resonance-engine/docs/parameter-glossary.md

Lattice Physics Parameter Glossary

For Scientific Verification and Understanding

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Core Parameters

1. Node Count (N_{node})

Attribute	Value
Definition	Elemental Identity — number of standing wave nodes in fundamental pattern
Symbol	N_{node}
Units	Integer (≥1)
Maps To	Atomic Number (Z)
Physical Meaning	Determines elemental identity; stable configurations maintain N_{node}; isotopes vary phase density

Example:

• Hydrogen: N_{node} = 1
• Carbon: N_{node} = 6
• Gold: N_{node} = 79

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2. Phase Density (\rho_{phase})

Attribute	Value
Definition	Isotopic Mass Difference — internal wave tension representing neutron count
Symbol	\rho_{phase}
Units	Phase Quanta (PQ) — dimensionless
Maps To	Neutron number (N)
Physical Meaning	Internal wave tension; determines isotope stability

Values:

• Stable Isotope: \rho_{phase} = \rho_{stable} (baseline equilibrium)
• Radioactive Isotope: \rho_{phase} > \rho_{stable} (metastable, seeking decay)

Example:

• Carbon-12: \rho_{phase} = baseline
• Carbon-14: \rho_{phase} = baseline + 2 PQ

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3. Harmonic Mode (H_{mode})

Attribute	Value
Definition	Standing Wave Tier — the harmonic tier of the wave pattern
Symbol	H_{mode}
Units	Integer (≥1)
Maps To	Principal Quantum Number (n)
Physical Meaning	Energy level tier; determines periodic table period

Relation to Quantum Numbers:

• Principal (n): H_{mode} = n
• Angular (l): Derived from Asymmetry (l \propto \sqrt{A})
• Magnetic (m): Derived from Vorticity Mean (m \propto \omega_{vort})
• Spin (s): Derived from Stress Tensor (\sigma_{xy})

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4. Asymmetry (A)

Attribute	Value
Definition	Phi-Harmonic Scaling Index — deviation from perfect symmetry
Symbol	A
Units	Dimensionless
Maps To	Orbital Angular Momentum (l)
Physical Meaning	Measures orbital angular momentum; scales as \phi^n

Scaling Law:

A \approx \phi^k \text{ where } k \text{ is harmonic tier}

Band Values:

Band	Asymmetry Range
Ground	13.2
Primary	14.0–14.2
Secondary	14.8
Phase Gap	15.78
Tertiary	16.0+

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5. Coherence (C)

Attribute	Value
Definition	Wave Function Stability — degree of phase locking
Symbol	C
Units	[0, 1]
Maps To	$
Physical Meaning	Higher = more stable standing wave

Thresholds:

• Stable: C > 0.7
• Metastable: 0.5 < C < 0.7
• Decaying: C < 0.5

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6. Omega (\omega)

Attribute	Value
Definition	Relaxation/Viscosity Parameter — controls damping
Symbol	\omega
Units	Dimensionless (1.0–2.0)
Maps To	Dissipation coefficient
Physical Meaning	Damping of perturbations; higher = more viscous

Current Value: \omega = 1.97 (high damping, stable attractor)

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7. Khra & Gixx Amplitudes

Parameter	Definition	Maps To
K_{amp}	Large-Scale Wave Amplitude	Orbital precession
G_{amp}	Fine-Grain Wave Amplitude	Spin-orbit coupling

Key Ratio: K_{amp} / G_{amp} = 16:1 (fundamental harmonic lock)

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8. Velocity Statistics

Parameter	Definition	Units	Maps To
v_{mean}	Mean Wave Velocity	[0,1]	Phase propagation speed
v_{max}	Maximum Velocity	[0,1]	Peak phase velocity
v_{var}	Velocity Variance	[0,1]	Thermal fluctuations (temperature proxy)

Relation: v_{var} \propto k_B T (thermal energy)

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9. Stress Tensor

Component	Definition	Maps To
\sigma_{xx}	Normal Stress (X diagonal)	Pressure along X
\sigma_{yy}	Normal Stress (Y diagonal)	Pressure along Y
\sigma_{xy}	Shear Stress	Spin-orbit coupling strength

Key Insight: Negative values indicate tensile wave tension (implosive)

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10. Vorticity Mean (\omega_{vort})

Attribute	Value
Definition	Mean Vorticity — average rotation of wave pattern
Symbol	\omega_{vort}
Units	Dimensionless
Maps To	Orbital angular momentum (m quantum number)
Physical Meaning	Higher vorticity → higher m quantum number

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Complete Parameter Mapping Table

Lattice Parameter	Symbol	Units	Quantum Analog	Physical Meaning
Node Count	N_{node}	integer	Atomic Number (Z)	Elemental identity
Phase Density	\rho_{phase}	PQ	Neutron number (N)	Isotopic mass/tension
Harmonic Mode	H_{mode}	integer	Principal quantum (n)	Energy level tier
Asymmetry	A	dimensionless	Angular momentum (l)	Orbital shape
Coherence	C	[0,1]	$	\Psi
Omega	\omega	dimensionless	Dissipation coefficient	Damping/viscosity
Khra Amplitude	K_{amp}	dimensionless	Orbital frequency	Large-scale wave
Gixx Amplitude	G_{amp}	dimensionless	Spin frequency	Fine-grain wave
Vorticity	\omega_{vort}	dimensionless	Magnetic quantum (m)	Rotation field
Shear Stress	\sigma_{xy}	dimensionless	Spin quantum (s)	Spin-orbit coupling

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Measurement Methods

Direct from Lattice Snapshots

1. Node Count: Count distinct peaks in density field
2. Coherence: Measure phase alignment across lattice
3. Asymmetry: Calculate deviation from perfect symmetry
4. Vorticity: Integrate rotation field

Derived from Telemetry

1. Phase Density: Ratio of wave intensity to baseline
2. Stress Tensor: Calculate from velocity gradients
3. Omega: Measure perturbation decay rate

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Verification Experiments

Testable Predictions

1. Phi-harmonic scaling: Asymmetry values should follow \phi^n not linear progression
2. Phase density: Radioactive isotopes should show excess phase quanta
3. Coherence threshold: Stable elements should have C > 0.7
4. Stress tensor: Negative \sigma_{xy} correlates with metallic bonding

Copper Wire Experiment Correlation

Frequency	Observed	Lattice Prediction
404.5 kHz	Standing wave	Primary band (14.0-14.2)
654.5 kHz	Reverse propagation	Secondary band (~14.8)
Both	Observer effect	Phase gap threshold

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Summary

The Lattice Physics Framework provides:

• Deterministic wave mechanics (no probability amplitudes)
• Visualizable standing wave patterns
• Measurable parameters from density fields
• Unified explanation of elements, isotopes, and bonding

Key Difference from Standard Model:

• Standard: Particles in empty space, quantum probability
• Lattice: Standing waves in plenum, deterministic coherence

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The lattice does not lie. It reports the density field as it is.