+## 1. Introduction: The Crisis in Fundamental Physics and a Novel Approach +### 1.1. The Hierarchy Problem: A Challenge to Naturalness in the Standard Model +### 1.2. Limitations of Existing Beyond-Standard-Model Solutions +### 1.3. Introducing a Process Ontology and Frequency-Centric View +### 1.4. The Core Hypothesis: Mass as a Stable Frequency/Resonant State +### 1.5. Research Aims and Objectives + +## 2. Foundational Concepts: Process, Frequency, and Mass +### 2.1. The Process Ontology: Autaxys, Dynamic Medium, and Patterns +#### 2.1.1. Reality as a Dynamically Self-Generating and Self-Organizing System (Autaxys) +#### 2.1.2. The Fundamental Dynamic Medium and Continuous Processing +#### 2.1.3. Observable Phenomena as Dynamic Relational Patterns +### 2.2. The Frequency-Centric View of Reality +#### 2.2.1. All Phenomena Characterized by Intrinsic Processing Frequencies +#### 2.2.2. Two Perspectives on Energy: Mass vs. Oscillation (E=mc², E=ħω) +### 2.3. The Mass-Frequency Identity: m=ω in Natural Units +#### 2.3.1. The Bridge Equation: ħω_C = m_0c² +#### 2.3.2. The Veil of Constants: ħ and c as Parameters of the Dynamic Medium and Autaxys +#### 2.3.3. The Power of Natural Units to Reveal Fundamental Identity (ω_C = m_0) +### 2.4. Physical Interpretation: Mass as a Resonant State of Fundamental Patterns +#### 2.4.1. Resonance, Stability, and the Pattern Hierarchy +#### 2.4.2. The Compton Frequency and Zitterbewegung as Manifestations of Intrinsic Processing +#### 2.4.3. Elementary Particles as Stable, Self-Sustaining Standing Waves/Resonant Patterns +#### 2.4.4. The Particle Mass Hierarchy as a Discrete Spectrum of Allowed Resonant Frequencies +#### 2.4.5. Unstable Particles as Transient, Dissonant States + +## 3. Theoretical Framework: The Generative Principle and Spectrum Structure +### 3.1. The Dynamic Substrate: The Fundamental Medium and Vacuum Energy +#### 3.1.1. Quantum Fields as Emergent from the Dynamic Medium +#### 3.1.2. The Vacuum as a Plenum of Zero-Point Energy Fluctuations (Ongoing Processing) +#### 3.1.3. The Higgs Mechanism Reinterpreted: Impedance to Oscillation/Propagation +### 3.2. The Generative Principle: Identifying the Mechanism for Stable Frequencies +#### 3.2.1. The Spectrum of Stable Frequencies Arises from the Medium's Dynamics/Generative Principle +#### 3.2.2. Exploring Candidate Spectrum-Generating Mechanisms +##### 3.2.2.1. Spectral Geometry and Operator Theory +##### 3.2.2.2. Non-linear Dynamics and Stable Excitations (Solitons) +##### 3.2.2.3. Direct Connections to Number Theory and L-Functions +### 3.3. Formalizing the "Prime Frequency" Analogy and Physical Stability +#### 3.3.1. Fundamental Stability and Physical Irreducibility ("Primeness") +#### 3.3.2. Composite Structures and Derived Stability +#### 3.3.3. The Nature of "Primeness" as Intrinsic Stability Derived from the Substrate +#### 3.3.4. Spectral Distribution and the Analogy to Number Theory (Non-uniformity, Sparsity, Gaps) +### 3.4. Reframing the Hierarchy Problem as an Intrinsic Spectral Gap +#### 3.4.1. The "Spectral Desert" Between Electroweak and Planck Scales +#### 3.4.2. Hierarchy as a Consequence of Fundamental Absence of Stable States in the Gap + +## 4. Analytical Engine and Generative Application (The Autaxys Framework) +### 4.1. The Autaxys Formal Toolkit: Modeling and Analyzing System Structure and Harmonic Patterns +### 4.2. Harmonic Pattern Synthesis: Translating Insights into Structured Outputs and Guiding Interventions + +## 5. Interactions and Emergent Phenomena +### 5.1. Reinterpreting Fundamental Forces: Altering Resonant States, Transferring Modulatory Information +### 5.2. Reinterpreting Gravity and Spacetime: Macroscopic Emergence from Collective Dynamics +#### 5.2.1. Spacetime as a Dynamic Entity Connected to Fundamental Patterns +#### 5.2.2. Gravitational Redshift as Spacetime Modulating Local Processing Tempo/Resonant Frequencies + +## 6. An Information-Theoretic Framework: Mass, Frequency, and Cosmic Computation +### 6.1. Dynamic Relational Patterns as Fundamental Ontological Units +### 6.2. Mass as Informational Complexity +### 6.3. Frequency as Operational Tempo/Processing Rate +### 6.4. Resonance (Physical Stability) <=> Self-Validation (Informational Coherence) +### 6.5. The Identity ω_C = m_0 as a Law of Cosmic Computation +### 6.6. Dissolving Dualisms (Information/Substance, Discrete/Continuous) + +## 7. Explanatory Power and Unification +### 7.1. Accounting for Cosmic Drive Towards Increasing Complexity (Autaxys) +### 7.2. Explaining Mathematical Elegance and Robustness of Physical Laws +### 7.3. Unifying Matter and Energy as Dynamic Relational Patterns +### 7.4. Unifying General Relativity and Quantum Mechanics +#### 7.4.1. GR as Emergent Macroscopic Geometry from Collective Dynamics +#### 7.4.2. QM as Describing Fundamental Discrete Processes and Excitations +#### 7.4.3. Dissolving the Discrete/Continuous Divide +### 7.5. Insights into Cosmological Puzzles +#### 7.5.1. The Vacuum (Dynamic Medium, Zero-Point Energy) +#### 7.5.2. Dark Energy (Cosmological Expression of Autaxys Dynamism) +#### 7.5.3. Dark Matter Candidates (Stable, Non-luminous Patterns) +#### 7.5.4. Quantum Measurement Problem (Resolution to Solidified Patterns) + +## 8. Analogies and Broader Implications +### 8.1. The Analogy with Neural Processing (Frequency Bands, Binding-by-Synchrony) +### 8.2. Frequency as a Universal Principle and Code for Energy and Information + +## 9. Empirical Touchpoints and Testable Predictions +### 9.1. Prediction of a Discrete Mass Spectrum and Explicit Spectral Gaps +### 9.2. Resonances and New Particles in High-Energy Collisions (Targeted Searches, Absence in Gaps) +### 9.3. Signatures of Fundamental Processing Granularity (Deviations from Continuity, Noise) +### 9.4. Detection of Intrinsic Medium Resonances/Relational Harmonics (Background Frequency Signatures) +### 9.5. Anomalies in Extreme Regimes Challenging Process Dynamics (High Energy Density, Black Holes, Early Universe) +### 9.6. Context-Dependent Variation in Emergent Parameters (Constants, Mass Ratios) +### 9.7. Cosmological Observables (CMB, Large-Scale Structure, Primordial Nucleosynthesis) + +## 10. Methodology +### 10.1. Phase 1: Foundational Literature Review +### 10.2. Phase 2: Mathematical Model Construction and Formalization (Generative Principle, Stability Criterion) +### 10.3. Phase 3: Phenomenological Analysis and Testable Prediction Derivation +### 10.4. Phase 4: Refinement and Iteration + +## 11. Conclusion and Future Work +### 11.1. Summary of the Framework +### 11.2. Potential Impact +### 11.3. Future Directions (Mathematical Development, Experimental Interaction, Interactions/Gravity, Computational Methods, Quantum Information/Holography) +### 11.4. Assessing Validity via Comprehensive Coherence (Logical Consistency, Explanatory Breadth, Compatibility with Observation, Productive Foundation)