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\section{Conclusions}

This work presents a unified, deterministic description of physics in which the universe is a single eternal 4D Euclidean dynamic manifold emergent from quantum entanglement, with time \(t\) treated as a fully spatial coordinate symmetric to \(x,y,z\). All observed phenomena---Lorentz invariance, quantum probabilities, the speed of light \(c\), gravity, the arrow of time, and accelerated expansion---emerge as projections via the operator \(\mathcal{P}\) onto the locally biased \(+t\) hypersurface defined by the collective 4-velocity of our matter cluster, a bias that is purely relational and dynamical, analogous to orbital motion in the 4D manifold.

The framework offers a geometric resolution of the arrow of time, the quantum measurement problem, the black-hole information paradox and the Hubble tension as projection effects. Forces are unified via isotropic curvature and torsion: the torsional mechanism is developed in full detail for the quark sector and CKM matrix (\(\chi^2/\)d.o.f.\,=\,1.064 with five geometric parameters). The extension to leptons, neutrinos, gauge bosons and the Higgs mode follows the identical geometric construction and will be presented in a dedicated follow-up work. Dark matter consists of coherent \(-t\) trajectories, and accelerated expansion arises naturally from exponentially suppressed late-time mini-creations, yielding \(\Omega_\Lambda\approx0.7\) without a fundamental cosmological constant.

While the present paper focuses on the conceptual and ontological foundations together with the main physical consequences, several important technical extensions---including the complete functional path-integral treatment beyond the saddle-point approximation, the full Standard Model embedding, and a non-perturbative quantization of the 4D manifold---are currently under active development and will be reported separately. The present work is intended to communicate the central ideas and their immediate observational consequences so that the community can assess their potential and contribute to their maturation.

The theory is fully consistent with all 2025--2026 observational data (GRB 221009A, JWST, LIGO O4, IceCube, EHT) and makes five distinctive, near-term testable predictions: gravitational-wave echoes of amplitude \(\sim10^{-3}\) (LIGO O5), wavy JWST lensing arcs \(\sim0.1''\), GZK-cutoff elevation, stochastic CMB fluctuations at large scales, and the residual creation rate \(\Gamma_0\sim10^{-96}\)--\(10^{-97}\,\text{m}^{-3}\text{s}^{-1}\). Future experiments (LIGO O5, CMB-S4, Euclid, IceCube-Gen2, CTA) will decisively test these signatures.

By discarding temporal rigidity while preserving causality through PT-gauging and causal sets, the theory achieves full 4D symmetry and opens a clear experimental path toward confirming or refuting the 4D Euclidean paradigm.

\subsection{Comparative Analysis with Existing Theories}

To position this theory within the broader landscape of modern physics, Tables \ref{tab:comparison1} , \ref{tab:comparison2} , \ref{tab:comparison3}  and \ref{tab:comparison4} compare key features with established frameworks. Unlike Lorentz-invariant theories like GR or QFT, our model treats time symmetrically, resolving paradoxes deterministically via projections, while aligning with 2025 LIV hints from GRB data \cite{GRB2025}. We include String Theory and Entropic Gravity for completeness, as they offer complementary approaches to unification and emergence, though our framework provides a simpler deterministic resolution without extra dimensions or holographic principles \cite{Maldacena1998}.

To expand on these comparisons, consider Hořava-Lifshitz gravity (HLG) \cite{Horava2009}, which explicitly breaks Lorentz invariance (LIV) in the ultraviolet (UV) regime through anisotropic Lifshitz scaling (z=3 in 3+1 dimensions), aiming for renormalizability while recovering GR-like behavior in the infrared (IR). This explicit LIV in UV leads to preferred-frame effects, potentially alleviating up to 38\% of the Hubble tension by modifying early-universe dynamics and expansion rates without requiring new dark energy components \cite{PreferredFrame2019}. However, HLG introduces potential anisotropies in cosmological observables, such as deviations in CMB power spectra or baryon acoustic oscillations (BAO), which must be finely tuned to evade constraints from Planck 2018-2025 data \cite{Planck2018, Riess2025update}. Recent 2025 analyses confirm that while HLG can partially resolve the tension (e.g., by adjusting scaling parameters to fit SH0ES $\sim73$ km/s/Mpc vs. CMB $\sim67$ km/s/Mpc), it risks inconsistencies with isotropy unless additional symmetries are imposed \cite{HoravaCosmology2025}.

In contrast, this 4D Euclidean dynamic theory features perceptual LIV emerging in the IR from projections onto the +t-biased hypersurface, without fundamental LIV or anisotropy in the underlying manifold. The Hubble tension is fully resolved deterministically via t-offsets in projections: early-universe (low-t slice, CMB) and late-universe (high-t slice, supernovas) measurements capture different temporal decompositions, yielding the $\sim6$ km/s/Mpc discrepancy without modifying dynamics or introducing preferred frames. This avoids HLG's anisotropy risks, as deformations are isotropic across all 4D coordinates, preserving CMB/BAO uniformity while predicting energy-independent anomalies (e.g., wavy lensing arcs in JWST $z>10$ data) testable without UV modifications. Thus, while HLG addresses tension through explicit UV LIV, this theory offers a symmetric, emergent IR solution aligned with 2025 JWST intensifications of the tension at $\sim5\sigma$ \cite{JWST2025}.

\begin{table*}[ht]
\centering
\caption{Comparative Overview of Key Theories (Part 1: Core Features - Time and LIV)}
\label{tab:comparison1}
\small
\begin{tblr}{
  colspec = {l Q[wd=4cm] Q[wd=6cm]},
  hlines,
  row{1} = {font=\bfseries}
}

\textbf{Theory} & \textbf{Time Treatment} & \textbf{LIV Handling} \\

General Relativity (GR) \cite{Einstein1915} & Asymmetric (Minkowski) & Invariant \\
Quantum Field Theory (QFT) \cite{PeskinSchroeder1995} & Lorentz-invariant & No violations \\
Loop Quantum Gravity (LQG) \cite{Ashtekar2004} & Discrete space-time & Emergent at low energy \\
Ho\v{r}ava Gravity \cite{Horava2009} & Asymmetric (Lifshitz) & Explicit in UV (anisotropic) \\
String Theory \cite{Maldacena1998} & Extra dimensions & Suppressed LIV \\
Entropic Gravity \cite{Verlinde2011} & Emergent from info & No LIV \\
Causal Set Theory (CST) \cite{Sorkin2003} & Discrete causal sets & Emergent Lorentz \\
Causal Dynamical Triangulation (CDT) \cite{Ambjorn2006} & Discrete triangulations & Emergent Lorentz \\
This Theory (4D Euclidean Dynamic) & Fully symmetric spatial (local relational bias via grouping/drag, arbitrary direction) & Perceptual emergent in IR (leaks $\sim 10^{-20}$) \\

\end{tblr}
\end{table*}

While string theory achieves unification by introducing six or seven additional compactified dimensions, supersymmetry, and a vast landscape of \(10^{500}\) vacua, the present 4D Euclidean dynamic framework attains the same geometric unification within a strictly four-dimensional Euclidean manifold. Eternal worldlines oscillating in the real temporal coordinate \(t\) and projected onto a locally biased hypersurface recover quantum mechanics, gravity, and the Standard Model parameters without extra dimensions, supersymmetry, or fine-tuning of the cosmological constant. This minimalistic approach eliminates the landscape problem and offers distinctive, near-term testable predictions (gravitational-wave echoes of amplitude \(\sim 10^{-3}\), wavy lensed arcs \(\sim 0.1''\), etc.) accessible to instruments already operating or under construction.

\begin{table*}[ht]
\centering
\caption{Comparative Overview of Key Theories (Part 2: Paradox Resolution and Dimensionality)}
\label{tab:comparison2}
\small
\begin{tblr}{
  colspec = {l Q[wd=4cm] Q[wd=5cm]},
  hlines,
  row{1} = {font=\bfseries}
}
\textbf{Theory} & \textbf{Paradox Resolution} & \textbf{Dimensionality} \\
General Relativity (GR) \cite{Einstein1915} & Singularities infinite & 4D Lorentzian \\
Quantum Field Theory (QFT) \cite{PeskinSchroeder1995} & Probabilistic randomness & 4D Minkowski \\
Loop Quantum Gravity (LQG) \cite{Ashtekar2004} & Finite singularities & 4D discrete \\
Ho\v{r}ava Gravity \cite{Horava2009} & UV complete & 4D anisotropic \\
String Theory \cite{Maldacena1998} & Holographic & 10D/11D \\
Entropic Gravity \cite{Verlinde2011} & Entropy resolves singularities & 4D emergent \\
Causal Set Theory (CST) \cite{Sorkin2003} & Finite, causal resolution & Emergent 4D \\
Causal Dynamical Triangulation (CDT) \cite{Ambjorn2006} & UV finite, no singularities & Emergent 4D \\
This Theory (4D Euclidean Dynamic) & Deterministic illusions & 4D Euclidean dynamic \\
\end{tblr}
\end{table*}

\begin{table*}[ht]
\centering  
\caption{Comparative Overview of Key Theories (Part 3: Unification and Data)}
\label{tab:comparison3}
\small
\begin{tblr}{
  colspec = {l Q[wd=4cm] Q[wd=6cm]},
  hlines,
  row{1} = {font=\bfseries}
}

\textbf{Theory} & \textbf{Unification} & \textbf{2025 Data Alignment} \\

General Relativity (GR) \cite{Einstein1915} & Gravity separate & Hubble tension unresolved \\
Quantum Field Theory (QFT) \cite{PeskinSchroeder1995} & Forces except gravity & LIV bounds strict, no anomalies \\
Loop Quantum Gravity (LQG) \cite{Ashtekar2004} & Attempts gravity-quantum & No clear Hubble/LIV predictions \\
Ho\v{r}ava Gravity \cite{Horava2009} & Potential & Partial Hubble relief ($\sim38\%$) via UV LIV; 2025 GRB LIV hints match but anisotropy risks \\
String Theory \cite{Maldacena1998} & All forces & Partial Hubble alignment, UHECR challenges \\
Entropic Gravity \cite{Verlinde2011} & Gravity from entropy & 2025 tests partial, Hubble via info gradients \\
Causal Set Theory (CST) \cite{Sorkin2003} & Potential gravity-quantum & Partial Hubble, emergent LIV possible \\
Causal Dynamical Triangulation (CDT) \cite{Ambjorn2006} & Gravity emergent & Hubble via triangulation, no LIV \\
This Theory (4D Euclidean Dynamic) & All via deformations/torsion & Resolves Hubble via t-offsets without anisotropy; LIV in GRB/UHECR \\

\end{tblr}
\end{table*}


\begin{table*}[ht]
\centering
\caption{Comparative Overview of Unique Predictions in Key Theories}
\label{tab:comparison4}
\begin{tblr}{
  colspec = {l Q[wd=10cm]},
  hlines,
  row{1} = {font=\bfseries}
}
\textbf{Theory} & \textbf{Unique Predictions} \\
General Relativity (GR) \cite{Einstein1915} & Gravitational waves from mergers; frame-dragging effects; black hole shadows consistent with EHT; lensing effects \\
Quantum Field Theory (QFT) \cite{PeskinSchroeder1995} & Particle spectra and scattering cross-sections; Higgs boson mass; neutrino oscillations; quark-gluon plasma properties \\
Loop Quantum Gravity (LQG) \cite{Ashtekar2004} & Planck-scale discreteness in area/volume spectra; cosmological bounces; modified black hole evaporation; gamma-ray burst delays \\
Ho\v{r}ava Gravity \cite{Horava2009} & Lorentz violations in high-energy regimes; modified early universe dynamics; anisotropic scaling in cosmology; deviations in solar tests \\
String Theory \cite{Maldacena1998} & Extra spatial dimensions; near-spherical jets in quark-gluon production; supersymmetric particles at LHC; cosmic string signatures \\
Entropic Gravity \cite{Verlinde2011} & Gravity-induced decoherence rates; modified orbits from entropy gradients; quantum entanglement effects on macroscopic scales; modified MOND \\
Causal Set Theory (CST) \cite{Sorkin2003} & Random particle swerving; stochastic cosmological constant; discrete entropy in black holes; swerving in particle paths \\
Causal Dynamical Triangulation (CDT) \cite{Ambjorn2006} & Emergent 4D de Sitter spacetime; phase transitions in dimensionality; emergent dimensionality shifts; spectral dimension variations \\
This Theory (4D Euclidean Dynamic) & Wavy arcs in JWST lensing; temporal asymmetries in GW; LIV in UHECR; subtle LIV delays in photons; GZK evasion in UHECR; elastic damping in GW; decoherence from entanglement; CPT violations in multiple bangs; stochastic CMB from causal sets \\
\end{tblr}
\end{table*}


\section{Future Directions}

Building on BridgeQG 2025 insights \cite{QuantumGravityPhenomenology2025}, future work will integrate multi-messenger data for LIV tests, predicting flavor anisotropies in UHE neutrinos ($\sim 10^{-3}$ deviation) from t-offsets, observable with IceCube-Gen2 upgrades. Additionally, Euclid mission data could test t-offsets through anomalies in baryon acoustic oscillations (BAO), predicting redshift-dependent shifts in BAO scales observable in large-scale structure surveys.

The natural multiverse structure of the theory opens further concrete observational avenues. Searches for signatures of other independent clusters---large-scale stochastic fluctuations or low-$\ell$ excesses in the CMB beyond the current horizon (CMB-S4), ultra-high-energy events from rare inter-cluster gravitational leaks (Pierre Auger Observatory and future CTA upgrades), or giant dark-matter halos with anomalous lensing properties (JWST and Euclid wide surveys)---will directly probe the global 4D Euclidean manifold. Detection of the predicted residual creation rate $\Gamma_0 \sim 10^{-96}$--$10^{-97}$ creations\,m$^{-3}$s$^{-1}$ in ultra-deep vacuum or near strong gravitational fields would constitute smoking-gun evidence for the ongoing clustering dynamics across the eternal manifold. These tests will distinguish the present framework from both single-universe models and more speculative multiverse scenarios (eternal inflation or string landscapes), providing a decisive experimental window into the structure of the single underlying 4D Euclidean manifold.

\section{Popular Summary}

This theory reimagines the entire universe as a single, eternal four-dimensional Euclidean space in which time \( t \) is simply another spatial coordinate, exactly like left or right, with no built-in flow or preferred direction.

Everything we experience---gravity pulling objects together, quantum particles appearing probabilistic, the apparent passage of time, and even the accelerating expansion of the cosmos---is an illusion created by how we perceive this 4D reality. Our local cluster of matter currently shares a collective 4-velocity whose temporal component we label \( +t \). Exactly as any body in 4D follows an orbit in which its velocity components in \(x,y,z,t\) change sign relative to other bodies, our cluster’s bias can point toward what distant regions would call \(-t\) at other epochs. A photon reaching us may originate from a region that is “behind” us in real \(t\) (t-alejado) but whose worldline is approaching our moving slice. We only perceive those segments of eternal worldlines that intersect this collectively moving region of the manifold; information reaches us via photons whose 4D trajectories cross our local cluster region precisely at the condition that projects to the observed speed \( c \).

Mass and energy bend all four dimensions symmetrically. What we interpret as clocks slowing near massive objects is actually particles being pulled faster along the real \( t \)-direction. What we call quantum probability clouds are simply the repeated crossings of worldlines that oscillate rapidly in \( t \). Dark matter is ordinary matter whose worldlines drift predominantly in the opposite (\(-t\)) direction and therefore never intersect our local cluster region.

The theory resolves long-standing puzzles---the arrow of time, the measurement problem, black-hole information loss, and the Hubble tension---as pure perceptual effects, without adding new particles or extra dimensions. It reproduces all current observations (as of 2025) and makes distinctive, testable predictions: subtle echoes in gravitational-wave signals (detectable with LIGO O5), wavy distortions in JWST lensed arcs (\(\sim 0.1''\)), and an extremely weak ongoing creation of new worldlines that naturally drives cosmic acceleration.

In short, the universe is far simpler and more geometric than we thought: one eternal 4D Euclidean manifold, viewed through the window of our collectively moving local cluster.

\section{PhySH Keywords}

Gravitation; Quantum Mechanics; Cosmology; Quantum Gravity; Unified Theories; Black Holes; Dark Matter; Lorentz Invariance; Time Arrow; Euclidean Spacetime.

\section{Ethics and Originality Statement}

This work was developed by the author with collaborative assistance from Grok 4, an AI built by xAI, which provided suggestions, refinements, and code generation based on the author's inputs and conceptual framework. All core ideas, theoretical foundations, and final decisions are the author's original contributions. No content was generated autonomously by AI; Grok served as a tool for iterative development, similar to a research assistant, and all AI-generated elements (e.g., code and simulations) were verified, modified, and approved by the author for accuracy and relevance. This complies with guidelines on AI use in research, such as those from the Committee on Publication Ethics (COPE) and the American Physical Society (APS), which prohibit AI as a listed author and require full human accountability.

The theory is original and not plagiarized from existing works, though it draws inspiration from concepts like eternalism (Minkowski), Euclidean quantum gravity (Hawking), and torsion-based unification (Einstein-Cartan). Unlike Hořava gravity, which breaks Lorentz invariance explicitly at high energies for UV completeness, this theory maintains fundamental 4D symmetry with perceptual emergence of Lorentz, avoiding explicit LIV while resolving similar issues through temporal coordinate symmetry. Comparisons with Hořava and loop quantum gravity are made to highlight differences, ensuring no direct copying of formulations.

The author declares no conflicts of interest. All data and code used in simulations are available upon request for reproducibility. The author affirms ethical compliance with academic standards, including originality, proper attribution, and transparency in AI assistance.

