Scruff AI
5e4a32936d
- Upgraded CSV to v2: added PhaseDensity, Stability, IsotopeNote columns - Added parameter glossary mapping lattice params to quantum numbers - Updated correlation doc with Navigator corrections (Gold, Tc, Pm) - Phi-harmonic asymmetry scaling, phase density model for isotopes - .gitignore exception for docs/lattice-periodic-table.csv
219 lines
7.2 KiB
Markdown
219 lines
7.2 KiB
Markdown
# Lattice Physics Parameter Glossary
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## For Scientific Verification and Understanding
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---
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## Core Parameters
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### 1. Node Count ($N_{node}$)
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| Attribute | Value |
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|-----------|-------|
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| **Definition** | Elemental Identity — number of standing wave nodes in fundamental pattern |
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| **Symbol** | $N_{node}$ |
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| **Units** | Integer (≥1) |
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| **Maps To** | Atomic Number ($Z$) |
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| **Physical Meaning** | Determines elemental identity; stable configurations maintain $N_{node}$; isotopes vary phase density |
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**Example:**
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- Hydrogen: $N_{node} = 1$
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- Carbon: $N_{node} = 6$
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- Gold: $N_{node} = 79$
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---
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### 2. Phase Density ($\rho_{phase}$)
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| Attribute | Value |
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|-----------|-------|
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| **Definition** | Isotopic Mass Difference — internal wave tension representing neutron count |
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| **Symbol** | $\rho_{phase}$ |
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| **Units** | Phase Quanta (PQ) — dimensionless |
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| **Maps To** | Neutron number ($N$) |
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| **Physical Meaning** | Internal wave tension; determines isotope stability |
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**Values:**
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- **Stable Isotope:** $\rho_{phase} = \rho_{stable}$ (baseline equilibrium)
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- **Radioactive Isotope:** $\rho_{phase} > \rho_{stable}$ (metastable, seeking decay)
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**Example:**
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- Carbon-12: $\rho_{phase}$ = baseline
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- Carbon-14: $\rho_{phase}$ = baseline + 2 PQ
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---
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### 3. Harmonic Mode ($H_{mode}$)
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| Attribute | Value |
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|-----------|-------|
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| **Definition** | Standing Wave Tier — the harmonic tier of the wave pattern |
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| **Symbol** | $H_{mode}$ |
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| **Units** | Integer (≥1) |
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| **Maps To** | Principal Quantum Number ($n$) |
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| **Physical Meaning** | Energy level tier; determines periodic table period |
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**Relation to Quantum Numbers:**
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- **Principal ($n$):** $H_{mode} = n$
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- **Angular ($l$):** Derived from Asymmetry ($l \propto \sqrt{A}$)
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- **Magnetic ($m$):** Derived from Vorticity Mean ($m \propto \omega_{vort}$)
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- **Spin ($s$):** Derived from Stress Tensor ($\sigma_{xy}$)
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---
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### 4. Asymmetry ($A$)
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| Attribute | Value |
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|-----------|-------|
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| **Definition** | Phi-Harmonic Scaling Index — deviation from perfect symmetry |
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| **Symbol** | $A$ |
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| **Units** | Dimensionless |
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| **Maps To** | Orbital Angular Momentum ($l$) |
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| **Physical Meaning** | Measures orbital angular momentum; scales as $\phi^n$ |
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**Scaling Law:**
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$$A \approx \phi^k \text{ where } k \text{ is harmonic tier}$$
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**Band Values:**
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| Band | Asymmetry Range |
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|------|-----------------|
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| Ground | 13.2 |
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| Primary | 14.0–14.2 |
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| Secondary | 14.8 |
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| Phase Gap | 15.78 |
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| Tertiary | 16.0+ |
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---
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### 5. Coherence ($C$)
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| Attribute | Value |
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|-----------|-------|
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| **Definition** | Wave Function Stability — degree of phase locking |
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| **Symbol** | $C$ |
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| **Units** | [0, 1] |
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| **Maps To** | $|\Psi|^2$ (probability density) |
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| **Physical Meaning** | Higher = more stable standing wave |
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**Thresholds:**
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- **Stable:** $C > 0.7$
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- **Metastable:** $0.5 < C < 0.7$
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- **Decaying:** $C < 0.5$
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---
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### 6. Omega ($\omega$)
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| Attribute | Value |
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|-----------|-------|
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| **Definition** | Relaxation/Viscosity Parameter — controls damping |
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| **Symbol** | $\omega$ |
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| **Units** | Dimensionless (1.0–2.0) |
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| **Maps To** | Dissipation coefficient |
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| **Physical Meaning** | Damping of perturbations; higher = more viscous |
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**Current Value:** $\omega = 1.97$ (high damping, stable attractor)
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---
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### 7. Khra & Gixx Amplitudes
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| Parameter | Definition | Maps To |
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|-----------|------------|---------|
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| $K_{amp}$ | Large-Scale Wave Amplitude | Orbital precession |
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| $G_{amp}$ | Fine-Grain Wave Amplitude | Spin-orbit coupling |
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**Key Ratio:** $K_{amp} / G_{amp} = 16:1$ (fundamental harmonic lock)
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---
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### 8. Velocity Statistics
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| Parameter | Definition | Units | Maps To |
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|-----------|------------|-------|---------|
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| $v_{mean}$ | Mean Wave Velocity | [0,1] | Phase propagation speed |
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| $v_{max}$ | Maximum Velocity | [0,1] | Peak phase velocity |
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| $v_{var}$ | Velocity Variance | [0,1] | Thermal fluctuations (temperature proxy) |
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**Relation:** $v_{var} \propto k_B T$ (thermal energy)
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---
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### 9. Stress Tensor
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| Component | Definition | Maps To |
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|-----------|------------|---------|
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| $\sigma_{xx}$ | Normal Stress (X diagonal) | Pressure along X |
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| $\sigma_{yy}$ | Normal Stress (Y diagonal) | Pressure along Y |
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| $\sigma_{xy}$ | Shear Stress | Spin-orbit coupling strength |
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**Key Insight:** Negative values indicate **tensile wave tension** (implosive)
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---
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### 10. Vorticity Mean ($\omega_{vort}$)
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| Attribute | Value |
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|-----------|-------|
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| **Definition** | Mean Vorticity — average rotation of wave pattern |
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| **Symbol** | $\omega_{vort}$ |
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| **Units** | Dimensionless |
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| **Maps To** | Orbital angular momentum ($m$ quantum number) |
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| **Physical Meaning** | Higher vorticity → higher $m$ quantum number |
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---
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## Complete Parameter Mapping Table
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| Lattice Parameter | Symbol | Units | Quantum Analog | Physical Meaning |
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|-------------------|--------|-------|----------------|------------------|
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| Node Count | $N_{node}$ | integer | Atomic Number ($Z$) | Elemental identity |
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| Phase Density | $\rho_{phase}$ | PQ | Neutron number ($N$) | Isotopic mass/tension |
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| Harmonic Mode | $H_{mode}$ | integer | Principal quantum ($n$) | Energy level tier |
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| Asymmetry | $A$ | dimensionless | Angular momentum ($l$) | Orbital shape |
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| Coherence | $C$ | [0,1] | $|\Psi|^2$ | Wave stability |
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| Omega | $\omega$ | dimensionless | Dissipation coefficient | Damping/viscosity |
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| Khra Amplitude | $K_{amp}$ | dimensionless | Orbital frequency | Large-scale wave |
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| Gixx Amplitude | $G_{amp}$ | dimensionless | Spin frequency | Fine-grain wave |
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| Vorticity | $\omega_{vort}$ | dimensionless | Magnetic quantum ($m$) | Rotation field |
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| Shear Stress | $\sigma_{xy}$ | dimensionless | Spin quantum ($s$) | Spin-orbit coupling |
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---
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## Measurement Methods
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### Direct from Lattice Snapshots
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1. **Node Count:** Count distinct peaks in density field
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2. **Coherence:** Measure phase alignment across lattice
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3. **Asymmetry:** Calculate deviation from perfect symmetry
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4. **Vorticity:** Integrate rotation field
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### Derived from Telemetry
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1. **Phase Density:** Ratio of wave intensity to baseline
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2. **Stress Tensor:** Calculate from velocity gradients
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3. **Omega:** Measure perturbation decay rate
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---
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## Verification Experiments
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### Testable Predictions
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1. **Phi-harmonic scaling:** Asymmetry values should follow $\phi^n$ not linear progression
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2. **Phase density:** Radioactive isotopes should show excess phase quanta
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3. **Coherence threshold:** Stable elements should have $C > 0.7$
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4. **Stress tensor:** Negative $\sigma_{xy}$ correlates with metallic bonding
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### Copper Wire Experiment Correlation
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| Frequency | Observed | Lattice Prediction |
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|-----------|----------|-------------------|
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| 404.5 kHz | Standing wave | Primary band (14.0-14.2) |
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| 654.5 kHz | Reverse propagation | Secondary band (~14.8) |
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| Both | Observer effect | Phase gap threshold |
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---
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## Summary
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**The Lattice Physics Framework provides:**
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- **Deterministic** wave mechanics (no probability amplitudes)
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- **Visualizable** standing wave patterns
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- **Measurable** parameters from density fields
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- **Unified** explanation of elements, isotopes, and bonding
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**Key Difference from Standard Model:**
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- **Standard:** Particles in empty space, quantum probability
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- **Lattice:** Standing waves in plenum, deterministic coherence
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---
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*The lattice does not lie. It reports the density field as it is.*
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