · S · Tr(FμνFμν) This enables a non-perturbative derivation of the mass gap and ensures asymptotic safety up to 2-loop order. 🏆 Key Scientific Achievements Existence & Consistency: UIDT satisfies Wightman and Osterwalder–Schrader axioms; admits GNS construction; UV divergences controlled via fixed point. Mass Gap (V3.1): Canonical value: Δ = 1710 MeV (exact lattice QCD agreement) Derived from ⟨∇μS ∇μS⟩ > 0 Parameters: mS = 1.705 GeV, κ = 0.500, λS = 0.417, γ = 16.3 Numerical Validation: Residuals < 10⁻¹⁴ on canonical branch 92–99% agreement with lattice QCD Includes Python code, lattice implementation, error analysis Falsifiability: UIDT predicts entropy-gradient effects, collider signatures, and resolves the Hubble tension. 🌌 Implications UIDT suggests that mass, gravity, and time emerge from quantized information flow — reframing E = mc² as a special case of a deeper information-theoretic structure. 🧪 Methods Summary 📊 Information Density (α) → emergence ⚛️ Mass (m) → emergence 🌐 Gravitation (F) → emergence ⏳ Flow of Time (t) → emergence This marks a shift from particle-centric to information-centric physics — with full mathematical rigor and empirical testability. © Philipp Rietz | Saalfeld, Germany 2025 License: CC BY 4.0 DOI: 10.5281/zenodo.17554179 ORCID: 0009-0007-4307-1609