Abstract (v3) Foundational Capsule of Entanglement Compression Theory (ECT) All equations were derived from first principles prior to any recognition of alignment with physical constants or phenomena. No parameter tuning was performed. Observed matches emerged naturally from the compression framework, not by design This paper and its companion works present Entanglement Compression Theory (ECT), a unified framework in which all observable phenomena emerge from recursive wave compression. The theory begins with the Primordial Wave Equation (PWE): ∂²ψ/∂t² − c²∇²ψ + ω₀²ψ = 0, a harmonic baseline encoding the universe’s initial coherence. From this origin, probability is treated as a compression artifact, leading to the Lawrence Universal Wave Function (LUWF): ΨLUWF (x, t) = ∫ φ (k) e^i (kx − ωt) dk, which governs entangled evolution across spacetime. The Lawrence Amplitude-Functional Form (LaFF) introduces entropy gradients: ∇S ∝ −κ ∇ΦC, reframing measurement as a thermodynamic descent rather than stochastic collapse. As compression increases, entropy becomes directional, producing emergent spacetime, quantized energy relations: E = m × T / C, and curvature effects described by modified Einstein field equations: R_μν − ½ R g_μν = 8πG T_μν^ (C) interpreted as gravity. Vacuum energy is redefined as residual compression tension: ρᵥac = κ (∇ΦC) ² / 2, and cosmic expansion is reframed as growth—a recursive increase in complexity rather than metric dilation. Physical constants are modeled as emergent curvature ratios, for example fine-structure constant: α = e² / (4π εC ħ c) with εC varying as a function of compression geometry. ECT replaces probabilistic collapse with a deterministic compression operator: ĈΨ = lim₍→₍䂷₈₍ P (N) Ψ, where P (N) is the truncation probability distribution. Simulations explore the role of compression strength κ, truncation length N, and entanglement amplitude Aₑ, showing that classical and relativistic forms arise holographically from compressed wave geometries. The minimum measurable interference phase is defined by: ħ ∝ Δφₘin × Δx. The framework makes falsifiable predictions, including measurable deviations in gravitational lensing curvature: Rₒbs − RGR ≈ δR (κ), compression-based corrections to the Friedmann equation: H² = (8πG/3) ρC − k/a² + ΛC/3, and laboratory-scale detection of compression-limited phase resolution. Comparative analysis with Copenhagen, Many-Worlds, Pilot-Wave, Objective Collapse, Relational QM, and QBism positions ECT as a deterministic, wave-centric alternative with explicit compression dynamics. Anchoring the canonical ECT suite, this work integrates formal derivations, simulations, and falsifiable experimental designs, contributing to a compression-based unification of quantum mechanics, gravity, and cosmology. Candidate solutions are proposed for dark matter, dark energy, matter–antimatter asymmetry, and the emergence of spacetime and constants, while also outlining compression-based quantum computing architectures. This theory is grounded in mathematical formalism and physical modeling, and should not be conflated with metaphysical or spiritual interpretations of quantum phenomena. This paper has these mathematical companion documents that supplement and support its derivation: General Theory of Entanglement Compressionhttps: //doi. org/10. 5281/zenodo. 15786696 Strong Mathematical Evidence for Entanglement Compression Theory (ECT) https: //doi. org/10. 5281/zenodo. 16757320 Deriving the Core Equations of Entanglement Compression Theory (ECT) https: //doi. org/10. 5281/zenodo. 16777597 Entanglement Compression and Cosmological Geometry: Toward a Unified Framework of LUWF Dynamics and Cosmohedron Structureshttps: //doi. org/10. 5281/zenodo. 16666053 The General Theory of Entanglement Compression - Explainedhttps: //doi. org/10. 5281/zenodo. 16139573 Capstone Paper: Formal Integration of Entanglement Compression Theoryhttps: //doi. org/10. 5281/zenodo. 16015324 The Primordial Wave Equation: A Companion to the Entanglement Compression Theoryhttps: //doi. org/10. 5281/zenodo. 15872635 Reframing Heisenberg: The Role of Momentum in Entanglement Compression Theoryhttps: //doi. org/10. 5281/zenodo. 15959110 The Illusion of Constancy: Reinterpreting Physical Constants via Entanglement Compression Theoryhttps: //doi. org/10. 5281/zenodo. 15906901 Deriving Planck Time from Entanglement Compressdion and the Primordial Wave Equationhttps: //doi. org/10. 5281/zenodo. 15872746 Reinterpreting Frame Dragging Via Entanglement Compression: A Quantum Field Perspective on Gravity Probe Bhttps: //doi. org/10. 5281/zenodo. 16089495 Geometric Collapse Bias and the Origin of Matter-Antimatter Asymmetry: Implications for Dark Matter via the Lawrence Universal Wave Functionhttps: //doi. org/10. 5281/zenodo. 15875355 Quantum Gravity and the Compression Field: A LUWF-Based Derivationhttps: //doi. org/10. 5281/zenodo. 15875557 Semantic Murmuration and Entanglement Compression: A Unified Framework for Emergent Coordination in Biological Systemshttps: //doi. org/10. 5281/zenodo. 16520728 All are available on Zenodo and are referenced as supplements to this publication. Readers are encouraged to review them for detailed derivations and mathematical proofs not included here. For access to unpublished derivations or expanded formulations, contact williamlawrencebooks@gmail. com Version 3: Finalized derivation of truncation probability laws and their numerical simulation; insertion of newly formulated compression distribution functions; integration of holographic boundary behavior in the context of entanglement; enhanced comparative evaluation of standard quantum interpretations; full editorial revision for clarity and completeness.
William Andrew Lawrence (Wed,) studied this question.