Experiment A4: SDKP Scaling Function Validation - FatherTimeSDKP/CEN- GitHub Wiki
🧪 Experiment A4: SDKP Scaling Function Validation
Objective:
To validate the SDKP (Scale–Density–Kinematic Principle) scaling function across particle classes by simulating and comparing mass predictions against known physical data using Shape–Dimension–Number (SD&N) encodings.
📌 Theoretical Background
The SDKP mass equation is derived from foundational axioms and is structured as:
[ M = \gamma \cdot (N \cdot S) + \beta \cdot S + \alpha \cdot N ]
Where:
- ( M ): mass of the particle/system
- ( N ): Number factor (SD&N vector)
- ( S ): Shape index (topological encoding)
- ( \alpha, \beta, \gamma ): Tuned scaling coefficients
- ( \rho ): Density scaling parameter (subsumed if nonlinear term added)
Extended form including density and orbital factors:
[ M = \gamma \cdot \rho^{\delta} \cdot (N \cdot S) + \beta \cdot S + \alpha \cdot N + \omega \cdot \text{EOS} ]
Where:
- ( \omega ): Orbital mass modifier coefficient
- EOS: Earth Orbit Speed or contextual orbital scalar
🧬 Simulation Parameters
Symbol | Meaning |
---|---|
( N ) | Discrete quantum number (1–12) |
( S ) | Topological shape value (trefoil = 3, unknot = 1, etc.) |
( \rho ) | Density scalar (composite/macro mass) |
( \alpha ) | Weight for number |
( \beta ) | Weight for shape |
( \gamma ) | Main kinetic scaling parameter |
( \omega ) | EOS orbital influence factor |
🧪 Procedure
- Select particle class (e.g., proton, electron, muon, composite systems)
- Assign SD&N vectors:
- Example (electron):
[ N = 1,\quad S = 1,\quad \rho = 1,\quad \text{EOS} = 1 ] - Example (proton):
[ N = 3,\quad S = 2,\quad \rho = 1.67,\quad \text{EOS} = 1.33 ]
- Example (electron):
- Plug into SDKP equation with selected constants
- Compare ( M_{\text{predicted}} ) with ( M_{\text{known}} )
- Adjust ( \alpha, \beta, \gamma, \delta, \omega ) for best fit
- Iterate across particle types and plot prediction error
📊 Expected Results
- Close agreement (within 5%) of predicted vs. actual mass for fundamental particles
- Nonlinear deviations for composite systems → support CEN scaling adjustments
- Identification of stable coefficient ranges for α, β, γ, ω
🔁 Iterative Refinement Model
Use matrix inversion and regression learning (or least squares fit) to:
- Optimize [α, β, γ, δ, ω]
- Reduce residual error across full particle data set
- Feed learned weights back into simulation kernel
🔗 Related Frameworks
- SDKP: Scale–Density–Kinematic Principle
- SD&N: Shape–Dimension–Number
- EOS: Earth Orbit Speed
- CEN: Axioms of Primordial Mass Genesis