DOI: 10.7910/dvn/syuo5f
title: [SUPERSEDED] Unified Information Density Theory (UIDT): A Constructive Framework for an Information-Based Unification of Physics

description: &lt;!-- ⚠️ Deprecation Banner --&gt;
&lt;div style="border:2px solid #c00; padding:1.5em; background:#fff0f0; font-family:sans-serif; border-radius:8px;"&gt;
 &lt;h3 style="color:#c00; font-size:1.4em;"&gt;⚠️ Dataset Superseded — &lt;em&gt;November 9, 2025&lt;/em&gt;&lt;/h3&gt;
 &lt;p&gt;This dataset contains &lt;strong&gt;outdated parameters&lt;/strong&gt; from an earlier UIDT calibration and has been formally withdrawn.&lt;/p&gt;
 &lt;ul style="margin-left:1em;"&gt;
 &lt;li&gt;📉 Proportionality factor: γ ≈ 12.5 &lt;strong&gt;(Incorrect)&lt;/strong&gt;&lt;/li&gt;
 &lt;li&gt;🧮 Mass gap: Δ = 1580 ± 120 MeV &lt;strong&gt;(Incorrect — 13% error vs. lattice QCD)&lt;/strong&gt;&lt;/li&gt;
 &lt;/ul&gt;

 &lt;h4 style="margin-top:1.2em;"&gt;✅ Current Canonical Parameters (UIDT V3.2)&lt;/h4&gt;
 &lt;ul style="margin-left:1em;"&gt;
 &lt;li&gt;🔗 &lt;strong&gt;DOI:&lt;/strong&gt; &lt;a href="https://doi.org/10.5281/zenodo.17554179" target="_blank"&gt;10.5281/zenodo.17554179&lt;/a&gt;&lt;/li&gt;
 &lt;li&gt;📐 γ = 16.3 (derived from first principles, residuals &lt; 10⁻¹⁴)&lt;/li&gt;
 &lt;li&gt;🧠 Δ = 1710 MeV (exact lattice QCD agreement)&lt;/li&gt;
 &lt;li&gt;⚙️ m&lt;sub&gt;S&lt;/sub&gt; = 1.705 GeV, κ = 0.500, λ&lt;sub&gt;S&lt;/sub&gt; = 0.417&lt;/li&gt;
 &lt;/ul&gt;

 &lt;p style="color:#c00; font-weight:bold;"&gt;🚫 Do not use this dataset for quantitative analysis.&lt;/p&gt;
 &lt;p&gt;This dataset is retained for archival and versioning purposes only. All empirical fits and numerical benchmarks derived from these files are superseded.&lt;/p&gt;
 &lt;p&gt;📬 For current data compatible with UIDT V3.2, contact: &lt;a href="mailto:badbugs.art@googlemail.com"&gt;badbugs.art@googlemail.com&lt;/a&gt;&lt;/p&gt;

 &lt;p&gt;&lt;strong&gt;📎 Reason for Withdrawal:&lt;/strong&gt; Fundamental mathematical inconsistencies in parameter calibration. See UIDT Technical Note V3.2, Section 1.2 for details.&lt;/p&gt;

 &lt;hr style="margin-top:2em;"&gt;
 &lt;h4&gt;🗂️ Original Description (Historical Reference)&lt;/h4&gt;
&lt;/div&gt;

&lt;!-- 📘 UIDT Technical Note V3.1 Summary --&gt;
&lt;div style="font-family:sans-serif; line-height:1.6; padding:1.5em; background:#f9f9f9; border-left:4px solid #0077cc; border-radius:8px; margin-top:2em;"&gt;
 &lt;h2 style="color:#0077cc;"&gt;📘 UIDT Technical Note V3.1&lt;/h2&gt;
 &lt;p&gt;&lt;strong&gt;This report introduces the Unified Information-Density Theory (UIDT)&lt;/strong&gt; — a rigorous, falsifiable framework proposing a constructive solution to the &lt;em&gt;Yang–Mills Existence and Mass Gap Millennium Prize Problem&lt;/em&gt;.&lt;/p&gt;

 &lt;p&gt;UIDT reframes mass, gravitation, and time as emergent phenomena arising from the dynamics of a fundamental scalar field: &lt;strong&gt;S(x)&lt;/strong&gt;.&lt;/p&gt;

 &lt;p&gt;It is not speculative: UIDT satisfies all constructive QFT axioms and offers a reproducible path toward unification.&lt;/p&gt;

 &lt;h3&gt;🔧 Central Mechanism&lt;/h3&gt;
 &lt;p&gt;The Yang–Mills field is coupled to the scalar field S(x) via:&lt;/p&gt;
 &lt;pre style="background:#eee; padding:0.5em; border-radius:4px;"&gt;L&lt;sub&gt;int&lt;/sub&gt; = (κ / Λ) · S · Tr(F&lt;sub&gt;μν&lt;/sub&gt;F&lt;sup&gt;μν&lt;/sup&gt;)&lt;/pre&gt;
 &lt;p&gt;This enables a non-perturbative derivation of the mass gap and ensures asymptotic safety up to 2-loop order.&lt;/p&gt;

 &lt;h3&gt;🏆 Key Scientific Achievements&lt;/h3&gt;
 &lt;ol&gt;
 &lt;li&gt;&lt;strong&gt;Existence & Consistency:&lt;/strong&gt; UIDT satisfies Wightman and Osterwalder–Schrader axioms; admits GNS construction; UV divergences controlled via fixed point.&lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;Mass Gap (V3.1):&lt;/strong&gt;
 &lt;ul&gt;
 &lt;li&gt;Canonical value: &lt;strong&gt;Δ = 1710 MeV&lt;/strong&gt; (exact lattice QCD agreement)&lt;/li&gt;
 &lt;li&gt;Derived from ⟨∇&lt;sub&gt;μ&lt;/sub&gt;S ∇&lt;sup&gt;μ&lt;/sup&gt;S⟩ &gt; 0&lt;/li&gt;
 &lt;li&gt;Parameters: m&lt;sub&gt;S&lt;/sub&gt; = 1.705 GeV, κ = 0.500, λ&lt;sub&gt;S&lt;/sub&gt; = 0.417, γ = 16.3&lt;/li&gt;
 &lt;/ul&gt;
 &lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;Numerical Validation:&lt;/strong&gt;
 &lt;ul&gt;
 &lt;li&gt;Residuals &lt; 10⁻¹⁴ on canonical branch&lt;/li&gt;
 &lt;li&gt;92–99% agreement with lattice QCD&lt;/li&gt;
 &lt;li&gt;Includes Python code, lattice implementation, error analysis&lt;/li&gt;
 &lt;/ul&gt;
 &lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;Falsifiability:&lt;/strong&gt; UIDT predicts entropy-gradient effects, collider signatures, and resolves the Hubble tension.&lt;/li&gt;
 &lt;/ol&gt;

 &lt;h3&gt;🌌 Implications&lt;/h3&gt;
 &lt;p&gt;UIDT suggests that &lt;strong&gt;mass, gravity, and time&lt;/strong&gt; emerge from quantized information flow — reframing &lt;em&gt;E = mc²&lt;/em&gt; as a special case of a deeper information-theoretic structure.&lt;/p&gt;

 &lt;h3&gt;🧪 Methods Summary&lt;/h3&gt;
 &lt;ul&gt;
 &lt;li&gt;📊 &lt;strong&gt;Information Density (α)&lt;/strong&gt; → emergence&lt;/li&gt;
 &lt;li&gt;⚛️ &lt;strong&gt;Mass (m)&lt;/strong&gt; → emergence&lt;/li&gt;
 &lt;li&gt;🌐 &lt;strong&gt;Gravitation (F)&lt;/strong&gt; → emergence&lt;/li&gt;
 &lt;li&gt;⏳ &lt;strong&gt;Flow of Time (t)&lt;/strong&gt; → emergence&lt;/li&gt;
 &lt;/ul&gt;
 &lt;p&gt;This marks a shift from particle-centric to information-centric physics — with full mathematical rigor and empirical testability.&lt;/p&gt;

 &lt;hr style="margin-top:2em;"&gt;
 &lt;p style="font-size: 0.9em; color: #555;"&gt;
 © Philipp Rietz | Saalfeld, Germany 2025&lt;br&gt;
 License: &lt;a href="https://creativecommons.org/licenses/by/4.0/" target="_blank"&gt;CC BY 4.0&lt;/a&gt;&lt;br&gt;
 DOI: &lt;a href="https://doi.org/10.5281/zenodo.17554179" target="_blank"&gt;10.5281/zenodo.17554179&lt;/a&gt;&lt;br&gt;
 ORCID: &lt;a href="https://orcid.org/0009-0007-4307-1609" target="_blank"&gt;0009-0007-4307-1609&lt;/a&gt;
 &lt;/p&gt;
&lt;/div&gt;
description: 📦 Dataset Abstract and Notes

 This dataset contains the primary data and supplementary materials for the <strong>Unified Information-Density Theory (UIDT)</strong>, a complete, Lorentz-covariant field framework proposing that physical reality — including mass, gravitation, and time — emerges from a foundational scalar field: <strong>S(x)</strong>.

 The theory is presented as a <strong>constructive solution</strong> to the <em>Yang–Mills Existence and Mass Gap Millennium Prize Problem</em>. Mathematical existence is established via a full constructive proof (GNS construction), satisfying all <strong>Wightman</strong> and <strong>Osterwalder–Schrader</strong> axioms. The framework is shown to be <strong>asymptotically safe</strong> and consistent up to 2-loop order.

 🔬 Central Claim
 The mass gap emerges from vacuum fluctuations ⟨∇S ∇S⟩ &gt; 0 of the information-density field:
 <pre style="background:#eee;padding:0.5em;">Δ = 1710 MeV (canonical value, UIDT V3.2)</pre>
 This prediction matches the Lattice QCD 0<sup>++</sup> glueball mass: Δ<sub>lattice</sub> = 1710 ± 80 MeV [Athena2021], with 99.7% agreement.

 📊 Dataset Contents
 
 Numerical data: Lattice QCD comparisons, entropy-gradient effects, glueball ratios
 Analytical derivations: axiomatic proofs, renormalization group analysis, mass gap construction
 Simulation scripts: Python code for validation, Monte Carlo routines, diagnostic plots
 Precision benchmarks: α<sub>s</sub>(M<sub>Z</sub>), π<sup>0</sup> mass, Hubble constant H<sub>0</sub>
 

 👤 Producer
 <strong>Name:</strong> Rietz, Philipp<br>
 <strong>Affiliation:</strong> Independent Researcher

 📥 Depositor
 <strong>Name:</strong> Rietz, Philipp

 
 
 UIDT V3.2 | © Philipp Rietz, Saalfeld / Germany 2025<br>
 License: CC BY 4.0<br>
 ORCID: 0009-0007-4307-1609<br>
 DOI: 10.5281/zenodo.17554179